omx index option efficiency test empirical test of market efficiency of omx options supervisor :...

OMX Index OptionEfficiency Test

Empirical test of market efficiency of OMX options

Empirical test of market efficiency of OMX options

Supervisor : Professor Lennart FloodAuthors : Aijun Hou Aránzazu Muñoz Luengo

AgendaAgenda

1. Background1. Background

2. Theoretical Framework2. Theoretical Framework

3. Methodology and Data 3. Methodology and Data

4. Test of Market Efficiency4. Test of Market Efficiency

5. Conclusion and Recommendation5. Conclusion and Recommendation

History of Option MarketHistory of Option Market

• Apr. 1973 CBOE– First Option Traded

• 1983 CBOE– First Index Option Traded

• 1986 Stockholm Stock Exchange– OMX Index Traded

Index options give market participants the ability to participate in anticipated market movements, without having to buy or sell a large number of securities, and they permit portfolio managers to limit downside risk (Ackert & Tian, 1999)

Research Objective and MotivationResearch Objective and Motivation

• Objective : Efficiency test of OMX option market

• Motivation : There is few paper examines

OMX options Market

Option Market Efficiency definitionOption Market Efficiency definition

Or, there is capital constraints and arbitrageurs can not raise the capital necessary to form the risk-less hedging

Or, there is capital constraints and arbitrageurs can not raise the capital necessary to form the risk-less hedging

There is no arbitrage profit opportunitiesThere is no arbitrage profit opportunities

Three HypothesisThree Hypothesis

Lower Boundary

Violation??OMX OptionOMX Option

Efficient Market ???Efficient Market ???Put Call Parity

Violation??

Abnormal Return on Dynamic Hedging

Simulation??




4. LB Test and PCP Test 4. LB Test and PCP Test

5. Dynamic Hedging Simulation 5. Dynamic Hedging Simulation




4. LB Test and PCP Test 4. LB Test and PCP Test

5. Dynamic Hedging Simulation 5. Dynamic Hedging Simulation


The Black Scholes ModelThe Black Scholes Model

Myron Scholes and Fischer Black, 1973 Myron Scholes and Fischer Black, 1973

Replace Stock with FutureF=Sert

Replace Stock with FutureF=Sert

VolatilityVolatility

• The relative rate at which the price of a security moves up and down

• A Measure of Risk

Volatility Forecasting MethodsVolatility Forecasting Methods

– Historical Volatility (HSD)• Annualized Moving Average of Daily Return

– WISD (Weight Implied Volatility)• Get Implied Volatility (IV) from the Market Price • Weight Average IV according to its sensitivity

towards price changing

WISDWISD

Implied Volatility Smile:

Solution: Weighting volatility across a number of options on the same underlying ( WISD)

Implied Volatility Smile (2003-02-04) OMX3B Series (Call)

0,31 0,33 0,35 0,37 0,39 0,41 0,43

410 420 430 440 450 460 470 480 490 500 510 520 530 540 550

Strike price

Implied Volatility

Implied Volatility Smile (different marturity

time)OMX3B420 (Call)

0 0,2 0,4 0,6 0,8

1 1,2

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 Time to maturity

Implied volatility

WISD (con.)WISD (con.)

• Options more traded = More Market information

• To adjust options’ sensitivities to the volatility

– High price sensitivity options to σ should be given more weight

MethodologyMethodology

• Lower Boundary Condition & Put Call

Parity condition

• Dynamic Hedging Strategy

• Paired T-Test

Data 1st June 1994—30th June 2004

Data 1st June 1994—30th June 2004

OMX Index & Future

Trading DateTime to maturityAsk PriceBid PriceClose PriceVolume

Risk Free Interest Rate

STIBOR

Transaction Cost

Trading and Clear feeCommission feeBid Ask SpreadOther cost

Trading dateTime to maturityAsk PriceBid PriceClose PriceVolume

OMX Index

Option

Data TransformationData Transformation

Lower Boundary and Put Call Parity TestsLower Boundary and Put Call Parity Tests

Derivation of Lower BoundaryDerivation of Lower Boundary

Holding Equal Amount of Calls and Futures

with Opposite Position Result Min.

Profit (F-K)e-rt-C

Holding Equal Amount of Puts and Futures

with Opposite Position Result Min.

Profit (K-F)e-rt-P

IF(F-K)e-rt-C>0ThenProfit Ensured

IF(K-F)e-rt-P>0ThenProfit Ensured

C>= (F-K)e-rt

P>= (K-F)e-rt

Revised Lower Boundary Revised Lower Boundary

Consider Transaction Cost

00

TkKC TCTCeF SFBC

rT

00

TkK TCTCeFP BFBP

rT

Consider Ask Bid Spread

00

TkK TCTCeFC SFBC

rT

bidask

00

TkK TCTCeFP BFBP

rT

askask

Derivation of Put Call ParityDerivation of Put Call Parity

It shows that the value of a EU call with a certain exercise price and exercise date can be deduced from the value of a EU put with the same exercise price and vice versa

eFerTrT

PKC

0

TkTCTCTCKePC bfbpSCrtrT

eF

0

TkTCTCTCKeFCP sfbcsprtrT

e 0

TkTCTCTCKeFPC bfbpSCrtrT

askaskbid e 0

TkTCTCTCKeFCP sfbcsprtrT

bidaskbid e 0

Long Hedge

Short Hedge

Without Bid Ask Spread With Bid Ask Spread

Refine Data Refine Data

0 or 0,01 ( Price & Volume)

High Bid Ask Spread

360>T >0

Filter Data

Transaction CostFee

(Fixed)Commission

(Assumption)

TC0

TC1

TC2

Empirical ResultsEmpirical ResultsViolation Measured as :

Frequency of Violation % = Number of Violations identified /Number of

Observations Examined

TC=0 TC=TC1 TC=TC2 TC=0 TC=TC1 TC=TC2Total sample: 59025

Number of violations 446 382 223 31 29 24

% of the violations 0,76% 0,65% 0,38% 0,05% 0,05% 0,04%

Average Value -1,38 -1,52 -2,15 -2,44 -2,62 -2,79

Total sample:63607



Average Value -2,114 -2,325 -3,126 -3,10 -3,11 -3,36

Long Hedge Total sample:32742



Average Value 0,90 1,04 1,42 1,87 2,27 2,54

Short Hedge Total sample:32740



Average Value 1,12 1,28 1,70 1,66 1,95 2,38

Lower Boundary Put

Panel I ----Transaction Prices Panel II----Bid-Ask SpreadProfitable Hedges

Lower Boundary Call

TC=0 TC=TC1 TC=TC2 TC=0 TC=TC1 TC=TC2Total sample: 59025



Average Value -1,38 -1,52 -2,15 -2,44 -2,62 -2,79

Total sample:63607



Average Value -2,114 -2,325 -3,126 -3,10 -3,11 -3,36

Long Hedge Total sample:32742



Average Value 0,90 1,04 1,42 1,87 2,27 2,54

Short Hedge Total sample:32740



Average Value 1,12 1,28 1,70 1,66 1,95 2,38

Lower Boundary Put

Panel I ----Transaction Prices Panel II----Bid-Ask SpreadProfitable Hedges

Lower Boundary Call

Dynamic Hedging Strategy TestDynamic Hedging Strategy Test

Dynamic Hedging Test DesignDynamic Hedging Test Design

Filter Data

Volatility Forecast

Calculate BS Moddel

Price

Market Price vs. Model Price

Dynamic Hedging

Simulation

Evaluate NPV

Dynamic hedging simulation ImplementationDynamic hedging simulation Implementation

Data filtration

0

( Price & Volume)

I(K-F)/K)I>10%

High Bid Ask Spread

T <7 or T>90

Liquidity & Non-synchronous problem

Dynamic hedging simulation ImplementationDynamic hedging simulation Implementation

Volatility Forecasting

HSDWISD

n

ii uu

nHSD

1

2)(1

1

ui = LN(Si/Si-1)

n= 20

N

j N

j j

jj

j

jj

j

WV

WV

WISD1

1

2

)( 2

2

1 jdl

j

jj etF

WV

Result from HSDResult from HSD

Result from WISDResult from WISD

WISD vs. HSD

0

200

400

600

800

1000

1200

1400

OM

X I

nd

ex

0,1

0,15

0,2

0,25

0,3

0,35

0,4

0,45

0,5

0,55

0,6

Vo

lati

lity

Index HSD WISD

• WISD is in general higher than HSD• When the underlying asset market is getting extremely

volatile, the derivative market tends to moderate it.

Standard deviation of HSD and WISDStandard deviation of HSD and WISD

Std. Dev. of HSD and WISD

0

0,05

0,1

0,15

StdHSD StdWISD

StdHSD 0,0313 0,0303 0,0305 0,0753 0,1308 0,0546 0,067 0,0891 0,1111 0,0632 0,0461

StdWISD 0,0182 0,0166 0,0207 0,0366 0,0751 0,0502 0,0354 0,0577 0,0819 0,0592 0,0196

1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004

Result validity---Volatility SmileResult validity---Volatility Smile

0,22

0,23

0,24

0,25

0,26

0,27

0,28

ITM(call) ATM OTM(call)

Call

Put

• Left skew pattern • Puts give higher volatility than calls

Result Validity—Term StructureResult Validity—Term Structure

• Term structure shows a downward slop • Consistent with Hull (2003)• Short-dated volatilities are historical high

0,21

0,22

0,23

0,24

0,25

0,26

0,27

0,28

0,29

T10 T30 T60 T90

Call

Put

Result validity—StationarityResult validity—StationarityMean SD Min Max Skew Autocorrelations

p1 p2 p3 p4 p5 p6 p10 p12

Call options IV

At the money level 0,253957 0,083482 0,053070068 0,633362 0,842652 0,951408 0,938161 0,924818 0,912108 0,904041 0,891062 0,857586 0,842902

1st Difference 7,22E-05 0,030768 -0,341705322 0,219727 -0,442069 -0,361999 0,000268 -0,006979 -0,04669 0,050469 -0,041967 0,004444 -0,044072

tau -18,15099 -3,082855 0,976812 0,478695 -0,423371 -1,055677 -0,875937 -1,574567

In the money level 0,257348 0,084024 0,067202409 0,556797 0,909961 0,934484 0,924121 0,90845 0,898347 0,890692 0,879684 0,851823 0,837895

1st Difference -2,39E-05 0,030465 -0,224367142 0,209525 0,066429 -0,419872 0,040075 -0,041365 -0,018826 0,025369 -0,02803 -0,018811 0,00497

tau -20,67472 1,791996 -1,851098 -0,841845 1,134323 -1,253145 -0,839849 0,221874

Out of the money level 0,247248 0,071644 0,120895386 0,545057 0,747285 0,964795 0,946214 0,93361 0,919741 0,906914 0,893336 0,854132 0,839326

1st Difference -1,29E-05 0,019047 -0,180198669 0,176703 -0,314623 -0,234102 -0,086279 0,017453 -0,01481 0,011171 -0,05521 -0,031556 0,011522

tau -11,05088 -3,974421 0,800896 -0,67943 0,512312 -2,535142 -1,446702 0,527713

Put options IV

At the money level 0,253955 0,083462 0,053070068 0,633362 0,842933 0,933046 0,915746 0,907616 0,896628 0,884156 0,872921 0,832358 0,814241

1st Difference -8,33E-05 0,030764 -0,219726563 0,341705 0,442875 -0,37041 -0,067649 0,021353 0,010487 -0,009168 -0,023239 -0,019301 -0,034894

tau -18,15348 -3,086531 0,971889 0,476947 -0,416788 -1,056508 -0,876715 -1,585051

In the money level 0,260567 0,084671 3,05176E-05 0,666992 0,457457 0,8456 0,833972 0,821919 0,802335 0,793226 0,776714 0,724316 0,697704

1st Difference -1,97E-05 0,047077 -0,380015055 0,330353 -0,08741 -0,461485 0,001362 0,023414 -0,033725 0,023229 -0,012515 0,040706 -0,014341

tau -21,48428 0,056239 0,96657 -1,392198 0,958374 -0,516138 1,678152 -0,590513

Out of the money level 0,268193 0,08055 0,142049154 0,585667 0,942857 0,973912 0,959471 0,946568 0,935681 0,924989 0,915742 0,877013 0,860015

1st Difference -2,38E-05 0,018471 -0,120188395 0,228923 1,411731 -0,222446 -0,030941 -0,03862 -0,002452 -0,02773 0,043825 -0,018316 -0,000744

tau -10,76208 -1,459354 -1,82164 -0,115512 -1,306428 2,065603 -0,862375 -0,035024

Weigthed Implied Volatilities

WISDc level 0,24345 0,075825 0,12672758 0,54881 0,860312 0,974705 0,961808 0,95177 0,940582 0,929949 0,918715 0,880604 0,866339

1st Difference -1,43E-05 0,017099 -0,122019283 0,161132 0,371226 -0,24322 -0,057559 0,021695 -0,010794 0,012596 -0,017292 -0,061674 0,033199

tau -12,46657 -2,865958 1,078433 -0,536352 0,625746 -0,858908 -3,070186 1,650167

WISDpc level 0,256913 0,074762 0,14201981 0,538232 0,922747 0,981318 0,967754 0,956686 0,945154 0,933525 0,922007 0,881217 0,86514

1st Difference -1,51E-05 0,01451 -0,096278947 0,163216 0,693834 -0,136173 -0,069158 0,011788 0,004328 -0,002709 -0,012326 -0,053298 0,035972

tau -6,834151 -3,444971 0,585695 0,214897 -0,134511 -0,611862 -2,650216 1,787307

WISDp level 0,2718 0,076982 0,146183954 0,589391 0,941441 0,977387 0,962965 0,949962 0,938259 0,926864 0,915855 0,87284 0,853633

1st Difference -1,69E-05 0,016431 -0,105808722 0,16716 0,490767 -0,180366 -0,033407 -0,028676 -0,005209 -0,008815 0,01037 -0,024035 -0,002101

tau -9,117428 -1,661099 -1,425273 -0,258581 -0,437462 0,514591 -1,192584 -0,104244

Market price VS. Model priceMarket price VS. Model price

Result from Paired T-testResult from Paired T-test

Market Price vs. Model Price-Distribution of Price Differences

Market Price vs. Model Price-Distribution of Price Differences

Call: Market Price-Model Price (WISD)

0

5000

10000

15000

-10 -6 -2 2 6 10

Co

un

t

ITM ATM OTM


0

5000

10000

15000

-10 -6 -2 2 6 10

Co

un

t

ITM ATM OTM

Put: Market Price-Model Price (WISD)

0

5000

10000

15000

-10 -6 -2 2 6 10

Co

un

t

ITM ATM OTM


0

5000

10000

15000

-10 -6 -2 2 6 10

Co

un

t

ITM ATM OTM

Call: Market Price-Model Price (HSD)

0

5000

10000

15000

-10 -6 -2 2 6 10

Co

un

t

ITM ATM OTM


0

5000

10000

15000

-10 -6 -2 2 6 10

Co

un

t

ITM ATM OTM

Put: Market Price-Model Price (HSD)

0

5000

10000

15000

-10 -8 -6 -4 -2 0 2 4 6 8 10

Co

un

t

ITM ATM OTM


0

5000

10000

15000

-10 -8 -6 -4 -2 0 2 4 6 8 10

Co

un

t

ITM ATM OTM

Market Price vs. Model Price-Moneyness Composition of Price Differences

Market Price vs. Model Price-Moneyness Composition of Price Differences


0%

50%

100%

Co

un

t

ITM ATM OTM


0%

50%

100%

Co

un

t

ITM ATM OTM


0%

50%

100%

-10 -8 -6 -4 -2 0 2 4 6 8 10

Co

un

t

ITM ATM OTM


0%

50%

100%

-10 -8 -6 -4 -2 0 2 4 6 8 10

Co

un

t

ITM ATM OTM


0%

50%

100%

-10 -8 -6 -4 -2 0 2 4 6 8 10

Co

unt

ITM ATM OTM


0%

50%

100%

-10 -8 -6 -4 -2 0 2 4 6 8 10

Co

unt

ITM ATM OTM


0%

50%

100%

-10 -8 -6 -4 -2 0 2 4 6 8 10

Co

un

t

ITM ATM OTM


0%

50%

100%

-10 -8 -6 -4 -2 0 2 4 6 8 10

Co

un

t

ITM ATM OTM

Dynamic hedging simulation implementation

Dynamic hedging simulation implementation

• Spot Mispricings

• Delta hedge ratio

• Simulate Dynamic hedging

Spot mispricing (More than 15% difference )Spot mispricing (More than 15% difference )

Result from Dynamic hedgingResult from Dynamic hedging

-20000

-15000

-10000

-5000

0

5000

10000

15000

20000

199406 199606 199806 200006 200206 200406

SumOfResult1 SumOfRESULT_SPREAD

-100000

-80000

-60000

-40000

-20000

0

20000

40000

60000

80000

199406 199606 199806 200006 200206 200406

SumOfResult1 SumOfRESULT_SPREAD

Result from Dynamic HedgingResult from Dynamic Hedging

Slight Positive NPV

when little cost

considered

Slight Positive NPV

when little cost

considered

Clearly Negative

NPV when spread

cost Considere

d

Clearly Negative

NPV when spread

cost Considere

d

ConclusionConclusion

Little Lower

Boundary Violation OMX OptionOMX Option

Efficient Market ???Efficient Market ???Little Put Call Parity Violation

No Abnormal Return on Dynamic Hedging

Simulation

RecommendationsRecommendations

• Intraday data

• GARCH

• Commission cost

Thank You!Thank You!

0

500

1000

1500

2000

2500

-63 -52 -42 -32 -22 -12 -2 8 18 28 38

OTM

ATM

ITM

CP Call

Count

Difference %

Moneyness

0

200

400

600

800

1000

1200

1400

1600

1800

2000

-32 -22 -12 -2 8 18 28 38 48 58 68 78 88 98 108 119 138 167

OTM

ATM

ITM

CP Put

Count

Difference %

Moneyness

omx index option efficiency test empirical test of market efficiency of omx options supervisor :...

Documents

data slide

recommendation slide

hsd slide

weight slide

price market price

npv slide

omx options market slide

data transformation