Penalty methods for American options with stochastic volatility
Journal of Computational and Applied Mathematics
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We consider the problem of pricing American options when the volatility of the underlying asset price is stochastic. No specific stochastic volatility model is assumed for the stochastic process. We propose a simulation-based approach to pricing such options. Iteratively, the method determines the optimal exercise boundary and the associated price function for a general stochastic volatility model. Given an initial guess of the optimal exercise boundary, the Retrospective Approximation (RA) technique is used to calculate the associated value function. Using this function, the exercise boundary is improved and the process repeated till convergence. This method is a simulation based variant of the exercise-policy improvement scheme developed in Chockalingam and Muthuraman (2007). An illustration of the method is provided when using the Heston (1993) model to represent the dynamics of the volatility, together with comparisons against existing methods to validate our numerical results.