Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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COMPARISON OF STOCHASTIC VOLATILITY MODELS: EMPIRICAL STUDY ON KOSPI 200 INDEX OPTIONS

  • Published : 2009.03.31
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Abstract

We examine a unified approach of calculating the closed form solutions of option price under stochastic volatility models using stochastic calculus and the Fourier inversion formula. In particular, we review and derive the option pricing formulas under Heston and correlated Stein-Stein models using a systematic and comprehensive approach which were derived individually earlier. We compare the empirical performances of the two stochastic volatility models and the Black-Scholes model in pricing KOSPI 200 index options.

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References

  1. G. S. Bakshi, C. Cao, and Z. W. Chen, Empirical performance of alternative option pricing models, Journal of Finance 52 (1997), no. 5, 2003–2049
  2. D. Bates, Post-$8\gamma$ crash fears in the S&P 500 futures option market, Journal of Econometrics 94 (2000), 181–238
  3. F. Black and M. Scholes, 1973, The pricing of options and corporate liabilities, Journal of Political Economy 81 (1973), 637–659
  4. M. Chen and Y. Gau, Pricing currency options under stochastic volatility, 2004 NTU International Conference on Finance, 2004
  5. J. C. Cox, J. E. Ingersoll, and S. A. Ross, A theory of the term structure of interest rates, Econometrica 53 (1985), no. 2, 385–407
  6. B. Dupoyet, Information content of cross-sectional option prices: A comparison of alternative currency option pricing models on the Japanese yen, Journal of Futures Markets 26 (2006), 33–59 https://doi.org/10.1002/fut.20177
  7. S. L. Heston, A closed-form solution for options with stochastic volatility with applications to bonds and currency options, The Review of Financial Studies 6 (1993), 327–343 https://doi.org/10.1093/rfs/6.2.327
  8. J. Hull and A. White, The pricing of options on assets with stochastic volatilities, Journal of Finance 42 (1987), 281–300 https://doi.org/10.2307/2328253
  9. J. Johnson and D. Shanno, Option pricing when the variance is changing, Journal of Financial and Quantitative Analysis 22 (1987), 143–151
  10. I. J. Kim and S. Kim, Empirical comparison of alternative stochastic volatility option pricing models: Evidence from Korean KOSPI 200 index options market, Pacific-Basin Finance Journal 12 (2004), 117–142 https://doi.org/10.1016/S0927-538X(03)00042-8
  11. Y.-N. Lin, N. Strong, and X. Xu, Pricing FTSE 100 index option under stochastic volatility, Journal of Futures Markets 21 (2001), 197–211 https://doi.org/10.1002/1096-9934(200103)21:3<197::AID-FUT1>3.0.CO;2-3