American Options Pricing under Stochastic Volatility: Approximation of the Early Exercise Surface and Monte Carlo Simulations

TL;DR

This paper introduces new methods for pricing American options with stochastic volatility, focusing on approximating the early exercise boundary and employing Monte Carlo simulations to improve accuracy and computational efficiency.

Contribution

It develops semi-analytic formulas and numerical techniques for American options under stochastic volatility, enhancing modeling of the early exercise surface and comparing with traditional methods.

Findings

Semi-analytic pricing formulas were derived.

Numerical results showed improved accuracy over models ignoring volatility smile.

Calibration demonstrated the effectiveness of the proposed methods.

Abstract

The aim of this study was to develop methods for evaluating the American-style option prices when the volatility of the underlying asset is described by a stochastic process. As part of this problem were developed techniques for modeling the early exercise surface of the American option. These methods of present work are compared to the complexity of modeling and computation speed. The paper presents the semi-analytic expression for the price of American options with stochastic volatility. The results of numerical computations and their calibration are also presented. The obtained results were compared with results excluding the effect of volatility smile.