Pricing exotic option under stochastic volatility model
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Technická Univerzita v Liberci
Technical university of Liberec, Czech Republic
Technical university of Liberec, Czech Republic
Abstract
This paper studies supershare and chooser options in a stochastic volatility economy. These two options are typical exotic options which suggest a broad range of usage and application in different financial market conditions. Despite the popularity and longevity of the Black-Scholes model, the assumption of constant volatility in the Black-Scholes model contradicts to the existence of the non-flat implied volatility surface observed in empirical studies. Although many studies are devoted to option pricing under stochastic volatility model in recent years, to the best of our knowledge, research on exotic option such as supershare and chooser option pricing have not been carried out in the stochastic volatility case. Supershare and chooser options are both important financial instruments, research on these two exotic options in stochastic volatility model may give more insights on the pricing of supershare and chooser options. By extending the constant volatility in the Black-Scholes model, this paper studies the pricing problem of the supershare option and chooser options in a fast mean-reverting stochastic volatility scenario. Analytic approximation formulae for these two exotic options in fast mean-reverting stochastic volatility model are derived according to the method of asymptotic expansion which shows the approximation option price can be expressed as the combination of the zero-order and first-order approximations. By incorporating the stochastic volatility effect, the numerical analysis in our model shows that stochastic volatility of underlying asset underprices the supershare options, while in the case of the chooser options its price in stochastic volatility model is higher than the price in the constant volatility model.
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exotic options, supershare, chooser, stochastic volatility, mean-reverting
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1212-3609