An Analytic Approximation for Valuation of the American Option Under the Heston Model in Two Regimes

Junkee Jeon (), Jeonggyu Huh () and Kyunghyun Park ()
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Junkee Jeon: Kyung Hee University
Jeonggyu Huh: Korea Institute for Advanced Study
Kyunghyun Park: Seoul National University

Computational Economics, 2020, vol. 56, issue 2, No 9, 499-528

Abstract: Abstract This paper studies the valuation of the American call-option under the Heston model in two regimes, i.e., fast-mean reverting and slow-mean reverting regimes. In the case of the European-style option under the Heston model, a closed-form solution for one-dimensional integration can be derived. However, in the case of the American-style option, it is impossible to obtain a general analytic integral equation for the price. By using singular and regular perturbation techniques introduced by Fouque et al. (Multiscale stochastic volatility for equity, interest-rate and credit derivative, Cambridge University Press, Cambridge, 2011) and the maturity randomization method introduced by Carr (Rev Financ Stud 11:597–626, 1998), we provide an approximate analytic solution of the American call-option and describe a numerical scheme to evaluate the value of this solution. Numerical results show that our method is accurate and efficient compared to the finite-difference method and the Longstaff and Schwartz (Rev Financ Stud 14(1):113–147, 2001) method.

Keywords: American option; Heston model; Singular perturbation; Maturity randomization (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s10614-019-09939-2

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