Efficient Pricing of European-Style Options under Heston’s Stochastic Volatility Model

Oleksandr Zhylyevskyy

Department of Economics, Iowa State University, Ames, IA, USA.

DOI: 10.4236/tel.[phone]                

Abstract

Heston’s stochastic volatility model is frequently employed by finance researchers and practitioners. Fast pricing of European-style options in this setting has considerable practical significance. This paper derives a computationally efficient formula for the value of a European-style put under Heston’s dynamics, by utilizing a transform approach based on inverting the characteristic function of the underlying stock’s log-price and by exploiting the characteristic function’s symmetry. The value of a European-style call is computed using a parity relationship. The required characteristic function is obtained as a special case of a more general solution derived in prior research. Computational advantage of the option value formula is illustrated numerically. The method can help to mitigate the time cost of algorithms that require repeated evaluation of European-style options under Heston’s dynamics.

Keywords

Heston’s Model; European-Style Option; Characteristic Function Inversion

Conflicts of Interest

The authors declare no conflicts of interest.

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