Valuation of power options under Heston's stochastic volatility model

Jerim Kim, Bara Kim, Kyoung-Sook Moon and In-Suk Wee

Journal of Economic Dynamics and Control, 2012, vol. 36, issue 11, 1796-1813

Abstract: We derive semi-analytic solutions for power option prices under the Heston model; specifically, the pricing formula is shown to be valid whenever the power of the underlying asset price has a finite moment. Unlike the majority of stochastic volatility models, there remains a significant problem to check the existence of moments of assets prices of order higher than one. Fortunately, the moment explosion property under the Heston model is examined systematically in Andersen and Piterbarg (2000). Incorporating with their results, we present explicit formulas for moment generating function of log price and for power option prices under the circumstances when the corresponding moments are finite. In case that the corresponding moment explodes, we provide two numerical methods to derive prices of power put and capped power call options. In spite of a simple idea, numerical examples show that the approximations are extremely accurate and efficient.

Keywords: Power option; Stochastic volatility; Heston model; Change of numeraire; Fourier transform (search for similar items in EconPapers)
JEL-codes: C02 G13 (search for similar items in EconPapers)
Date: 2012
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (6)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:dyncon:v:36:y:2012:i:11:p:1796-1813

DOI: 10.1016/j.jedc.2012.05.005

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