model of stock index futures.pdf

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International Research Journal of Finance and EconomicsISSN 1450-2887 Issue 10 (2007) EuroJournals Publishing, Inc. 2007http://www.eurojournals.com/finance.htm

Testing the General Equilibrium Model of Stock Index Futures:Evidence from the Asian Crisiss

Janchung Wang

Department of Financial Operations

National Kaohsiung First Universityof Science and Technology1 University Road, Yanchao,Kaohsiung 824, Taiwan, ROC

Tel: 886-7-6011000ext3112; Fax: 886-7-6011039E-mail: [email protected]

Abstract

Hemler and Longstaff (1991) followed the CIR (Cox, Ingersoll and Ross, 1985a&b)framework and developed a closed-form general equilibrium model of stock index futureswith both stochastic market volatility and interest rates. Using the Nikkei 225, the HangSeng, and the KOSPI 200 (South Korean composite stock index 200) index futurescontracts, this study represents the first attempt to apply the Hemler and Longstaff (1991)model to the case of the Asian crisis, and compares the power of the cost of carry andHemler-Longstaff models in predicting stock index futures prices. The empirical resultsfrom the Hang Seng and the KOSPI 200 futures markets imply that in highly volatile

periods, such as the Asian crisis period, incorporating stochastic market volatility into thepricing model helps in predicting stock index futures prices. Therefore, when selecting apricing model to estimate the theoretical values of stock index futures, practitioners shouldidentify the degree of market volatility for the markets they are participating in.

Keywords: Asian Financial Crisis, Pricing of Stock Index Futures, Stochastic Volatility,EGARCH

JEL Classifications: C00, G13.

1. Introduction

Until now, the cost of carry model has been the most widely used model for pricing stock indexfutures. This model was based on the assumption of perfect markets with non-stochastic interest rates.However, if interest rates are stochastic, Cox, Ingersoll, and Ross (1981) showed that futures andforward prices cannot be equal. Some studies [e.g., Cornell and French (1983a&b), Modest andSundaresan (1983), Figlewski (1984), Eytan and Harpaz (1986), and Gay and Jung (1999)] foundsignificant deviations between actual futures prices and theoretical prices estimated by the cost of carrymodel. Additionally, the cost of carry model implies that market volatility should not have explanatorypower for futures prices. However, Resnick and Hennigar (1983), Kamara (1988), and Fung andDraper (1999) found that pricing deviations from the cost of carry model are a function of the volatilityof the underlying security price. Motivated by these considerations, Hemler and Longstaff (1991)followed the CIR (Cox, Ingersoll and Ross, 1985a&b) framework and developed a closed-form general

equilibrium model of stock index futures prices with both stochastic market volatility and interest rates(hereafter the Hemler-Longstaff model).


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International Research Journal of Finance and Economics - Issue 10 (2007) 108

Moreover, the empirical tests in the study of Hemler and Longstaff also indicated that theirmodel is superior to the cost of carry model for the NYSE futures contract when the October 1987observation is included in the sample. However, when October 1987 is excluded, the cost of carrymodel has lower pricing errors. Hemler and Longstaff (1991) pointed out that the difference in results

occurs because the October 1987 market variance estimate is much larger than the variance estimatesfor the other months. This implies that the Hemler-Longstaff model appears particularly suitable forstock markets with high price volatility. Tuluca, Zwick, and Seiler (2003) pointed out that the Asiancrisis variances of daily returns are larger than the pre-crisis daily variances for Asian stock markets.This study also finds that for the Hong Kong and the Korean stock markets, the Asian crisis period hasclearly higher stock price volatility than the other periods (see Table 2). Thus the question is whetherthe Hemler-Longstaff model with stochastic market volatility can effectively predict stock indexfutures prices during the Asian crisis. Using the Nikkei 225, the Hang Seng, and the KOSPI 200 (SouthKorean composite stock index 200) index futures contracts, this study represents the first attempt toapply the Hemler-Longstaff model to the case of the Asian crisis, and compares the predictive power ofthe cost of carry and Hemler-Longstaff models.1

2. Pricing Models of Stock Index FuturesOne common way of calculating futures prices is to use the cost of carry model. If interest rates andcontinuous dividend yields are non-stochastic, then in the absence of taxes and other marketimperfections, the cost of carry model can be written as

Ft= Ste(r - q)(T - t) (1)

where Ftis the theoretical futures price at time t; Stdenotes the current stock index; rrepresents therisk-free interest rate; qis the dividend yield; and T-tdenotes the time to expiration.

If the underlying stock index pays irregular lumpy dividends, under the concept of continuouscompounding, the cost of carry model will be

Ft (St Dt)er(T-t)

(2)

Dtn

i ti

iit

p

wdS

1 ,

)(()( ttr ie )

where Dt is the sum of the present values of all cash dividends distributed by the underlyingcomponent stocks at time tduring the life of the futures contract; diis the cash dividend per share forstockiduring the life of the futures contract; wiis the weight of stock iin the index; tiis the time thatstockipays the cash dividend; andpi,tis the price of stock iat time t.

For the Hang Seng index futures, following Fung and Draper (1999), the theoretical futuresprices can be estimated by the cost of carry model with continuous dividend yields (that is, Equation(1)). Furthermore, in Japan and Korea, the cash dividend payouts are relatively lumpy. 2 Thus,substituting the known risk-free rate rand the lumpiness of cash dividendDt, together with the current

index price Stand time to maturity Tt, into the cost of carry model (2), the theoretical prices of theNikkei 225 and the KOSPI 200 stock index futures can then be obtained.

The cost of carry model was developed under the assumption of non-stochastic interest rates.Moreover, the cost of carry model implies that market volatility should not have explanatory power forfutures prices. Hemler and Longstaff (1991) followed the framework of CIR and developed a closed-form general equilibrium model of stock index futures with both stochastic market volatility andinterest rates. The general equilibrium model of stock index futures is given by Equation (15) inHemler and Longstaff (1991). The natural logarithm of the general equilibrium model yields thefollowing regression equation

1

Although the Hemler-Longstaff model with both stochastic market volatility and interest rates has been developed, empirical evidence remains scarce.To our knowledge, this is the first such study of the Asian crisis.

2 In Japan, cash dividends are clustered at the end of March and September. As for the Korean stock market, most of the companies pay dividends at the

end of the year.


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109 International Research Journal of Finance and Economics - Issue 10 (2007)

Lt rt Vt t (3)

whereLt= ln(q

teF St);Ftis the theoretical futures price; denotes the time to expiration (i.e., T-

t); and Vtrepresents the variance of stock index returns. With a lumpiness of cash dividends, Ltwill be

ln(Ft/(St-Dt)). Substituting the data rt, Vtand the coefficient estimates , , and into the regression

model (3) to generate theLtestimate, the theoretical futures price can then be inferred fromLt.Additionally, if 0, T-t, and 0 (that is, market volatility should not have explanatory

power) hold, Equation (3) reduces to

Lt rt (4)Equation (4) can be rearranged to demonstrate (1), the cost of carry model. Thus, the cost of

carry model can be regarded as a special case of the Hemler-Longstaff model.

3. Comparison of the Cost of Carry and the Hemler-Longstaff Models3.1. Data and Basic Statistics

The Nikkei 225 index futures based on the Nikkei 225 stock index began trading on the OsakaSecurities Exchange (OSE) on September 3, 1988. The futures contract is a major stock index futurescontact in Japan. The Hang Seng index futures contract is based on the Hang Seng index, whichcomprises 33 representative stocks listed on the Stock Exchange of Hong Kong. The KOSPI 200 indexfutures contract is based on the KOSPI 200 stock index. The KOSPI 200 index is a value-weightedindex comprising 200 leading stocks which represent over 70% of the total market capitalization of theKorean Stock Exchange. Table 1 describes the main features of the three futures contracts and theirunderlying indexes.

For the three stock index futures, the nearest maturity contracts all have significant tradingvolume. To reduce thin trading problems, this study only considers the near-month contracts. The dailydata cover the period from July 2, 1997 through December 31, 2005. To capture different market

conditions during the sample period, two approximately equal length sub-samples were considered.The first and second sub-periods are from July 2, 1997 to December 31, 2001 and from January 1,2002 to December 31, 2005, respectively. Additionally, the Asian financial crisis period is defined asbeing from July 2, 1997 to September 30, 1998.

3

For the Nikkei 225 futures, the three-month Gensaki rates are used as the risk-free interestrates. The dividend data of the underlying component stocks in the index were obtained from theQUICK Research Institute and the Tokyo Stock Exchange. For the Hang Seng stock index futures, themiddle quotes of one-month Hong Kong inter-bank rates are

3 Although pinpointing the start of the Asian financial crisis is difficult , analysts often point to the 17% devaluation of the Thai baht on July 2, 1997 as the

triggering event. From July of 1997 to September of 1998, stock markets in the Asia-Pacific region displayed dramatic declines. For example, the

Nikkei 225 index dropped from 20575 on July 28, 1997 to 13406 on September 30, 1998. Meanwhile, the KOSPI 200 index dropped from 82.38 on July4, 1997 to 33.17 on September 22, 1998. It was not until October 1998 that most Asian governments made effort to restore the confidence of investors.

This led to a strong improvement in the stock markets. Thus, following the wide definition of the Asian crisis of Baig and Goldfajn (1998), this study

defines the Asian crisis period as the period from July 2, 1997 to September 30, 1998.


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Table 1: Main features of the Nikkei 225, the Hang Seng, and the KOSPI 200 index futures contracts

Nikkei 225 futures Hang Seng futures KOSPI 200 futures

1.Opening date September 3, 1988 May 6, 1986 May 3, 19962.Underlying index Nikkei Stock Average

(Nikkei 225)

Hang Seng ifndex KOSPI 200 index

KRW$500,0004.Contract months March, June, September,

December cycle (five contractmonths open at a time)

the spot month, the next calendarmonth, and the next two calendarquarterly months

March, June, September andDecember

5.Minimum pricechange

HK$50 per contract 0.05 index pointKRW$25,000 per contract

6.Last trading day the business day prior to thesecond Friday of eachcontract month

The business day immediatelypreceding the last business day ofthe contract month

the second Thursday of thecontract month

7.Settlement cash cash cashSource:Osaka Securities Exchange (OSE), Hong Kong Exchanges and Clearing Limited (HKEx), and Korea Exchange (KRX).

used as the substitute of risk-free interest rates. The annualized month-end dividend yields of HangSeng index for the same period were obtained from the Hang Seng Index Services Ltd. In the case ofthe KOSPI 200 futures, the three-month inter-bank rates are used as the substitute of risk-free interestrates. The dividend data of the underlying component stocks in the index come from the Korea StockExchange.

Table 2 lists descriptive statistics for the spot and futures return series. During the Asian crisis,the daily standard deviations are 1.77%, 3.08%, and 3.52% for the Nikkei 225, the Hang Seng, and theKOSPI 200 indexes, respectively. Furthermore, Table 2 also indicates that for the Nikkei 225 index,the price volatility for the Asian crisis period is only slightly larger than for the other periods.However, for the Hang Seng and the KOSPI 200 indexes, the Asian crisis period has clearly higher

price volatility than the other periods. Additionally, in Table 2, the Jarque-Bera statistics for all returnseries are statistically significant at the 1% level. Thus, as is commonly found for daily equity returns,normality is significantly rejected.

Table 2: Descriptive statistics

Spot Returns Futures Returns

Mean Std. Dev. Skewness Kurtosis Jarque-

Bera

Mean Std. Dev. Skewnes

s

Kurtosis Jarque-Bera

Nikkei 225Full sample -0.00011 0.0149 -0.0272 4.8464 294.72*** -0.00011 0.0154 -0.0925 4.9084 317.52***Period 1 -0.00059 0.0164 0.0669 4.8720 161.44*** -0.00059 0.0171 0.0226 4.7792 145.18***Period 2 0.00044 0.0131 -0.1639 3.9965 44.61*** 0.00044 0.0132 -0.2833 4.2090 72.28***Crisis period -0.00133 0.0177 0.1483 4.6700 36.92*** -0.00133 0.0188 0.0046 4.4508 27.01***

Hang SengFull sample 0.00001 0.0180 0.1773 13.3513 9341.88*** 0.00001 0.0204 0.3805 14.6782 11926.97***Period 1 -0.00026 0.0227 0.1863 9.7355 2097.07*** -0.00027 0.0259 0.3845 10.6159 2700.15***Period 2 0.00028 0.0103 0.0771 4.0481 46.02*** 0.00029 0.0115 -0.0908 4.2796 68.48***Crisis period -0.00212 0.0308 0.4266 8.7388 433.39*** -0.00220 0.0351 0.6085 9.8717 627.02***KOSPI 200

Full sample 0.00039 0.0243 0.0619 5.9516 760.01*** 0.00037 0.0284 0.3532 7.2761 1635.76***Period 1 0.00008 0.0296 0.1225 4.7535 144.06*** 0.00005 0.0354 0.4076 5.4819 313.64***Period 2 0.00072 0.0165 -0.2352 4.4549 96.15*** 0.00073 0.0176 -0.3679 4.8448 162.23***Crisis period -0.00263 0.0352 0.4911 4.5741 43.89*** -0.00284 0.0477 0.7532 4.7087 66.16***

Note: *** denotes significance at the 1% level.


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3.2. Methodology

One major approach to evaluating model pricing performance is via the most popular accuracymeasures, mean percentage errors (MPE) and mean absolute percentage errors (MAPE). MPE andMAPE are defined as follows:

MPE =n

t t

tt

AF

FAF

n 1

1 (5)

MAPE =n

t t

tt

AF

FAF

n 1

1 (6)

whereAFtis the actual futures price at time t.Ftis the theoretical futures price estimated by the cost ofcarry model or the Hemler-Longstaff model.

Additionally, for the Hemler-Longstaff model the only variable that cannot be directly observed

is the volatility of the underlying index (Vt). To accommodate time-varying volatility in index returns,estimators based on the moving average method or the GARCH model are commonly employed. This

study employs the exponential GARCH model (EGARCH) modified by Nelson (1991) to estimate Vt.

4

The exponential GARCH model of Nelson (1991), which allows for asymmetric volatilityresponse to stock price shocks, is specified as follows:

ttR (7)

t t-1, t-2, N(0, ht)

2)ln()ln(

1

13

1

12110

t

t

t

ttt

hhhh (8)

whereRtis the spot index return on day t; tdenotes an error term; and htis the conditional variance on

day t. In the EGARCH (1,1) Model, since 02 , negative stock price shocks (i.e., 01t ) will have

a greater impact on the conditional variance, th , than positive stock price shocks (i.e., 01t ).

Furthermore, if 03 and2

1

1

t

t

h, then the lagged residuals will have a positive impact on the

conditional variance.Finally, to compare the relative performance between the cost of carry and the Hemler-

Longstaff models, the t-test was used to test whether the MAPE statistics generated from each modelwere significantly different.

4. Empirical ResultsTable 3 summarizes the pricing errors of the two models. First, the percentage error column shows

that the cost of carry model tends to overprice all three futures contracts. This finding is consistent withthe findings of previous studies, for example Bailey (1989) for the Nikkei 225 contract. Next, Table 3shows that for all of the markets and periods the magnitude of MPE of the cost of carry model clearlyexceeds that of the Hemler-Longstaff model. Particularly in the Asian crisis period, the MPE measuresof the cost of carry model are extremely high, ranging from -0.0675% (Nikkei 225) to as high as -2.2014% (KOSPI 200). However, the MPE values of the Hemler-Longstaff model are 0.0053% and -0.0692% for the Nikkei 225 and the KOSPI 200 index futures, respectively.

Table 4 further classifies the percentage errors as either premiums or discounts for the Asiancrisis period.5 The Hemler-Longstaff model displays no clear difference between the number and

4

This study also uses the GARCH(1,1) model to estimate Vt. The EGARCH (1,1) Model has slightly better pricing performance than the GARCH(1,1)model.

5 If actual futures prices are higher than theoretical futures prices, the percentage errors are classified as premiums. Conversely, percentage errors are

classified as discounts.


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magnitude of premiums and discounts for all three markets. However, as for the cost of carry model, interms of magnitude, discounts are about 195.40 percent and 384.25 percent of premiums for the HangSeng and the KOSPI 200 markets, respectively. Overall, for the cost of carry model, the Asian crisisperiod shows that the magnitude of the discounts obviously exceeds that of the premiums for the Hang

Seng and the KOSPI 200 markets with high stock price volatility.

Table 3: Summary statistics for the pricing errors of the cost of carry and Hemler-Longstaff models

Cost of carry model Hemler-Longstaff model

Percentage error Absolute percentage

error

Percentage error Absolute percentage

error

Mean (%) Std (%) Mean (%) Std (%) Mean (%) Std (%) Mean (%) Std (%)

Nikkei 225

Full sample -0.0421 0.3552 0.2579 0.2477 0.0001 0.3550 0.2565 0.2453Period 1 -0.0390 0.4013 0.2920 0.2779 0.0010 0.4008 0.2901 0.2764Period 2 -0.0456 0.2945 0.2193 0.2016 -0.0006 0.2938 0.2177 0.1972Crisis period -0.0675 0.4767 0.3304 0.3497 0.0053 0.4746 0.3225 0.3478

Hang SengFull sample -0.1310 0.6309 0.4056 0.5006 -0.0051 0.6091 0.4001 0.4592Period 1 -0.1912 0.7894 0.5169 0.6263 -0.0092 0.7599 0.5048 0.5679Period 2 -0.0633 0.3695 0.2805 0.2485 -0.0037 0.3743 0.2846 0.2429Crisis period -0.4690 1.0972 0.8053 0.8797 -0.0060 1.0504 0.6943 0.6753

KOSPI 200

Full sample -0.3877 1.7763 1.0014 1.5173 -0.0206 1.5733 0.9481 1.2444Period 1 -0.6535 2.3546 1.5448 1.8929 -0.0646 2.0875 1.4071 1.4620Period 2 -0.0904 0.5642 0.3937 0.4139 0.0071 0.5511 0.3751 0.4037Crisis period -2.2014 3.4802 3.0221 2.7949 -0.0692 2.9917 2.4158 1.7605

Table 4: Summary statistics for the premiums and discounts for the Asian crisis period

Cost of carry model Hemler-Longstaff model

Number

of

premiums

Number

of

discounts

Mean

premium

(%)

Mean

discount

(%)

Number

of

premiums

Number

of

discounts

Mean

premium

(%)

Mean

discount

(%)

Nikkei 225 123 185 0.3301 -0.3298 153 155 0.3299 -0.3151Hang Seng 105 204 0.4955 -0.9682 177 132 0.6008 -0.8191

KOSPI 200 114 192 1.0868 -4.1761 157 149 2.2869 -2.5517

Figures 1 to 3 further plot the premiums and discounts for two alternative models. Clearly,during the Asian crisis, the cost of carry model tends to seriously overprice the Hang Seng and theKOSPI 200 futures contracts relative to the Hemler-Longstaff model. To summarize, as can be seenfrom Tables 3 to 4 and Figures 1 to 3, in highly volatile periods, such as the Asian crisis period, themagnitude of MPE of the cost of carry model is much larger than that of the Hemler-Longstaff model.


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Figure 1: Percentage Errors of Two Alternative Pricing Models during the Asian Crisis for the Nikkei 225Futures

-0.020

-0.015

-0.010

-0.005

0.000

0.005

0.010

0.015

0.020

0.025

0.030

0.035

07/02/97 08/02/97 09/02/97 10/02/97 11/02/97 12/02/97 01/02/98 02/02/98 03/02/98 04/02/98 05/02/98 06/02/98 07/02/98 08/02/98 09/02/98

Time

cost of carry model

Hemler-Longstaff model

Figure 2: Percentage Errors of Two Alternative Pricing Models during the Asian Crisis for the Hang SengFutures

-0.070

-0.060

-0.050

-0.040

-0.030

-0.020

-0.010

0.000

0.010

0.020

0.030

0.040

07/03/97 08/03/97 09/03/97 10/03/97 11/03/97 12/03/97 01/03/98 02/03/98 03/03/98 04/03/98 05/03/98 06/03/98 07/03/98 08/03/98 09/03/98

Time

cost of carry model


Figure 3: Percentage Errors of Two Alternative Pricing Models during the Asian Crisis for the KOSPI 200Futures

-0.160

-0.140

-0.120

-0.100

-0.080

-0.060

-0.040

-0.020

0.000

0.020

0.040

0.060

0.080

0.100

07/02/97 08/02/97 09/02/97 10/02/97 11/02/97 12/02/97 01/02/98 02/02/98 03/02/98 04/02/98 05/02/98 06/02/98 07/02/98 08/02/98 09/02/98

Time

cost of carry model



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To robustly test the relative pricing performance of the cost of carry and Hemler-Longstaffmodels, this study also calculates the MAPE measures of these two models. Table 3 lists the empiricalresults. Table 5 summarizes the results of statistical tests for differences in MAPE between the twopricing models. First, in the case of the Nikkei 225 futures, Tables 3 and 5 indicate that the MAPE

values are similar across the two models for the Asian crisis period, with the Hemler-Longstaff modelbeing marginally preferred. Thus, overall, for the Nikkei 225 market with low price volatility, theHemler-Longstaff model provides no significant improvement over the cost of carry model inestimating stock index futures prices. One reason is that, as indicated in Table 2, the Asian crisis periodonly has slightly higher price volatility than the other periods for the Nikkei 225 index. Another reasonis that this comparison involves just one particular method (that is, the EGARCH(1,1) model) forestimating the volatility of the underlying index in the Hemler-Longstaff model. Hence, the Hemler-Longstaff model does not significantly outperform the cost of carry model during the Asian crisis.

Next, for the Hang Seng and the KOSPI 200 futures, from Tables 3 and 5, the MAPE value ofthe Hemler-Longstaff model is significantly smaller than that of the cost of carry model during theAsian crisis. For example, for the KOSPI 200 futures, the MAPE value of the cost of carry model

reached as high as 3.0221%, with a standard deviation of 2.7949%, whereas the MAPE value when theHemler-Longstaff model is used is substantially reduced to 2.4158%, with a standard deviation of1.7605%. The reduction in MAPE (relative to the cost of carry model), shown in Table 5, isstatistically significant at the 1% level, based on a t-test of the mean difference. This result occursbecause the Hemler-Longstaff model appears particularly suitable for stock markets with high pricevolatility and the Asian crisis period indeed has clearly higher price volatility than

Table 5: Statistical tests for differences in MAPE between the two pricing models

Cost of carry model (MAPE) vs. Hemler-Longstaff model (MAPE)

Full sample Period 1 Period 2 Crisis period

Nikkei 225 0.308 0.162 0.177 0.281

Hang Seng 0.371 0.476 -0.368 1.766*

KOSPI 200 1.245 1.914* 1.010 3.220***

Notes: If the MAPE of the cost of carry model is greater than that of the Hemler-Longstaff model, t-value is positive. Conversely, t-value is negative. *and *** denote statistical significance at the 10% and 1% levels, respectively.

the other periods for the Hang Seng and the KOSPI 200 indexes (see Table 2). Thus, as one wouldexpect, the Hemler-Longstaff model with stochastic market volatility yields significantly better pricingperformance than the cost of carry model during the Asian crisis. The empirical results from the Hang

Seng and the KOSPI 200 futures markets imply that in highly volatile periods, such as the Asian crisisperiod, incorporating stochastic market volatility into the pricing model helps in predicting the pricesof these two futures.

Table 6 summarizes the results of statistical tests for differences in MAPE between period 1,period 2, and the Asian Crisis period. The Asian Crisis period has a significantly higher MAPE valuethan periods 1 and 2 (except for crisis period vs. period 1 for the Nikkei 225). Additionally, Table 6also indicates that the MAPE value of the second sub-period is significantly smaller than that of thefirst sub-period for all the index futures contracts and for all the models. This implies that theefficiency of these three markets appears to increase over time.


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Table 6: Results of statistical tests for differences in MAPE between the sub-periods

Nikkei 225 Hang Seng KOSPI 200

Cost of carry modelCrisis period vs. Period 1 1.778* 5.402*** 8.722***

Crisis period vs. Period 2 5.307*** 10.373*** 16.422***period 1 vs. Period 2 6.865*** 11.571*** 19.686***

Hemler-Longstaff modelCrisis period vs. Period 1 1.508 4.503*** 9.175***Crisis period vs. Period 2 5.035*** 10.451*** 20.104***period 1 vs. Period 2 6.913*** 11.741*** 22.503***

Notes: If the MAPE of the former period is greater than that of the latter period in column 1, t-value is positive. Conversely, t-value is negative. * and ***denote statistical significance at the 10% and 1% levels, respectively.

5. ConclusionsHemler and Longstaff (1991) followed the CIR framework and developed a closed-form general

equilibrium model of stock index futures, characterized by both stochastic market volatility and interestrates. Furthermore, the empirical implication of the Hemler-Longstaff model indicates that this modelappears especially suitable when stock markets have high price volatility. Notably, the Asian crisisperiod has higher stock price volatility than the other periods. Thus, by using the Nikkei 225, the HangSeng, and the KOSPI 200 futures contracts, this study represents the first attempt to apply the Hemler-Longstaff model to the case of the Asian crisis, and examines the power of the cost of carry andHemler-Longstaff models in predicting stock index futures prices.

The results of MPE indicate that in highly volatile periods, such as the Asian crisis period, themagnitude of MPE is much larger for the cost of carry model than for the Hemler-Longstaff model.Based on MAPE, the results from the Hang Seng and the KOSPI 200 futures markets also indicate thatthe Hemler-Longstaff model with stochastic market volatility provides more accurate pricing

performance than the cost of carry model during the Asian crisis. This finding implies thatincorporating market volatility into pricing models is beneficial for predicting stock index futuresprices for periods with high stock price volatility. Therefore, when selecting a pricing model toestimate the theoretical values of stock index futures, practitioners should identify the degree of marketvolatility for the markets they are participating in.


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model of stock index futures.pdf

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