Abstract
The exotic options with curved nonlinear payoffs have been traded in financial markets, which offer great flexibility to participants in the market. Among them, power options with the payoff depending on a certain power of the underlying asset price are widely used in markets in order to provide high leverage strategy. In pricing power options, the classical Black–Scholes model which assumes a constant volatility is simple and easy to handle, but it has a limit in reflecting movements of real financial markets. As the alternatives of constant volatility, we focus on the stochastic volatility, finding more exact prices for power options. In this paper, we use the stochastic volatility model introduced by Schöbel and Zhu to drive the closed-form expressions for the prices of various power options including soft strike options. We also show the sensitivity of power option prices under changes in the values of each parameter by calculating the resulting values obtained from the formulas.
Highlights
Power options are a class of exotic options in which the payoff at maturity is related to the certain positive power of the underlying asset price, which allows investors to a provide high leverage strategy and to hedge nonlinear price risks according to Tompkins [1]
With the numerical computation, we investigate the sensitivity of power option prices under changes in the values of each parameter along with the increase of power α from 1.00 to 1.10
Since our pricing formula is available in closed form, it is theoretically possible to differentiate the price formula with respect to each parameter to obtain sensitivity expressions in closed form
Summary
Power options are a class of exotic options in which the payoff at maturity is related to the certain positive power of the underlying asset price, which allows investors to a provide high leverage strategy and to hedge nonlinear price risks according to Tompkins [1]. It makes sense to consider a stochastic volatility model in valuing power options Stochastic volatility models, such as Heston [6], Hull–White [7], Schöbel–Zhu [8], and Stein–Stein [9], are more popular and frequently used in the pricing of various kinds of European options. We use the stochastic volatility model introduced by Schöbel and Zhu [8] to drive a closed-form expression for the price of various power options.
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