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Pricing and hedging index options under stochastic volatility: an empirical examination

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  • Saikat Nandi

Abstract

An empirical examination of the pricing and hedging performance of a stochastic volatility (SV) model with closed form solution (Heston 1993) is provided for options on the S&P 500 index in which the unobservable time varying volatility is jointly estimated with the time invariant parameters of the model. Although, out-of-sample, the mean absolute pricing error in the SV model is always lower than in the Black-Scholes model, still substantial mispricings are observed for deep out-of-the-money options. The degree of mispricing in different options classes is related to bid-ask spreads on options and options trading volume after controlling for moneyness and maturity biases. Taking into account the transactions costs (bid-ask spreads) in the options market and using S&P 500 futures to hedge, it is found that the stochastic volatility model yields lower variance for a minimum variance hedge portfolio than the Black-Scholes model for most classes of options and the differences in variances are statistically significant.

Suggested Citation

  • Saikat Nandi, 1996. "Pricing and hedging index options under stochastic volatility: an empirical examination," FRB Atlanta Working Paper 96-9, Federal Reserve Bank of Atlanta.
    • Handle: RePEc:fip:fedawp:96-9
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    Cited by:

    1. Bates, David S., 2000. "Post-'87 crash fears in the S&P 500 futures option market," Journal of Econometrics, Elsevier, vol. 94(1-2), pages 181-238.
    2. Lam, K. & Chang, E. & Lee, M. C., 2002. "An empirical test of the variance gamma option pricing model," Pacific-Basin Finance Journal, Elsevier, vol. 10(3), pages 267-285, June.
    3. Peter A. Abken & Saikat Nandi, 1996. "Options and volatility," Economic Review, Federal Reserve Bank of Atlanta, vol. 81(Dec), pages 21-35.
    4. Ruth Kaila, 2015. "Implied integrated variance and hedging," Quantitative Finance, Taylor & Francis Journals, vol. 15(9), pages 1515-1530, September.
    5. Steven Heston & Saikat Nandi, 1997. "A closed-form GARCH option pricing model," FRB Atlanta Working Paper 97-9, Federal Reserve Bank of Atlanta.

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    Keywords

    Hedging (Finance); options;

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