high-frequencytradinganditsimpactonexogenousliquidity...

Research ArticleHigh-Frequency Trading and Its Impact on Exogenous LiquidityRisk of Chinarsquos Stock Index Futures Market before and afterTrading Restrictions

GuangWei Shi12 and Yun Chen 1

1Shanghai University of Finance and Economics Shanghai China2Shanghai Financial Futures Information Technology Co Ltd Shanghai China

Correspondence should be addressed to Yun Chen chenyunsufeeducn

Received 14 May 2020 Accepted 30 June 2020 Published 27 August 2020

Guest Editor Benjamin Miranda Tabak

Copyright copy 2020 GuangWei Shi and Yun Chen -is is an open access article distributed under the Creative CommonsAttribution License which permits unrestricted use distribution and reproduction in anymedium provided the original work isproperly cited

Since Chinarsquos first stock index futures China Securities Index 300 (CSI300) stock index futures were published in 2010 andChinarsquos stock index futures market is now in a period of rapid development and play a key role in price discovery During 2014 to2015 Chinarsquos stock index futures market fluctuated abnormally and the overuse of high-frequency trading (HFT) strategies in thestock index futures market was blamed as the main reason of the abnormal volatility To lower down market fluctuation theregulatory institute then announced a series of trade restriction policy to prevent the overuse of HFT behaviour However untilnow the impact of such trade restriction policy for HFT remains uncertain To tackle this issue based on minute-level HFTdatafrom the CSI 300 index futures market this paper aims to investigate the relationship between HFT and the exogenous liquidityrisk and how HFT affects Chinarsquos stock index futures market on its liquidity using the liquidity-adjusted value at risk (LVaR)model -e findings indicate that HFT improves the return of the liquidity provider and reduces the exogenous liquidityrisk significantly

1 Introduction

Stock index futures are an important financial derivativeand their main function is to maintain capital values andavoid systematic risk in the stock market Since the stockindex futures market is closely related to its stock spotmarket coupled with the principle of leveraged trading offutures the marginal risk of the stock index futures marketmay cause risks in the spot market through the risktransmission mechanism Nowadays with the rapid devel-opment of trading technology in recent years high-fre-quency trading a kind of programmatic trading based onlow latency between order submission and execution orcancellation is booming in the China stock index futuresmarket However HFT may make bid-ask spread in lowlevel and hence it could easily cause liquidity risk and posenew challenges to the risk management of the China stock

index futures market In this circumstance investors maybear huge liquidity risk leading to huge losses and themarket will lose its function [1]

On June 12 2015 the Shanghai Stock Exchange Com-posite Index (SH index) reached 5178 a new peak in recentyears After that the spot market fluctuated violently over athousand stocks went through stock suspension during thatperiod trading volume dropped sharply and market li-quidity hit the freezing point Some scholars think that theoveruse of HFT in the stock index futures market is the keyfactor of the sharp fluctuation of the spot market FromAugust to September in 2015 the China Financial FuturesExchange (CFFEX) issued a series of stock index futurestrading restriction measures to lower the sharp fluctuationsof the stock market and reduce the excessive speculationbehaviour in the market -e policies aim to regulate thetrading behaviour of the stock index futures market through

HindawiComplexityVolume 2020 Article ID 9192841 11 pageshttpsdoiorg10115520209192841

lifting the HFT cost in order to promote the healthy de-velopment of the China stock index futures market How-ever it is reported that these regulatory measures such asincreasing margin and limiting opening positions have aseries of negative effects on the futures market and the spotmarket respectively especially for the liquidity level on bothmarkets Liquidity refers to the possibility that investors cantrade a certain asset with less trading time lower transactioncost reasonable price level and smaller price fluctuationwhile liquidity risk means all kinds of risks such as sharp risein transaction costs extended trading time and difficulty inrealizing due to the loss of investorsrsquo confidence Lack ofliquidity in the market may make it hard for investors tocomplete the transaction

In the existing research studies on liquidity risk manyresearchers have expounded the importance of the liquidityrisk Jorion [2] pointed out that liquidity is the most im-portant issue in risk management -e vast majority ofunforeseeable losses are caused by the sudden disappearanceof liquidity due to the lack of liquidity in the market or byincreased clearing costs due to the market moving in theopposite direction to the tradersrsquo positions Amihud andMendelson [3] described liquidity as ldquoeverything in themarketrdquo Lawrence and Robinson [4] mentioned that ig-noring liquidity risk is much likely to lead to undervaluationof the market risk which could be about 15 percent Dowd[5] thought that losses caused by liquidity risks may even beas large as those caused by market risks Pastor andStambaugh [6] proved in their empirical study that themarket shock cost in the direction of buying or selling is usedas the state variable to measure the market liquidity risk

Because of the characteristics of the liquidity risk as anindispensable systemic risk and its important position in riskmanagement researchers have been trying to conduct in-depth research on liquidity risk for decades in order to find amore suitable liquidity risk measurement model for thecapital market so as to better understand the market wherethey are located As to the measurement of the liquidity riskBangia Diebold and Stroughair [7] divide liquidity intoexogenous and endogenous components

Exogenous liquidity is determined by market charac-teristics and has the same impact on eachmarket participantindependent of the individual trading behaviour of indi-vidual market participants [8] Markets with good exoge-nous liquidity tend to have much trading volume and morestable bid-ask spread On the contrary bid-ask spread in themarket with poor exogenous liquidity fluctuates greatlywhile the depth of declaration and trading volume is rela-tively small Endogenous liquidity is related to the positionsheld by investors Generally speaking the larger the posi-tions held by investors the worse the endogenous liquidityHowever the measurement of endogenous liquidity needs tobe based on the assumption of positions and the data ofinvestorsrsquo positions are often not easy to obtain -ereforethe computation in this paper takes only the risk of exog-enous liquidity that will affect any investor into account andignores the possible impact of endogenous liquidity

With the development of financial theory and financialengineering financial market risk measurement technology

has become more comprehensive At present the mainmethods of financial market risk measurement include thesensitivity analysis method volatility analysis method VaRmethod [2] stress test [9] extreme value theory [10] andCopula [11] Among the above methods the value at riskmodel (VaR) is one of the mainstream methods on riskmeasurement in the financial market Since the 1990s it hasbeen introduced into risk management and gradually widelyused in the field of market risk measurement and supervi-sion However the traditional VaR model still has somelimitations For instance traditional VaR models do not takethe impact of investorsrsquo trading behaviors on market prices (ormarket shocks) into account -e traditional VaR model isbased on the assumption that investors can clear in a shorttime so it ignores the possible losses caused by price fluctu-ations Furthermore the impact of clearing on bid-ask spreadsin market makersrsquo markets is also not taken into account

However the VaR model ignores that the big deals maylead to market price and price fluctuation in order toimprove the deficiency of the VaRmodel Hisata and Yamai[12] argure that the uncertainty of bid-ask spread can beregarded as an indicator of liquidity risk so the volatility ofbid-ask spread is introduced into exogenous cost of li-quidity (ECL) and they propose the LVaR model (li-quidity-adjusted value at risk) As for domestic researchstudies in China on the liquidity risk study Hu and Song[13] took the stock price of 16 listed commercial banks inChina as samples to establish the VaR model after liquidityrisk adjustment Based on the day-level trading data ofShanghai stock exchange Zhu [14] defined the measureindex of liquidity risk from the perspective of the priceshock faced by investors in actual investment Xu et al [15]used the VaR model to verify the liquidity risks of enter-prises with different liquidity in the NEEQ (National Eq-uities Exchange and Quotations) market under differentmarket conditions and proposed the corresponding reg-ulation policy Tong et al [16] theoretically analyzed day-level liquidity risk studied the relationship between reg-ulatory indexes and day-level liquidity risk and exploredthe deficiencies of regulatory framework indexes

11 Highlights Despite considerable research results onliquidity risk they are mainly concentrated in the spotmarket such as the stock market At present due to thecomplexity of the liquidity risk formation mechanism in thefutures market relevant research on HFT in Chinarsquos stockindex futures market is still scarce and systematic researchwork has not yet been carried out not to speak at intradaylevel -e above detail illustrates the importance of liquidityrisk measurement of the stock index futures market and thelack of relevant theoretical research in China Given theimportance of that research on the stock index futuresmarket in China based on the financial market micro-structure theory is carried out in this paper Specifically theLVaR model is used to quantify the liquidity risk usingminute-level HFT data of CSI 300 index futures

-e main contribution of this study includes thefollowing

2 Complexity

(1) -e experimental data used in this paper are basedon minute-level HFTdata ranging from 2014 to 2016which spans the entire stock index futures marketturbulent period containing the period under tradingrestrictions which is beneficial to systematicallystudy the relationship between HFT and liquidityrisk in the stock index futures market and has anextremely valuable research value

(2) -e liquidity risk model is illustrated by LVaR todemonstrate how HFT affects liquidity on the CSI 300index futures market -e research results and conclu-sions are of great significance to the market risk man-agement of other financial futures such as providingreference for the risk monitoring of other stock indexfutures products treasury futures products and otherfinancial derivatives that may be launched in the future

-e rest of the paper is organized as follows Section 2briefly describes the problem statement including the basicconcepts of liquidity risk and why the specific range of data isselected for the experiment In Section 3 the relationshipbetween HFT and liquidity is demonstrated by the VARmodel In Section 4 the LVaR model is introduced to modelexogenous liquidity risk and the impact of HFT is deeplyanalyzed Section 5 concludes the paper

2 Problem Statement

Regarding if HFT is beneficial to the liquidity risk in thestock index futures or not the research community has beencontroversial Besides to the best of our knowledge theimpact of HFTon Chinarsquos stock index futures market has notbeen deeply analyzed before In this context the study ofHFT on Chinarsquos stock index futures market has both the-oretical and practical meanings

In this section the definition of liquidity risk is firstintroduced And the range of experimental data used in thispaper and why we choose that to demonstrate the liquidityrisk brought by HFT are then presented

21 Concepts of Liquidity Liquidity was first proposed byKeynes in 1936 and is now broadly defined as ldquoliquidity is aprice-balanced ability to buy and sell large amounts ofcertain financial assets without fluctuating their pricesrdquo

Bangia et al [7] think liquidity should be classified into twoparts endogenous liquidity and exogenous liquidity Exogenousliquidity is determined by market characteristics and is notaffected by the individual trading behaviour of individualmarket participants and is the same for eachmarket participant

-e market trade volume with good exogenous liquidity isvery large the bid-ask spread is small and stable and thequotation depth (the possible trading volume under theexisting bid-ask price level of the market maker) is high In thiscase the realization cost is relatively small and can even beignored Conversely a market with poor exogenous liquiditywould be characterized by a large fluctuation in bid-ask spreadsand a very small quotation depth and trading volume

As can be seen from Figure 1 the relationship betweenposition size and liquidation value is as follows when the

quantity of the buy order (sold) is less than the depth of the buyorder the transaction can be traded at the current quotationlevel At this time only the exogenous liquidity risk exists andthere is no endogenous liquidity risk On the contrary whenthe amount of buying (selling) is higher than the quotationdepth the realized cost of the asset will exceed the currentquotation level which will cause the exogenous liquidity riskand the endogenous liquidity risk to exist at the same time-eportion of the cost is reflected as the endogenous liquidity risk

Endogenous liquidity on the other hand is related topositions held by market participants Generally speakingthe larger the position held by market participants the worsethe endogenous liquidity Figure 1 shows the relationshipbetween position and the realized value -e measurementof endogenous liquidity needs to be based on the assumptionof the position volume which is not available -erefore inthe following liquidity risk calculation only the risk broughtby the exogenous liquidity is considered

22 Trade Regulation Change and Its Impact on CSI 300 IndexFutures Since the CSI 300 index future was published inApril in 2010 the trade regulation underwent a series ofchange and it is summarized in Table 1

As can be seen from Table 1 the trade restriction policyintroduced in September 2015 was the most severe one inwhich the transaction fee rose from 0115permil to 23permil whichgreatly increased the cost of speculative transactions whichobviously has a tremendous impact on the market structureand market liquidity

Figure 2 illustrates the trend of the closing price of CSI300 index futures It can be clearly seen that the market hasexperienced different market stages such as rising andplunging spanning the entire turbulent period before andafter the stock market crash which indicated that the tradingrestriction policy has had a tremendous impact on the stockindex future

Figure 3 presents the trading volume of the CSI 300index futures (logarithm) Compared with the tradingvolume before trade restriction (blue part) after the re-striction policy was implemented on September 7 in 2015due to the increase in margin the cost of high-frequencytransaction increased significantly and the trading volumeof the CSI 300 stock index futures (red part) was significantlyreduced indicating that the trading restriction policy hashad a tremendous impact on stock index futures

In order to effectively compare the impact of HFTon theliquidity of Chinarsquos stock index futures market this paperadopts an event-driven approach taking the strictest tradingrestriction measures implemented in September in 2015 asthe divided point-e experimental data samples are dividedinto two parts (see Table 2)-e first part is from July 1 2014to September 2 2015 and the second part ranges fromSeptember 7 2015 to December 31 2015 -e first part canbe simply thought as the active period of HFT and thesecond part is nonactive because of the extreme expensiverate of the transaction fee which is 20 times higher thanbefore and limited opening hands -erefore the first partof this period can be used to analyze how HFT affects the

Complexity 3

liquidity risk in the stock index future market while thesecond part is used for comparison

3 Correlation of HFT and Market Liquidity

In this section the basic explanation of the VAR model willbe given followed by experiments on how HFT is correlatedwith market liquidity -e purpose of this section is toexplore the relationship between HFT behaviour andmarketliquidity in the China stock index futures market using thetrading agent index and liquidity indicators

31 Correlation of HFTwith Market Liquidity Based on VARModel Vector autoregressionmodel (VAR) proposed by Simsin 1980 that has been widely used in the international financeand capital market is used in our study -e VAR modeldecomposes the variable y into linear combinations of othervariables and performs similar equation relations for othervariables It uses multiple simultaneous equations for modelingthe relationship between variables In each equation endog-enous variables will carry out regression of the lag value of allendogenous variables contained in the model so as to estimatethe dynamic relationship between all endogenous variables andmake predictions -e specific formula is as follows

y1t c1 + A1y1tminus1 + middot middot middot + Aky1tminusk + +B1y2tminus1 + middot middot middot

+ Bky2tminusk + u1t(1)

where y1t and y2t are the k vectors of endogenous variablesBased on the VAR model shown in equation (1) the cor-relation between y1t and y2t is established ut is the randomdisturbance term of each equation c is the constant con-straint term and A andB are the coefficients of the laggingvariable to be estimated

Based on the VARmodel introduced above the correlationanalysis between HFT and liquidity is given as follows

algot c1 + 11139443

j1δjalgotminusj + α1sprdt + 1113944

3

n1Πnsprdtminusn + v1tSizet

+ ψ1tVolt + u1t

(2)

sprdt c2 + 1113944

3

k1Πksprdtminusk +β1algot + 1113944

3

m1θmalgotminusm + v2tSizet

+ψ2tVolt + u2t

(3)

where algot represents the trading amount of AT which in-dicates the activeness of HFT behaviour sprdt as bid-askspread is a collection of the liquidity measurement index in-cluding itself and the other two indicators as follows eSprdt

represents the effective spread and rSprdt represents the re-alization spread which indicates the income and net com-pensation of the liquidity provider like HF traders BesidesadvSelt represents the adverse selection cost-ere are also twocontrol variables Sizet is the transaction size and Volt is thevolatility which is determined by calculating historical vola-tility at the midpoint of the buy-sell price Other variablesincluding δ α βΠ θ ψ and v are coefficients to be estimated

For determining lag length k we use two popular methodsthe Akaike Information Criteria (AIC) [17] and the SchwartzInformation Criteria (SIC) [18] to determine an appropriatelag period Both AIC and SIC suggest a lag period (k3)therefore the lag period (k3) is used in this study

32 Correlation Analysis Result Based on the VAR modelintroduced above in this section we compare the correla-tion analysis result to validate the correlation between HFTand market liquidity

-e experimental results are listed in Tables 3 and 4 wherethe correlation between the HFT agent index Algot and li-quidity indicators including sprdt rSprdt eSprdt and AdvSeltis investigated as shown in Model 1 to Model 4 respectively

First since the HFT activeness period is not known weuse HFT data during a long period spanning the HFT re-striction policy (20140701ndash20160531) for correlationanalysis and the result is shown in Table 3

In Table 3 the coefficient factor in Models 1ndash4 shows thecorrelation result between the HFT agent index algot anddifferent liquidity indicators including sprdt rSprdt eSprdtand AdvSelt respectively Panel C (Models 1ndash4) shows theweak correlation between HFT and liquidity indicators forwhich the coefficient of the lag term at time t-1 is minus00103minus0004 00333 and 00069 at a confidence level 005 re-spectively It indicates that to some extent HFT may cor-relate with the liquidity level from a large period which spansthe trade restriction policy

Considering a series of strict control measures on stockindex futures trading since September 2015 especially thestandard for setting the rule that abnormal trading isregarded as 10 hands per day the activity of high-frequencytrading has been greatly inhibited

Quote depth Position size

Security price

Point ofendogenous

liquidityAsk

Bid

Figure 1 Relationship between position size and security size

4 Complexity

In this part a more specific period range from July 12014 to September 2 2015 is selected to further analyze thecorrelation between HFT and market liquidity

Table 1 Trading rules of CSI 300 index futures (until the end of 2018)

Time Nonscheduled policy opening hands limit Nonhedging () hedging position trading margin () Transaction fee (permil)2012629 mdash 12 12 0035201491 mdash 10 10 00252015828 600 20 10 01152015831 100 30 10 0115201597 10 40 20 232017217 20 20 20 922017918 20 15 15 692018123 50 10 10 46

Before restrictionAer restriction

0

1000

2000

3000

4000

5000

6000

2014

0702

2014

0725

2014

0819

2014

0912

2014

1014

2014

1106

2014

1201

2014

1224

2015

0120

2015

0212

2015

0316

2015

0409

2015

0505

2015

0528

2015

0623

2015

0716

2015

0810

2015

0902

2015

0929

2015

1029

2015

1123

2015

1216

Figure 2 Closing price of CSI 300 index futures before and after trade restriction (201471ndash20151231)


0

100000000

200000000

300000000

400000000

500000000

600000000

700000000

800000000

2014

0701

2014

0718

2014

0806

2014

0825

2014

0912

2014

1008

2014

1027

2014

1113

2014

1202

2014

1219

2015

0109

2015

0128

2015

0216

2015

0312

2015

0331

2015

0420

2015

0508

2015

0527

2015

0615

2015

0703

2015

0722

2015

0810

2015

0827

2015

0917

2015

1013

2015

1030

2015

1118

2015

1207

2015

1224

Figure 3 Volume of CSI 300 index futures before and after trade restriction (201471ndash20151231)

Table 2 Experimental data

Before restriction After restriction2014071 sim 20150902 20150907 sim 20151231

Complexity 5

Comparedwith Table 3 in Table 4 the coefficients in Panel Cfrom lag term 1 to 3 all shows that the correlation between HFTand liquidity indicators increases to 01643 019926 00094 and00094 at a confidence level 005 which is far greater than thecorresponding coefficients in Table 3 It means before the re-striction policy HFTis obviouslymore active and the correlationbetween market liquidity level is stronger In Panel D all theliquidity indicators show a positive correlation with volatilityindicating that when the volatility is higher the liquidity is higherAT activity is negatively correlatedwith volatility and trading sizeindicating that algorithmic traders tend to trade when volatilityand trading size are smaller -is means that algorithmic traderslike HF traders tend to enter the market strategically with lowertransaction costs and less information asymmetry which indi-cates that HFT improves the market liquidity level

Based on the above experiments it can be concluded thatbefore trade restriction when HFT behaviour is active morealgorithm-based trades are correlated with market liquidityindicated by a larger absolute spread (Sprdt) larger effectivespread (eSprdt) larger realized spread (rSprdt) and less adverse

selection (advSelt) It also indicates that the trade restrictionpolicy greatly changes the activeness of HFT behaviour

4 Impact of HFT on Liquidity Risk

-e correlation between HFT and liquidity is demonstratedby the VARmodel in Section 3 To further analyze how HFTinfluences exogenous liquidity risk before and after traderestriction the LVaR is introduced in this section

41 Liquidity Risk Value Measurement Model -e classisVaR model and the improved LVaR model-added marketfactors are introduced in this section which is the basis foranalyzing the impact of HFTon liquidity risk with the LVaRmodel in the next section

411 VaR Model In Chinarsquos order-driven futures marketinvestorsrsquo trading orders are directly paired through the trading

Table 3 Relationship between algorithmic trading and liquidity indicators (July 1 2014ndashMay 31 2016)

Model 1 Model 2Algot Sprdt Algot rSprdt

c1 02154lowastlowastlowast c2 10475lowastlowastlowast c1 01487lowastlowastlowast c2 28018lowastlowastlowast

Panel A contemporaneous variablesSprdt 00236lowastlowastlowast Algot 00825lowastlowastlowast rSprdt 0005lowastlowastlowast Algot 13549lowastlowastlowast

Panel B autoregressive lagged variablesAlgotminus1 05215lowastlowastlowast Sprdtminus1 06896lowastlowastlowast Algotminus1 05214 rSprdtminus1 02288lowastlowastlowast

Algotminus2 01724lowastlowastlowast Sprdtminus2 01126lowastlowastlowast Algotminus2 01878lowast rSprdtminus2 00439lowastlowastlowast

Algotminus3 01648lowastlowastlowast Sprdtminus3 01029lowastlowastlowast Algotminus3 01598 rSprdtminus3 01057lowastlowastlowast

Panel C cross effect of lagged variablesSprdtminus1 minus00103 Algotminus1 minus00747lowastlowastlowast rSprdtminus1 minus00004 Algotminus1 minus02771Sprdtminus2 minus00043 Algotminus2 00319 rSprdtminus2 00041lowastlowastlowast Algotminus2 minus04124lowast

Sprdtminus3 minus00015 Algotminus3 00311 rSprdtminus3 00022lowastlowastlowast Algotminus3 minus03044Panel D control variables

Volt minus00251lowastlowastlowast Volt 00232lowastlowastlowast Volt minus00379lowastlowastlowast Volt 11059lowastlowastlowast

Sizet minus04785lowastlowastlowast Sizet minus04618lowastlowastlowast Sizet minus04203lowastlowastlowast Sizet 00059lowastlowastlowast

Model 3 Model 4Algot eSprdt Algot AdvSelt

c1 01171lowastlowast c2 00692lowastlowastlowast c1 01383lowastlowastlowast c2 18431lowastlowastlowast

Panel A contemporaneous variableseSprdt 01636lowast Algot 00032lowast AdvSelt minus00055lowastlowastlowast Algot minus06859lowastlowastlowast

Panel B autoregressive lagged variablesAlgotminus1 05201lowastlowastlowast eSprdtminus1 06776lowastlowastlowast Algotminus1 05372lowastlowastlowast AdvSeltminus1 02436lowastlowastlowast

Algotminus2 01723lowastlowastlowast eSprdtminus2 01199lowastlowastlowast Algotminus2 01869lowastlowastlowast AdvSeltminus2 01019lowastlowastlowast


Panel C cross effect of lagged variableseSprdtminus1 00333 Algotminus1 minus00038lowast AdvSeltminus1 00069lowastlowastlowast Algotminus1 09865lowastlowastlowast

eSprdtminus2 00737 Algotminus2 00036lowast AdvSeltminus2 00049lowastlowastlowast Algotminus2 minus01064eSprdtminus3 minus01213 Algotminus3 00038lowastlowast AdvSeltminus3 00024lowastlowastlowast Algotminus3 03277lowastlowast

Panel D control variablesVolt minus00257lowastlowastlowast Volt 00017lowastlowastlowast Volt minus00307lowastlowastlowast Volt 11320lowastlowastlowast

Sizet minus04324lowastlowastlowast Sizet minus00237lowastlowastlowast Sizet minus03814lowastlowastlowast Sizet 07659lowastlowastlowastlowast lowastlowast and lowastlowastlowastSignificant levels of 005 001 and 0001 respectively

6 Complexity

system and the flow of trading commissions is the fundamentaldriving force of liquidity

Supposing that the investorrsquos logarithmic return at time tin the long position dominant contract of the stock indexfutures conforms to the random walk process then

Pt Ptminus1eμ+σεt (4)

in which Pt is the midpoint price of the quote at time t μ isthe drift rate σ is the standard deviation of the return rate εt

is the random disturbance term and there is εt sim N(0 1)Assuming an offset rate of 0 the 1-day short position VaR at99 confidence level under a standard normal distributioncan be simplified as

VaR Pt 1 minus eminus 233θσt1113872 1113873 (5)

-ere will be a large price change when the dominantcontract rolls so VaR in the form of yield is more reasonableas the following

VaR 1 minus eminus 233θσt (6)

where θ is the correction factor and the calculation formulais

θ 1 + ϕlnk

31113888 1113889 (7)

where k is the kurtosis value of the return rate and empty is aconstant which can be obtained by regression of equation(5) When the return is a normal distribution k 3 so θ 1-e correction factor has a value greater than 1 when thereturn is a peak thick tail shape which is used to correct theundervalued value risk

412 LVaR Model -e traditional VaR model has an im-plicit assumption that regardless of the trading position ofinvestors the transaction can be completed at a fixed market

Table 4 Relationship between algorithmic trading and liquidity indicators (September 7 2015ndashDecember 31 2015 excluding opening andclosing time windows)


c1 00651 c2 06159lowastlowastlowast c1 03095lowastlowastlowast c2 minus07202Panel A contemporaneous variables

Sprdt minus01405lowastlowastlowast Algot minus00928lowastlowastlowast rSprdt minus00157lowastlowastlowast Algot minus22388lowastlowastlowast

Panel B autoregressive lagged variablesAlgotminus1 05563lowastlowastlowast Sprdtminus1 06350lowastlowastlowast Algotminus1 05653lowastlowastlowast rSprdtminus1 02318lowastlowastlowast

Algotminus2 01956lowastlowastlowast Sprdtminus2 minus00413lowast Algotminus2 02185lowastlowastlowast rSprdtminus2 01695lowastlowastlowast

Algotminus3 01648lowastlowastlowast Sprdtminus3 01945lowastlowastlowast Algotminus3 01528lowastlowastlowast rSprdtminus3 00814lowastlowastlowast

Panel C cross effect of lagged variablesSprdtminus1 01643lowastlowastlowast Algotminus1 00332lowastlowast rSprdtminus1 00094lowastlowastlowast Algotminus1 15264lowastlowastlowast

Sprdtminus2 00582lowastlowast Algotminus2 00154 rSprdtminus2 00098lowastlowastlowast Algotminus2 06386lowastlowast

Sprdtminus3 00257 Algotminus3 00404lowastlowastlowast rSprdtminus3 00028lowastlowast Algotminus3 03712lowast





eSprdt minus15548lowastlowastlowast Algot minus00069lowastlowastlowast AdvSelt minus00157lowastlowastlowast Algot minus22388lowastlowastlowast


Algotminus2 01894lowastlowastlowast eSprdtminus2 minus00705lowastlowastlowast Algotminus2 02183lowastlowastlowast AdvSeltminus2 01694lowastlowastlowast


Panel C cross effect of lagged variableseSprdtminus1 19926lowastlowastlowast Algotminus1 00047lowastlowastlowast AdvSeltminus1 00094lowastlowastlowast Algotminus1 15239lowastlowastlowast

eSprdtminus2 07224lowastlowast Algotminus2 00015 AdvSeltminus2 00098lowastlowastlowast Algotminus2 06369lowastlowast

eSprdtminus3 04966lowast Algotminus3 00033lowastlowast AdvSeltminus3 00028lowastlowast Algotminus3 03732lowast



Complexity 7

price within a fixed period of time [19] Obviously the VaRmodel ignores the fluctuations in market prices and spreadsthat large deals can bring In order to solve problemsmentioned above a liquidity risk estimation model isproposed

Hisata and Yamai [12] believe that the uncertainty ofbid-ask spread can be used as a performance of liquidity risk-erefore they introduced the volatility indicators of bid-ask spread to exogenous cost of liquidity (ECL) and pro-posed the liquidity-adjusted value at risk (LVaR) model

-e exogenous liquidity cost defined by the model is

ECL Pt

S + a 1113957σt( 1113857

2 (8)

where Pt is the midpoint price of the quoted price at time t Sis the mean of the relative bid spread 1113957σt is the volatility of therelative bid spread and α is the scale factor -erefore theECL is the maximum loss that can be caused by the ex-ogenous fluidity risk when there is a spread at α confidencelevel Correspondingly the maximum loss that may becaused by the exogenous liquidity risk of multiple shortcommodities expressed by the yield is

ECL s + a 1113957σt( 1113857

2 (9)

-e LVaR model is a liquidity-adjusted VaR model thatadds the exogenous liquidity cost to VaR Adding exogenousliquidity risk to the traditional VaR model is to correct thetraditional liquidity risk prediction model

LVaR Pt 1 minus eminus 233θσt1113872 1113873 + Pt

S + a 1113957σt( 1113857

2 (10)

-e liquidity risk ratio can be obtained by removing theabsolute price Pt

LVaR 1 minus eminus 233θσt1113872 1113873 +

S + a 1113957σt( 1113857

2 (11)

As can be seen from equation (11) the following pa-rameters are necessary to calculate the LVaR model

(1) S is the mean of the relative bid spread(2) 1113957σt is the volatility of the relative bid spread(3) α is the scale factor(4) 1113957σ is the volatility of the return rate

42 Impact Measurement with LVaR Model

421 Estimation of Volatility in Yield -e stock price indexis usually a nonstationary time series while the yield seriesshows stationarity -erefore this article takes the loga-rithmic yield of the CSI 300 index futures as the researchobject with following formula to calculate the yield

Rt ln Pt( 1113857 minus ln Ptminus1( 1113857 (12)

where Rt represents the logarithmic yield for period t and Pt

and Ptminus1 represent the closing price of the tth and (t minus 1)thperiods of the CSI 300 index futures

It is necessary to perform a stationary examination on theyield series before constructing the yield and volatility pre-diction model Figure 4 shows the yield curve of the CSI 300index futures at minute-level from July 1 2014 to December 312015 It can be observed that the yield curve fluctuates roughlywithin a range indicating that the yield seriesmay be stationary

In order to further analyze the stationarity of the yieldthe ADF unit root test is used To be specific if the ADFstatistic value is less than the critical value at the givensignificance level the null hypothesis that at least one unitroot exists is rejected indicating the time series is stationaryand conversely the time series is nonstationary According tothe unit root test result shown as minus752 it can be concludedthat the yield series of the CSI 300 index futures is stationaryat the 5 significance level and can be fitted by regression

It is necessary to first perform the ARCH effect test onthe residual of the mean value equation of the yield seriesbefore modeling the volatility of the CSI 300 index futuresreturn yield Only the yield series satisfying the ARCH effectcan use the GARCH model to analyze the volatility rate Inthis paper the LjungndashBox examination [20] is used to ex-amine the autocorrelation of the square series of the yield-e statistic p value of the test is 0 so the null hypothesis thatthe square series of yield is white noise (no autocorrelation)can be rejected indicating that the original series (the yield)does have an ARCH effect

After proving that the yield series satisfies the stationaryand ARCH effect volatility is analyzed with the GARCHmodel in this section Considering that the order of theGARCH model is hard to determine the low-orderGARCH(11) model is selected

First the AR(3) model is used to fit the yield series of theCSI 300 index futures active period -en the volatility rate

ndash0015

ndash001

ndash0005

0

0005

001

0015

002

0025

Figure 4 Return yield curve at minute level of CSI 300 indexfutures

8 Complexity

of residual is modeled with the GARCH model -e resultsare shown in Table 5

According to the fitting results in Table 5 the meanequation can be derived as

Rt minus37198eminus 7

+ 00262Rtminus1 + 00013168Rtminus2 minus 00014527Rtminus3

(13)

Volatility (conditional variance) equation

σ2 44823eminus 8

+ 005ε2tminus1 + 078σ2tminus1 (14)

It can be observed in Table 5 that the GARCH(11) modelis remarkable at the 5 significance level indicating that thefitting effect is satisfactory

As shown in Table 6 the mean and volatility equationsduring the period that HFT is restricted can be calculatedwith the same method

According to the fitting results in Table 6 the meanequation of the yield during the period that HFT is restrictedcan be obtained as

Rt 25018eminus 5

+ minus00338Rtminus1 + 00328Rtminus2 + 00072765Rtminus3

(15)

Volatility rate (conditional variance) equation

σ2 25232eminus 8


Similarly the volatility rate equation of relative spreadbefore and after trade restriction can be calculated separatelyas follows

σ2 42112eminus 11


σ2 43319eminus 10


422 Estimation of the Correction Factor θ To estimate thevalue of θ we first calculate the yield VaR of the CSI 300index futures from the one year before trade restriction toone year after trade restriction at the 99 confidence withthe historical simulation method and estimate σt with theGARCH model With the above two parameters regressionto equation (6) obtains that θ of the CSI 300 index futures is1046 At the same time the kurtosis analysis of the yieldinferred that the kurtosis value is 350 After that the above

two values are brought into equation (7) which inferred thatϕ at the 99 confidence level is 03

423 Exogenous Liquidity Cost -e scale factor α in theexogenous liquidity cost model is an essential element of thecalculation In this section the CSI 300 index futures α isobtained at 5134 after regression to 20 with ECL S and 1113957σt

calculated by HFT data from July 1 2014 to December 312015

-erefore the calculation formula for the exogenousliquidity cost before trade restriction is

ECL 12

112eminus 4

+ 51341113957σt1113872 1113873 (19)

-e calculation formula for the exogenous liquidity costafter trade restriction is

ECL 12

386eminus 4

+ 51341113957σt1113872 1113873 (20)

-e LVaR model is a liquidity-adjusted VaR model thatadds the exogenous liquidity cost to VaR Adding exogenousliquidity risk to the traditional VaR model is to correct thetraditional low liquidity risk prediction model


s + aσt( 1113857

2 (21)



s + aσt( 1113857

2 (22)

43 Comparison of Impact ofHFTonLiquidity Risk before andafter Stock Index Futures Trade Restriction Firstly 1113957σ and 1113957σt

obtained by the yield equation and the relative price vola-tility rate equation constructed based on the GARCH modelin the previous section and the correction factor θ can beused to calculate the corresponding VaR value -en thevalue of exogenous liquidity cost ECL is calculated with thescale factor α and the relative price volatility rate equationFinally the final LVaR value is obtained according to (22)

ECLLVaR is defined as the exogenous liquidity riskratio an indicator that shows the proportion of liquidity riskin all risks of CSI 300 index futures It can be seen from

Table 5 -e fitting results of the GARCH(11) model in the activestage of HFT

Mean equation AR(3)Variable Coefficient Std error t-statistic ProbConst minus34198eminus07 1094eminus05 minus3127eminus02 0975AR(1) 00262 4203eminus03 6228 1794eminus02AR(2) 13168eminus03 4479eminus03 0294 minus7461eminus03AR(3) minus14527eminus03 4581eminus03 minus0317 minus1043eminus02Volatility equation GARCH(11)Omega 44823eminus08 3940eminus12 3956 4482eminus08Alpha(1) 00500 9623eminus03 5196 3114eminus02Beta(1) 07800 4204eminus02 18554 0698

Table 6 -e fitting results of the GARCH (11) model during theHFT restricted period

Mean equation AR(3)Variable Coefficient Std error t-statistic ProbConst 25018eminus05 7060eminus06 35440 3943eminus04AR(1) minus00338 6850eminus03 minus4940 minus4726eminus02AR(2) 00328 6966eminus03 4712 1917eminus02AR(3) 72765eminus03 7090eminus03 1026 minus6620eminus03Volatility equation GARCH(11)Omega 25232eminus08 3641eminus12 6930443 2522eminus08Alpha(1) 00125 5688eminus03 2197 1351eminus03Beta(1) 09300 3293eminus03 282391 0924

Complexity 9

Figure 5 that the mean value and volatility of ECLLVaR roseobviously after the trade restriction policy

To further analyze the impact on liquidity risk by HFTFigure 6 shows the average value of ECLLVaR and LVaRbefore and after trade restriction It is interesting to findthat the HFT restriction policy did not lift the liquidity risklevel (LVaR) both remain at 00031 However the pro-portion of exogenous liquidity risk in LVaR rose from404 before trade restriction to 1689 after trade re-striction It means that the trade restriction policy sig-nificantly increases the exogenous liquidity risk If theperiod before trade restriction is regarded as the envi-ronment in which HFT behaviour may occur the periodafter trade restriction is regarded as the environment inwhich no HFT behaviour occurs -e findings indicate thatthe behaviour of HFTcan effectively reduce the proportionof exogenous liquidity risk in the overall risk in the Chinesestock index future market

5 Conclusion

In this paper our aim was to analyze how HFT influencesexogenous liquidity risk of Chinarsquos stock index futuremarket First we make a problem statement about theconcepts of exogenous liquidity risk and then the experi-mental data are set according to the policy of trade re-striction published in September 2015 To validate therelationship between HFTand liquidity risk the VARmodelis introduced to analyze the correlation between four agentindexes related to liquidity and HFT activeness -e ex-perimental data have shown that HFT improves liquidityindicated by HFT causing fewer relative spread effectivespread adverse selection and larger realized spread

Furthermore the LVaR model is introduced to calculatehow HFT influences the exogenous liquidity risk -efinding is that the exogenous liquidity risk drops from1689 after trade restriction to 404 before trade

Before restriction Aer restriction

LVaR


ECLLVaR

0

00005

0001

00015

0002

00025

0003

00035

000200400600800

10001200140016001800

Figure 6 Comparison of ECLLVaR and LVaR influenced by HFT behaviour

000

010

020

040

030

050

06020140701-20150902 ECLLVaR ratio plot

0

01

02

03

04

05


Figure 5 ECLLVaR ratio chart before trade restriction of CSI 300 index futures (above) and after trade restriction (below) (minute level)

10 Complexity

restriction which in turn demonstrates HFT can reduce theexogenous liquidity risk level

However as the stock index future market and the spotmarket are highly related the research about analyzing theimpact of HFT on the spot market is a promising area-erefore for future research it is necessary to study thecross-market HFT behaviour and the cross-market risktransmission mechanism to provide further theoretical andmethod guidance for the healthy and orderly development ofChinarsquos stock index futures products and financial derivativemarkets

Data Availability

Access to data used in this paper is restricted due tocommercial confidentiality Limited data can be providedupon request

Conflicts of Interest

-e authors claim no conflicts of interest

References

[1] Y Zhang and S Ding ldquoReturn and volatility co-movement incommodity futures markets the effects of liquidity riskrdquoQuantitative Finance vol 18 no 9 pp 1471ndash1486 2018

[2] P Stoimenov ldquoPhilippe jorion value at risk 3rd ed the newbenchmark for managing financial riskrdquo Statistical Papersvol 52 no 3 pp 737-738 2011

[3] Y Amihud and H Mendelson ldquoLiquidity and asset pricesfinancial management implicationsrdquo Financial Management -FINAN MANAGE vol 17 p 03 1988

[4] C Lawrence and G N Robinson Liquidity dynamic hedg-ingand value at risk vol 63ndash72 Edition Risk PublicationsLondon UK 2019

[5] K Dowd Beyond Value at Risk gte New Science of RiskManagement John Wiley and Sons New York NY USA1998

[6] L Pastor and R F Stambaugh ldquoLiquidity risk and expectedstock returnsrdquo Journal of Political Economy vol 111 no 3pp 642ndash685 2003

[7] A Bangia F X Diebold T Schuermann and J StroughairModeling Liquidity Risk With Implications for TraditionalMarket Risk Measurement and Management Center for Fi-nancial Institutions Working Papers 99-06 Wharton SchoolCenter for Financial Institutions University of PennsylvaniaPhiladelphia PA USA 1998

[8] Z Lu A study on liquidity risk of open-ended fund and itsmanagementndashan analysis based on china securities marketduring its transition PhD thesis Jinan University JinanChina 2005

[9] J Danielsson Financial Risk Forecasting gte gteory And-Practice Of Forecasting Market RiskWith Implementation In RAndMatlab vol 588 JohnWiley amp Sons Hoboken NY USA2011

[10] L De Haan and Ana Ferreira Extreme Value gteory AnIntroduction Springer Science amp Business Media BerlinGermany 2007

[11] R B Nelsen An Introduction to Copulas Springer Science ampBusiness Media Berlin Germany 2007

[12] Y HisataY Yamai et al Research toward the Practical Ap-plication of Liquidity Risk Evaluation Methods Institute forMonetary and Economic Studies Bank of Japan Tokyo Ja-pan 2000

[13] F Hu and Q Song ldquoResearch on the market liquidity risk ofChina listed commercial banksndashbased on la-var modelrdquoJournal of Financial Development Research vol 9 2016

[14] X Zhu ldquoStock portfolio liquidity risk measurement modelconstruction and testrdquo Chinese Journal of Management Sci-ence vol 15 no 1 pp 6ndash11 2007

[15] X Xu H Wang and Z Zheng ldquoLiquidity risk measurementand analysis of Chinarsquos new otc marketrdquo ContemporaryEconomic Research vol 10 no 11 pp 82ndash89 2017

[16] Mu Tong He Yi and J Wen ldquoIntraday liquidity risk progressand shortages in international regulationrdquo Financial gteoryand Practices vol 6 no 8 pp 94ndash100 2017

[17] H A Akaike ldquoNew look at statistical model identificationrdquoIEEE Transactions on Automatic Control vol AC19p 716M723 1974

[18] G Schwarz ldquoEstimating the dimension of a modelrdquo gteAnnals of Statistics vol 6 no 2 pp 461ndash464 1978

[19] S Chen ldquoResearch on portfolio liquidity risk measurementbased on VaR modelrdquo PhD -esis Huazhong University ofScience and Technology Wuhan China 2005

[20] E P George GM J Box G C Reinsel andM L Greta TimeSeries Analysis Forecasting and Control John Wiley amp SonsHoboken NY USA 2015

Complexity 11

lifting the HFT cost in order to promote the healthy de-velopment of the China stock index futures market How-ever it is reported that these regulatory measures such asincreasing margin and limiting opening positions have aseries of negative effects on the futures market and the spotmarket respectively especially for the liquidity level on bothmarkets Liquidity refers to the possibility that investors cantrade a certain asset with less trading time lower transactioncost reasonable price level and smaller price fluctuationwhile liquidity risk means all kinds of risks such as sharp risein transaction costs extended trading time and difficulty inrealizing due to the loss of investorsrsquo confidence Lack ofliquidity in the market may make it hard for investors tocomplete the transaction

In the existing research studies on liquidity risk manyresearchers have expounded the importance of the liquidityrisk Jorion [2] pointed out that liquidity is the most im-portant issue in risk management -e vast majority ofunforeseeable losses are caused by the sudden disappearanceof liquidity due to the lack of liquidity in the market or byincreased clearing costs due to the market moving in theopposite direction to the tradersrsquo positions Amihud andMendelson [3] described liquidity as ldquoeverything in themarketrdquo Lawrence and Robinson [4] mentioned that ig-noring liquidity risk is much likely to lead to undervaluationof the market risk which could be about 15 percent Dowd[5] thought that losses caused by liquidity risks may even beas large as those caused by market risks Pastor andStambaugh [6] proved in their empirical study that themarket shock cost in the direction of buying or selling is usedas the state variable to measure the market liquidity risk

Because of the characteristics of the liquidity risk as anindispensable systemic risk and its important position in riskmanagement researchers have been trying to conduct in-depth research on liquidity risk for decades in order to find amore suitable liquidity risk measurement model for thecapital market so as to better understand the market wherethey are located As to the measurement of the liquidity riskBangia Diebold and Stroughair [7] divide liquidity intoexogenous and endogenous components

Exogenous liquidity is determined by market charac-teristics and has the same impact on eachmarket participantindependent of the individual trading behaviour of indi-vidual market participants [8] Markets with good exoge-nous liquidity tend to have much trading volume and morestable bid-ask spread On the contrary bid-ask spread in themarket with poor exogenous liquidity fluctuates greatlywhile the depth of declaration and trading volume is rela-tively small Endogenous liquidity is related to the positionsheld by investors Generally speaking the larger the posi-tions held by investors the worse the endogenous liquidityHowever the measurement of endogenous liquidity needs tobe based on the assumption of positions and the data ofinvestorsrsquo positions are often not easy to obtain -ereforethe computation in this paper takes only the risk of exog-enous liquidity that will affect any investor into account andignores the possible impact of endogenous liquidity

With the development of financial theory and financialengineering financial market risk measurement technology

has become more comprehensive At present the mainmethods of financial market risk measurement include thesensitivity analysis method volatility analysis method VaRmethod [2] stress test [9] extreme value theory [10] andCopula [11] Among the above methods the value at riskmodel (VaR) is one of the mainstream methods on riskmeasurement in the financial market Since the 1990s it hasbeen introduced into risk management and gradually widelyused in the field of market risk measurement and supervi-sion However the traditional VaR model still has somelimitations For instance traditional VaR models do not takethe impact of investorsrsquo trading behaviors on market prices (ormarket shocks) into account -e traditional VaR model isbased on the assumption that investors can clear in a shorttime so it ignores the possible losses caused by price fluctu-ations Furthermore the impact of clearing on bid-ask spreadsin market makersrsquo markets is also not taken into account

However the VaR model ignores that the big deals maylead to market price and price fluctuation in order toimprove the deficiency of the VaRmodel Hisata and Yamai[12] argure that the uncertainty of bid-ask spread can beregarded as an indicator of liquidity risk so the volatility ofbid-ask spread is introduced into exogenous cost of li-quidity (ECL) and they propose the LVaR model (li-quidity-adjusted value at risk) As for domestic researchstudies in China on the liquidity risk study Hu and Song[13] took the stock price of 16 listed commercial banks inChina as samples to establish the VaR model after liquidityrisk adjustment Based on the day-level trading data ofShanghai stock exchange Zhu [14] defined the measureindex of liquidity risk from the perspective of the priceshock faced by investors in actual investment Xu et al [15]used the VaR model to verify the liquidity risks of enter-prises with different liquidity in the NEEQ (National Eq-uities Exchange and Quotations) market under differentmarket conditions and proposed the corresponding reg-ulation policy Tong et al [16] theoretically analyzed day-level liquidity risk studied the relationship between reg-ulatory indexes and day-level liquidity risk and exploredthe deficiencies of regulatory framework indexes

11 Highlights Despite considerable research results onliquidity risk they are mainly concentrated in the spotmarket such as the stock market At present due to thecomplexity of the liquidity risk formation mechanism in thefutures market relevant research on HFT in Chinarsquos stockindex futures market is still scarce and systematic researchwork has not yet been carried out not to speak at intradaylevel -e above detail illustrates the importance of liquidityrisk measurement of the stock index futures market and thelack of relevant theoretical research in China Given theimportance of that research on the stock index futuresmarket in China based on the financial market micro-structure theory is carried out in this paper Specifically theLVaR model is used to quantify the liquidity risk usingminute-level HFT data of CSI 300 index futures

-e main contribution of this study includes thefollowing

2 Complexity




2 Problem Statement














Complexity 3









algot c1 + 11139443


3


+ ψ1tVolt + u1t

(2)

sprdt c2 + 1113944

3


3


+ψ2tVolt + u2t

(3)










Security price

Point ofendogenous

liquidityAsk

Bid


4 Complexity





0

1000

2000

3000

4000

5000

6000

2014

0702

2014

0725

2014

0819

2014

0912

2014

1014

2014

1106

2014

1201

2014

1224

2015

0120

2015

0212

2015

0316

2015

0409

2015

0505

2015

0528

2015

0623

2015

0716

2015

0810

2015

0902

2015

0929

2015

1029

2015

1123

2015

1216



0

100000000

200000000

300000000

400000000

500000000

600000000

700000000

800000000

2014

0701

2014

0718

2014

0806

2014

0825

2014

0912

2014

1008

2014

1027

2014

1113

2014

1202

2014

1219

2015

0109

2015

0128

2015

0216

2015

0312

2015

0331

2015

0420

2015

0508

2015

0527

2015

0615

2015

0703

2015

0722

2015

0810

2015

0827

2015

0917

2015

1013

2015

1030

2015

1118

2015

1207

2015

1224




Complexity 5





























6 Complexity










θ 1 + ϕlnk

31113888 1113889 (7)


























Complexity 7




ECL Pt

S + a 1113957σt( 1113857

2 (8)


ECL s + a 1113957σt( 1113857

2 (9)



S + a 1113957σt( 1113857

2 (10)



S + a 1113957σt( 1113857

2 (11)













ndash0015

ndash001

ndash0005

0

0005

001

0015

002

0025


8 Complexity





(13)


σ2 44823eminus 8





Rt 25018eminus 5


(15)


σ2 25232eminus 8



σ2 42112eminus 11


σ2 43319eminus 10







ECL 12

112eminus 4

+ 51341113957σt1113872 1113873 (19)


ECL 12

386eminus 4

+ 51341113957σt1113872 1113873 (20)



s + aσt( 1113857

2 (21)



s + aσt( 1113857

2 (22)








Complexity 9



5 Conclusion




LVaR


ECLLVaR

0

00005

0001

00015

0002

00025

0003

00035

000200400600800

10001200140016001800


000

010

020

040

030

050


0

01

02

03

04

05



10 Complexity



Data Availability




References





















Complexity 11




2 Problem Statement














Complexity 3









algot c1 + 11139443


3


+ ψ1tVolt + u1t

(2)

sprdt c2 + 1113944

3


3


+ψ2tVolt + u2t

(3)










Security price

Point ofendogenous

liquidityAsk

Bid


4 Complexity





0

1000

2000

3000

4000

5000

6000

2014

0702

2014

0725

2014

0819

2014

0912

2014

1014

2014

1106

2014

1201

2014

1224

2015

0120

2015

0212

2015

0316

2015

0409

2015

0505

2015

0528

2015

0623

2015

0716

2015

0810

2015

0902

2015

0929

2015

1029

2015

1123

2015

1216



0

100000000

200000000

300000000

400000000

500000000

600000000

700000000

800000000

2014

0701

2014

0718

2014

0806

2014

0825

2014

0912

2014

1008

2014

1027

2014

1113

2014

1202

2014

1219

2015

0109

2015

0128

2015

0216

2015

0312

2015

0331

2015

0420

2015

0508

2015

0527

2015

0615

2015

0703

2015

0722

2015

0810

2015

0827

2015

0917

2015

1013

2015

1030

2015

1118

2015

1207

2015

1224




Complexity 5





























6 Complexity










θ 1 + ϕlnk

31113888 1113889 (7)


























Complexity 7




ECL Pt

S + a 1113957σt( 1113857

2 (8)


ECL s + a 1113957σt( 1113857

2 (9)



S + a 1113957σt( 1113857

2 (10)



S + a 1113957σt( 1113857

2 (11)













ndash0015

ndash001

ndash0005

0

0005

001

0015

002

0025


8 Complexity





(13)


σ2 44823eminus 8





Rt 25018eminus 5


(15)


σ2 25232eminus 8



σ2 42112eminus 11


σ2 43319eminus 10







ECL 12

112eminus 4

+ 51341113957σt1113872 1113873 (19)


ECL 12

386eminus 4

+ 51341113957σt1113872 1113873 (20)



s + aσt( 1113857

2 (21)



s + aσt( 1113857

2 (22)








Complexity 9



5 Conclusion




LVaR


ECLLVaR

0

00005

0001

00015

0002

00025

0003

00035

000200400600800

10001200140016001800


000

010

020

040

030

050


0

01

02

03

04

05



10 Complexity



Data Availability




References





















Complexity 11









algot c1 + 11139443


3


+ ψ1tVolt + u1t

(2)

sprdt c2 + 1113944

3


3


+ψ2tVolt + u2t

(3)










Security price

Point ofendogenous

liquidityAsk

Bid


4 Complexity





0

1000

2000

3000

4000

5000

6000

2014

0702

2014

0725

2014

0819

2014

0912

2014

1014

2014

1106

2014

1201

2014

1224

2015

0120

2015

0212

2015

0316

2015

0409

2015

0505

2015

0528

2015

0623

2015

0716

2015

0810

2015

0902

2015

0929

2015

1029

2015

1123

2015

1216



0

100000000

200000000

300000000

400000000

500000000

600000000

700000000

800000000

2014

0701

2014

0718

2014

0806

2014

0825

2014

0912

2014

1008

2014

1027

2014

1113

2014

1202

2014

1219

2015

0109

2015

0128

2015

0216

2015

0312

2015

0331

2015

0420

2015

0508

2015

0527

2015

0615

2015

0703

2015

0722

2015

0810

2015

0827

2015

0917

2015

1013

2015

1030

2015

1118

2015

1207

2015

1224




Complexity 5





























6 Complexity










θ 1 + ϕlnk

31113888 1113889 (7)


























Complexity 7




ECL Pt

S + a 1113957σt( 1113857

2 (8)


ECL s + a 1113957σt( 1113857

2 (9)



S + a 1113957σt( 1113857

2 (10)



S + a 1113957σt( 1113857

2 (11)













ndash0015

ndash001

ndash0005

0

0005

001

0015

002

0025


8 Complexity





(13)


σ2 44823eminus 8





Rt 25018eminus 5


(15)


σ2 25232eminus 8



σ2 42112eminus 11


σ2 43319eminus 10







ECL 12

112eminus 4

+ 51341113957σt1113872 1113873 (19)


ECL 12

386eminus 4

+ 51341113957σt1113872 1113873 (20)



s + aσt( 1113857

2 (21)



s + aσt( 1113857

2 (22)








Complexity 9



5 Conclusion




LVaR


ECLLVaR

0

00005

0001

00015

0002

00025

0003

00035

000200400600800

10001200140016001800


000

010

020

040

030

050


0

01

02

03

04

05



10 Complexity



Data Availability




References





















Complexity 11





0

1000

2000

3000

4000

5000

6000

2014

0702

2014

0725

2014

0819

2014

0912

2014

1014

2014

1106

2014

1201

2014

1224

2015

0120

2015

0212

2015

0316

2015

0409

2015

0505

2015

0528

2015

0623

2015

0716

2015

0810

2015

0902

2015

0929

2015

1029

2015

1123

2015

1216



0

100000000

200000000

300000000

400000000

500000000

600000000

700000000

800000000

2014

0701

2014

0718

2014

0806

2014

0825

2014

0912

2014

1008

2014

1027

2014

1113

2014

1202

2014

1219

2015

0109

2015

0128

2015

0216

2015

0312

2015

0331

2015

0420

2015

0508

2015

0527

2015

0615

2015

0703

2015

0722

2015

0810

2015

0827

2015

0917

2015

1013

2015

1030

2015

1118

2015

1207

2015

1224




Complexity 5





























6 Complexity










θ 1 + ϕlnk

31113888 1113889 (7)


























Complexity 7




ECL Pt

S + a 1113957σt( 1113857

2 (8)


ECL s + a 1113957σt( 1113857

2 (9)



S + a 1113957σt( 1113857

2 (10)



S + a 1113957σt( 1113857

2 (11)













ndash0015

ndash001

ndash0005

0

0005

001

0015

002

0025


8 Complexity





(13)


σ2 44823eminus 8





Rt 25018eminus 5


(15)


σ2 25232eminus 8



σ2 42112eminus 11


σ2 43319eminus 10







ECL 12

112eminus 4

+ 51341113957σt1113872 1113873 (19)


ECL 12

386eminus 4

+ 51341113957σt1113872 1113873 (20)



s + aσt( 1113857

2 (21)



s + aσt( 1113857

2 (22)








Complexity 9



5 Conclusion




LVaR


ECLLVaR

0

00005

0001

00015

0002

00025

0003

00035

000200400600800

10001200140016001800


000

010

020

040

030

050


0

01

02

03

04

05



10 Complexity



Data Availability




References





















Complexity 11





























6 Complexity










θ 1 + ϕlnk

31113888 1113889 (7)


























Complexity 7




ECL Pt

S + a 1113957σt( 1113857

2 (8)


ECL s + a 1113957σt( 1113857

2 (9)



S + a 1113957σt( 1113857

2 (10)



S + a 1113957σt( 1113857

2 (11)













ndash0015

ndash001

ndash0005

0

0005

001

0015

002

0025


8 Complexity





(13)


σ2 44823eminus 8





Rt 25018eminus 5


(15)


σ2 25232eminus 8



σ2 42112eminus 11


σ2 43319eminus 10







ECL 12

112eminus 4

+ 51341113957σt1113872 1113873 (19)


ECL 12

386eminus 4

+ 51341113957σt1113872 1113873 (20)



s + aσt( 1113857

2 (21)



s + aσt( 1113857

2 (22)








Complexity 9



5 Conclusion




LVaR


ECLLVaR

0

00005

0001

00015

0002

00025

0003

00035

000200400600800

10001200140016001800


000

010

020

040

030

050


0

01

02

03

04

05



10 Complexity



Data Availability




References





















Complexity 11










θ 1 + ϕlnk

31113888 1113889 (7)


























Complexity 7




ECL Pt

S + a 1113957σt( 1113857

2 (8)


ECL s + a 1113957σt( 1113857

2 (9)



S + a 1113957σt( 1113857

2 (10)



S + a 1113957σt( 1113857

2 (11)













ndash0015

ndash001

ndash0005

0

0005

001

0015

002

0025


8 Complexity





(13)


σ2 44823eminus 8





Rt 25018eminus 5


(15)


σ2 25232eminus 8



σ2 42112eminus 11


σ2 43319eminus 10







ECL 12

112eminus 4

+ 51341113957σt1113872 1113873 (19)


ECL 12

386eminus 4

+ 51341113957σt1113872 1113873 (20)



s + aσt( 1113857

2 (21)



s + aσt( 1113857

2 (22)








Complexity 9



5 Conclusion




LVaR


ECLLVaR

0

00005

0001

00015

0002

00025

0003

00035

000200400600800

10001200140016001800


000

010

020

040

030

050


0

01

02

03

04

05



10 Complexity



Data Availability




References





















Complexity 11




ECL Pt

S + a 1113957σt( 1113857

2 (8)


ECL s + a 1113957σt( 1113857

2 (9)



S + a 1113957σt( 1113857

2 (10)



S + a 1113957σt( 1113857

2 (11)













ndash0015

ndash001

ndash0005

0

0005

001

0015

002

0025


8 Complexity





(13)


σ2 44823eminus 8





Rt 25018eminus 5


(15)


σ2 25232eminus 8



σ2 42112eminus 11


σ2 43319eminus 10







ECL 12

112eminus 4

+ 51341113957σt1113872 1113873 (19)


ECL 12

386eminus 4

+ 51341113957σt1113872 1113873 (20)



s + aσt( 1113857

2 (21)



s + aσt( 1113857

2 (22)








Complexity 9



5 Conclusion




LVaR


ECLLVaR

0

00005

0001

00015

0002

00025

0003

00035

000200400600800

10001200140016001800


000

010

020

040

030

050


0

01

02

03

04

05



10 Complexity



Data Availability




References





















Complexity 11





(13)


σ2 44823eminus 8





Rt 25018eminus 5


(15)


σ2 25232eminus 8



σ2 42112eminus 11


σ2 43319eminus 10







ECL 12

112eminus 4

+ 51341113957σt1113872 1113873 (19)


ECL 12

386eminus 4

+ 51341113957σt1113872 1113873 (20)



s + aσt( 1113857

2 (21)



s + aσt( 1113857

2 (22)








Complexity 9



5 Conclusion




LVaR


ECLLVaR

0

00005

0001

00015

0002

00025

0003

00035

000200400600800

10001200140016001800


000

010

020

040

030

050


0

01

02

03

04

05



10 Complexity



Data Availability




References





















Complexity 11



5 Conclusion




LVaR


ECLLVaR

0

00005

0001

00015

0002

00025

0003

00035

000200400600800

10001200140016001800


000

010

020

040

030

050


0

01

02

03

04

05



10 Complexity



Data Availability




References





















Complexity 11



Data Availability




References





















Complexity 11

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