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TITLE An Analytic Approximation for Valuation of the American Option Under the Heston Model in Two Regimes
KIAS AUTHORS Huh, Jeonggyu
JOURNAL COMPUTATIONAL ECONOMICS, 2020
ARCHIVE  
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.
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