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Implied integrated variance and hedging

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  • Ruth Kaila

Abstract

If the volatility is stochastic, stock price returns and European option prices depend on the time average of the variance, i.e. the integrated variance, not on the path of the volatility. Applying a Bayesian statistical approach, we compute a forward-looking estimate of this variance, an option-implied integrated variance. Simultaneously, we obtain estimates of the correlation coefficient between stock price and volatility shocks, and of the parameters of the volatility process. Due to the convexity of the Black-Scholes formula with respect to the volatility, pricing and hedging with Black-Scholes-type formulas and the implied volatility often lead to inaccuracies if the volatility is stochastic. Theoretically, this problem can be avoided by using Hull-White-type option pricing and hedging formulas and the integrated variance. We use the implied integrated variance and Hull-White-type formulas to hedge European options and certain volatility derivatives.

Suggested Citation

  • Ruth Kaila, 2015. "Implied integrated variance and hedging," Quantitative Finance, Taylor & Francis Journals, vol. 15(9), pages 1515-1530, September.
    • Handle: RePEc:taf:quantf:v:15:y:2015:i:9:p:1515-1530
    DOI: 10.1080/14697688.2014.1002418
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    References listed on IDEAS

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    1. 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.
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