nach oben

Review of Quantitative Finance and Accounting

Erschienen in:

01.07.2007

The role of stochastic volatility and return jumps: reproducing volatility and higher moments in the KOSPI 200 returns dynamics

verfasst von: In Joon Kim, In-Seok Baek, Jaesun Noh, Sol Kim

Erschienen in: Review of Quantitative Finance and Accounting | Ausgabe 1/2007

Einloggen

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config

KI-gestützte Suche

Aus

Abstract

This paper investigates the role of stochastic volatility and return jumps in reproducing the volatility dynamics and the shape characteristics of the Korean Composite Stock Price Index (KOSPI) 200 returns distribution. Using efficient method of moments and reprojection analysis, we find that stochastic volatility models, both with and without return jumps, capture return dynamics surprisingly well. The stochastic volatility model without return jumps, however, cannot fully reproduce the conditional kurtosis implied by the data. Return jumps successfully complement this gap. We also find that return jumps are essential in capturing the volatility smirk effects observed in short-term options.

Vorheriger Artikel Takeover motives in a weak regulatory environment surrounding a market shock: a case study of New Zealand with a comparison of Gondhalekar and Bhagwat’s (2003) US findings

Nächster Artikel Recap of the 17th Annual Conference on Financial Economics and Accounting (with PowerPoint of Professor Katherine Schipper's Keynote Speech)

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

über 102.000 Bücher
über 537 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Finance + Banking
Management + Führung
Marketing + Vertrieb
Maschinenbau + Werkstoffe
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 340 Zeitschriften

aus folgenden Fachgebieten:

Bauwesen + Immobilien
Business IT + Informatik
Finance + Banking
Management + Führung
Marketing + Vertrieb
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Nur mit Berechtigung zugänglich

See Bates (1996, 2000), Duffie et al. (2000), Eisenberg and Jarrow (1994), Heston (1993), Hull and White (1987), Scott (1987, 1997), and Wu (2006) among many others. See Johnson et al. (1997), Lee et al. (1991), and Lee et al. (2005) for the generalization of the binomial model of Cox et al. (1979).

For example, Wu (2003) examines the effects of jump components on the portfolio choice problem. Baixauli and Alvarez (2006) and Huang and Lin (2004) provide excellent analyses on the application of VaR (Value-at-Risk) calculation.

See Gallant and Tauchen (1998, 2002) for the general theory of reprojection and its applications.

See ABL for numerical difficulties with the derivative based optimization method in the estimation of jump diffusion models.

See Sect. 2 for a brief summary of recent empirical findings.

We find that there is no discernable difference in the marginal distribution between these two data sets. Daily returns constructed by using the price at 2:50 PM are slightly more negatively skewed and leptokurtic.

For example, recently, Chiang and Doong (2001) and Selçuk (2005) examine the volatility dynamics of many emerging stock market indices and find that there is a considerable volatility persistence in these markets. Cappiello et al. (2003) estimate unconditional moments of FTSE All-World Indices for 21 countries. Using weekly returns data, they find that all the equity indices are leptokurtic and the returns for 19 countries are negatively skewed.

Our main results are obtained by using daily returns of the KOSPI 200 index from January 4, 2000 to July 29, 2005. Daily returns from January 4, 1997 to December 28, 1999 are reserved for the analysis presented in Subsect. 5.4.

See their Table 1 on page 1250. All figures are expressed on a daily basis in percentage form.

For details of the EMM, see Gallant and Tauchen (1996a, 2001, 2002).

Therefore, we simulate log stock price in the second step of the EMM procedure.

The results are not reported here but are available upon request.

Strictly speaking, we report the quasi t-ratios, which are suggested by Gallant and Long (1997) and Tauchen (1997) and are commonly used in the papers that employ the EMM method. See, for example, CGGT, Gallant et al. (1997), and Gallant and Tauchen (1996b, 1997, 1998) among many others.

See their parameter estimates for SV ₂, ρ = 0 and SV ₂, ρ ≠ 0 in their Tables 3 and 6.

See their t-ratios for the scores of the GARCH terms for models termed AFF1V, AFF1V-J0, and AFF1V-J presented in their Table 5.

Convergence is in terms of the Sobolev norm specified by Gallant and Long (1997).

The reprojected conditional densities for the BS and SV0 model have wider domains than the projected and other reprojected densities. These two models overestimate the conditional variance when conditioned by the sample mean of the data. However, this result does not alter the shape of the density.

See Table 3.1 of Scott (1997).

The results are not reported here but are available upon request.

Therefore, the overall estimation procedure in this paper is a two-step scheme wherein the structural parameters of return dynamics are estimated from the time-series of stock returns, and then the volatility and jump risk premia are estimated from the cross-section of option prices. Our approach is similar to those of Fiorentini et al. (2002), Jiang (2002), and Jiang and van der Sluis (1999.

In calculating the theoretical option price, a subroutine QAGI by Piessens et al. (1983) of ?IMSL C library is applied to numerically integrate the imaginary part of the complex Fourier transform.

As shown in the third row of Table 11, the participation of foreign investors in the KOSPI 200 options market is on a steady increase. It was 5.27% at the end of 2000 and has increased to 14.39% at the end of 2005.

Korea does not have a liquid Treasury bill market, therefore the 91-day certificate of deposit (CD) yields are used in spite of the mismatch of maturity of options and interest rates.

As discussed in Sect. 4, there are simultaneous bids and offers from 2:50 PM to 3:00 PM in the KSE.

We thank an anonymous referee for recommending us this approach.

For each model, Table 12 presents the average and standard errors (in parentheses) of the risk-neutral parameters, which are estimated daily.

Therefore, out-of-sample approach used in this paper is different from that of Bakshi et al. (1997), in which the pricing performance evaluations rely on in-sample one-step ahead forecasts.

Anderson, G., Benzoni, L., & Lund, J. (2002). An empirical investigation of continuous-time models for equity returns. Journal of Finance, 57, 1239–1284.CrossRef

Baixauli, J. S., & Alvarez, S. (2006). Evaluating effects of excess kurtosis on VaR estimates: Evidence for international stock indices. Review of Quantitative Finance and Accounting, 27, 27–46.CrossRef

Bakshi, G., Cao, C., & Chen, Z. (1997). Empirical performance of alternative option pricing models. Journal of Finance, 52, 2003–2049.CrossRef

Bates, D. (1996). Jump and stochastic volatility: Exchange rate processes implicit in deutsche mark options. Review of Financial Studies, 9, 69–107.CrossRef

Bates, D. (2000). Post-’87 crash fears in S&P 500 futures options. Journal of Econometrics, 94, 181–238.CrossRef

Black, F., & Scholes, M. (1973). The pricing of options and corporate liabilities. Journal of Political Economy, 81, 637–659.CrossRef

Bollerslev, T., & Zhou, H. (2000). Estimating stochastic volatility diffusion using conditional moments of integrated volatility. Working Paper, Duke University.

Cappiello, L., Engle, R.F., & Shepard, K. (2003). Asymmetric dynamics in the correlations of global equity and bond returns. Working Paper, European Central Bank.

Chacko, G., & Viceira, L.M. (2003). Spectral GMM estimation of continuous-time processes. Journal of Econometrics, 116, 25–292.CrossRef

Chang, K.H. (1997). Jump risks and heteroskedasticity in Korean financial markets. Journal of Korean Securities Association, 20, 273–299.

Chernov, M., Gallant, A. R., Ghysels, E., & Tauchen, G. (2003). Alternative models for stock price dynamics. Journal of Econometrics, 116, 225–257.CrossRef

Chernov, M., & Ghysels, E. (2000). Towards a unified approach to the joint estimation of objective and risk neutral measures for the purpose of options valuation. Journal of Financial Economics, 56, 407–458.CrossRef

Chernozhukov, V., & Hong, H. (2003). An MCMC approach to classical estimation. Journal of Econometrics, 115, 293–346.CrossRef

Chiang, T. C., & Doong, S.-C. (2001). Empirical analysis of stock returns and volatility: Evidence from Seven Asian Stock Markets Based on TAR-GARCH Model. Review of Quantitative Finance and Accounting, 17, 301–318.CrossRef

Cox, J., Ross, S., & Rubinstein, M. (1979). Option pricing: A simplified approach. Journal of Financial Economics, 7, 229–263.CrossRef

Daniel, G., Joseph, N., & Brée, D. S. (2005). Stochastic volatility and the goodness-of-fit of the heston model. Quantitative Finance, 5, 199–211.CrossRef

Das, S. R., & Sundaram, R.K. (1999). Of smiles and smirks: A term-structure perspective. Journal of Financial and Quantitative Analysis, 34, 211–239.CrossRef

Duffie, D., Pan, J., & Singleton, K. (2000). Transform analysis and asset pricing for affine jump-diffusions. Econometrica, 68, 1343–1376.CrossRef

Eisenberg, L., & Jarrow, R. (1994). Option pricing with random volatilities in complete markets. Review of Quantitative Finance and Accounting, 4, 5–17.CrossRef

Engle, R.F., & Gonzales-Rivera, G. (1991). Semiparametric ARCH models. Journal of Business and Economic Statistics, 9, 345–360.CrossRef

Engle, R.F., & Kroner, K.F. (1995). Multivariate simultaneous generalized ARCH. Econometric Theory, 11, 122–150.CrossRef

Eraker, B. (2004). Do stock prices and volatility jump? Reconciling evidence from spot and option prices. Journal of Finance, 59, 1367–1403.CrossRef

Eraker, B., Johannes, M. S., & Polson, N. G. (2003). The impact of jumps in returns and volatility. Journal of Finance, 53, 1269–1300.CrossRef

Fiorentini, G., León, A., & Rubio, G. (2002). Estimation and Empirical performance of heston’s stochastic volatility model: The case of a thinly traded market. Journal of Empirical Finance, 9, 225–255.CrossRef

Gallant, A. R., Hsieh, D. A., & Tauchen, G. (1997). Estimation of stochastic volatility models with diagnostics. Journal of Econometrics 81:159–192.CrossRef

Gallant, A. R., Hsu, C.-T., & Tauchen, G. (1999). Using daily range data to calibrate volatility diffusions and extract the forward integrated variance. Review of Economics and Statistics, 81, 617–631.CrossRef

Gallant, A.R., & Long, J.R. (1997). Estimating stochastic differential equations efficiently by minimum chi-square. Biometrica, 84, 125–141.CrossRef

Gallant, A. R., & Nychka, D. W. (1987). Seminonparametric maximum likelihood estimation. Econometrica, 55, 363–390.CrossRef

Gallant, A. R., & Tauchen, G. (1989). Seminonparametric estimation of conditionally constrained heterogeneous processes: Asset pricing applications. Econometrica, 57, 1091–1120.CrossRef

Gallant, A. R., & Tauchen, G. (1996a). Which moments to match. Econometric Theory, 12, 657–681.

Gallant, A. R., & Tauchen, G. (1996b). Specification analysis of continuous time models in Finance. In P. E. Rossi (Ed.), Modeling stock market volatility: Bridging the gap to continuous time. New York: Academy Press.

Gallant, A. R., & Tauchen, G. (1997). Estimation of continuous-time models for stock returns and interest rates. Macroeconomic Dynamics, 1, 135–168.CrossRef

Gallant, A. R., & Tauchen, G. (1998). Reprojecting partially observed systems with application to interest rate diffusions. Journal of American Statistical Association, 93, 10–24.CrossRef

Gallant, A. R., & Tauchen, G. (2001). Efficient method of moments. Working paper, University of North-Carolina-Chapel Hill.

Gallant, A. R., & Tauchen, G. (2002). Simulated score methods and indirect inference for continuous-time models. Chapter in preparation for the Handbook of Financial Econometrics.

Gallant, A. R., & Tauchen, G. (2005). SNP: A Program for Nonparametric Time Series Analysis, Version 9.0, User’s Guide. Manuscript, Duke University.

Gallant A. R., & Tauchen, G. (2005). EMM: A Program for Efficient Method of Moments, Version 2.0, User’s Guide. Manuscript, Duke University.

Hastings, W. K. (1970). Monte carlo sampling methods using markov chains and their applications. Biometrica, 57, 97–109.CrossRef

Harvey, A. C., Ruiz, E., Shepard, N. (1994). Multivariate stochastic variance models. Review of Economic Studies, 61, 247–264.CrossRef

Heston, S.L. (1993). A closed-form solution for options with stochastic volatility with applications to bond and currency options. Review of Financial Studies, 6, 327–343.CrossRef

Huang, Y. C., & Lin, B.-J. (2004). Value-at-risk analysis for taiwan stock index futures: fat tails and conditional asymmetries in return innovations. Review of Quantitative Finance and Accounting, 22, 79–95.CrossRef

Hull, J., & White, A. (1987). The pricing of options on assets with stochastic volatilities. Journal of Finance, 42, 281–300.CrossRef

Jiang, G. J. (2002). Testing option pricing models with stochastic volatility, random jump and stochastic interest rate. International Review of Finance, 3, 233–272.CrossRef

Jiang, G. J., & Knight, J. L. (2002). Estimation of continuous-time processes via the empirical characteristic function. Journal of Business and Economic Statistics, 20, 198–212.CrossRef

Jiang, J., & van der Sluis, P. (1999). Pricing index options under stochastic volatility and stochastic interest rates with efficient method of moments estimation. European Finance Review, 3, 273–310.CrossRef

Johnson, R. S., Pawlukiewicz, J. E., & Mehta, J. M. (1997). Binomial option pricing with skewed asset returns. Review of Quantitative Finance and Accounting, 9, 89–101.CrossRef

Jones, C. S. (2003). The dynamics of stochastic volatility: Evidence from underlying and options markets. Journal of Econometrics, 116, 181–224.CrossRef

Kim, M. J., & Chang, K. H. (1996). Measuring stochastic volatility of the KOSPI 200 index. Korean Journal of Futures and Option, 4, 131–156.

Kim, I. J., & Kim, S. (2004). Empirical comparison of alternative stochastic volatility option pricing models: Evidence from Korean KOSPI 200 index options market. Pacific-Basin Finance Journal, 12, 117–142.CrossRef

Kim, I. J., & Kim, S. (2005). Is it important to consider the jump component for pricing and hedging short-term option? Journal of Futures Markets, 25, 989–1009.CrossRef

Lee, J., Lee, C. F., & John Wei, K. C. (1991). Binomial option pricing with stochastic parameters: A beta distribution approach. Review of Quantitative Finance and Accounting, 1, 435–448.CrossRef

Lee, C. F., Tzeng, G.-H., & Wang, S.-Y. (2005). A fuzzy set approach for generalized CRR model: An empirical analysis of S&P 500 index options. Review of Quantitative Finance and Accounting, 25, 255–275.CrossRef

Lin, Y. N., Strong, N., & Xu, X. (2001). Pricing FTSE 100 index options under stochastic volatility. Journal of Futures Markets, 21, 197–211.CrossRef

Metropolis, N., Rosenbluth, A. W., Rosenbluth, M. N., Teller, A. H., & Teller, E. (1953). Equations of state calculations by fast computing machines. Journal of Chemical Physics, 21, 1087–1092.CrossRef

Pan, J. (2002). The jump-risk premia implicit in options: Evidence from an integrated time-series study. Journal of Financial Economics, 63, 3–50.CrossRef

Piessens, R., de Doncker-Kapenga, E., Uberhuber, C. W., & Kahaner, D. K. (1983). QUADPACK. New York: Springer-Verlag.

Selçuk, F. (2005). Asymmetric stochastic volatility in emerging stock markets. Applied Financial Economics, 15, 867–874.CrossRef

Sepp, A. (2003). Pricing European-style options under jump diffusion processes with stochastic volatility. Working Paper, University of Tartu.

Scott, L.O. (1987). Option pricing when the variance changes randomly: Theory, estimators, and applications. Journal of Financial and Quantitative Analysis, 22, 419–438.CrossRef

Scott, L. O. (1997). Pricing stock options in a jump-diffusion model with stochastic volatility and interest rates: Applications of fourier inversion methods. Mathematical Finance, 7, 413–424.CrossRef

Tauchen, G. (1997). New minimum chi-square methods in empirical Finance. In D. Kreps and K. Wallis (Eds.), Advances in econometrics, seventh world congress (pp. 279–317). Cambridge UK: Cambridge University Press.

Tompkins, R. G. (2000). The Austrian stock market: Objective dispersion processes and option pricing. Financial Markets and Portfolio Management, 14, 152–179.

Tompkins, R. G. (2001). Stock index futures markets: stochastic volatility models and smiles. Journal of Futures Markets, 21, 43–78.CrossRef

Upper, C. (2005). Strong growth in East Asia equity derivatives. BIS Quarterly Review December, 47–48.

Wu, C.-C. (2006). The GARCH option pricing model: A modification of lattice approach. Review of Quantitative Finance and Accounting, 26, 55–66.CrossRef

Wu, L. (2003). Jumps and dynamic asset allocation. Review of Quantitative Finance and Accounting, 20, 207–243.CrossRef

Titel: The role of stochastic volatility and return jumps: reproducing volatility and higher moments in the KOSPI 200 returns dynamics
verfasst von: In Joon Kim
In-Seok Baek
Jaesun Noh
Sol Kim
Publikationsdatum: 01.07.2007
Verlag: Springer US
Erschienen in: Review of Quantitative Finance and Accounting / Ausgabe 1/2007
Print ISSN: 0924-865X
Elektronische ISSN: 1573-7179
DOI: https://doi.org/10.1007/s11156-007-0022-2

Springer Professional

Abstract

Bitte loggen Sie sich ein, um Zugang zu Ihrer Lizenz zu erhalten.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Springer Professional "Wirtschaft"

Weitere Artikel der Ausgabe 1/2007

Disclosure and the cost of equity in international cross-listing

The relation between R&D intensity and future market returns: does expensing versus capitalization matter?

Takeover motives in a weak regulatory environment surrounding a market shock: a case study of New Zealand with a comparison of Gondhalekar and Bhagwat’s (2003) US findings

Recap of the 17th Annual Conference on Financial Economics and Accounting (with PowerPoint of Professor Katherine Schipper's Keynote Speech)