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R. Zvan, P. A. Forsyth and K. R. Vetzal, “Penalty Methods for American Options with Stochas-tic Volatility,” Journal of Computational and Applied Mathematics, Vol. 91, No. 4, 1998, pp. 199-218. doi:10.1016/S0377-0427(98)00037-5

has been cited by the following article:

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

  AUTHORS: Oleksandr Zhylyevskyy

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

  JOURNAL NAME: Theoretical Economics Letters, Vol.2 No.1, February 23, 2012

  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.