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An application of closed-form GARCH option-pricing model on FTSE 100 option and volatility

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  • YongChern Su
  • MingDa Chen
  • HanChing Huang

Abstract

Many researches indicate that the Black-Scholes (BS) option-pricing model demonstrates systematic biases due to some unreasonable assumptions. In practice, implied volatilities tend to differ across exercise prices and time to maturities. To solve the problem, Heston and Nandi (HN) (2000) develop closed-form Generalized Autoregressive Conditional Heteroscedasticity (HN-GARCH) model. In this study, we apply their model on Financial Time Stock Exchange (FTSE) 100 index option. As a benchmark, we employ the ad hoc BS model which uses a separate implied volatility for each option to fit the smirk/smile in implied volatilities. The test finds that the HN GARCH has smaller valuation errors than the ad hoc BS model.

Suggested Citation

  • YongChern Su & MingDa Chen & HanChing Huang, 2010. "An application of closed-form GARCH option-pricing model on FTSE 100 option and volatility," Applied Financial Economics, Taylor & Francis Journals, vol. 20(11), pages 899-910.
    • Handle: RePEc:taf:apfiec:v:20:y:2010:i:11:p:899-910
    DOI: 10.1080/09603101003652417
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    References listed on IDEAS

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    1. Nelson, Daniel B., 1990. "ARCH models as diffusion approximations," Journal of Econometrics, Elsevier, vol. 45(1-2), pages 7-38.
    2. Geske, Robert, 1979. "The valuation of compound options," Journal of Financial Economics, Elsevier, vol. 7(1), pages 63-81, March.
    3. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    4. Engle, Robert F & Ng, Victor K, 1993. "Measuring and Testing the Impact of News on Volatility," Journal of Finance, American Finance Association, vol. 48(5), pages 1749-1778, December.
    5. Engle, Robert F. & Mustafa, Chowdhury, 1992. "Implied ARCH models from options prices," Journal of Econometrics, Elsevier, vol. 52(1-2), pages 289-311.
    6. Merton, Robert C., 1976. "Option pricing when underlying stock returns are discontinuous," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 125-144.
    7. Christoffersen, Peter & Jacobs, Kris, 2004. "The importance of the loss function in option valuation," Journal of Financial Economics, Elsevier, vol. 72(2), pages 291-318, May.
    8. Peter Ritchken & Rob Trevor, 1999. "Pricing Options under Generalized GARCH and Stochastic Volatility Processes," Journal of Finance, American Finance Association, vol. 54(1), pages 377-402, February.
    9. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
    10. repec:bla:jfinan:v:53:y:1998:i:6:p:2059-2106 is not listed on IDEAS
    11. Rubinstein, Mark, 1983. "Displaced Diffusion Option Pricing," Journal of Finance, American Finance Association, vol. 38(1), pages 213-217, March.
    12. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," The Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
    13. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
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    Cited by:

    1. Contreras, Javier & Rodríguez, Yeny E., 2014. "GARCH-based put option valuation to maximize benefit of wind investors," Applied Energy, Elsevier, vol. 136(C), pages 259-268.

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