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

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  • Yu. A. Kuperin
  • P. A. Poloskov

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.

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  • Yu. A. Kuperin & P. A. Poloskov, 2010. "American Options Pricing under Stochastic Volatility: Approximation of the Early Exercise Surface and Monte Carlo Simulations," Papers 1009.5495, arXiv.org.
    • Handle: RePEc:arx:papers:1009.5495
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    References listed on IDEAS

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    1. Longstaff, Francis A & Schwartz, Eduardo S, 2001. "Valuing American Options by Simulation: A Simple Least-Squares Approach," The Review of Financial Studies, Society for Financial Studies, vol. 14(1), pages 113-147.
    2. Montagna, Guido & Nicrosini, Oreste & Moreni, Nicola, 2002. "A path integral way to option pricing," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 310(3), pages 450-466.
    3. Andrew Ziogas & Carl Chiarella, 2005. "Pricing American Options under Stochastic Volatility," Computing in Economics and Finance 2005 77, Society for Computational Economics.
    4. Eleonora Bennati & Marco Rosa-Clot & Stefano Taddei, 1999. "A Path Integral Approach To Derivative Security Pricing I: Formalism And Analytical Results," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 2(04), pages 381-407.
    5. Marco Rosa-Clot & Stefano Taddei, 1999. "A Path Integral Approach to Derivative Security Pricing: I. Formalism and Analytical Results," Papers cond-mat/9901277, arXiv.org.
    6. Marco Rosa-Clot & Stefano Taddei, 1999. "A Path Integral Approach to Derivative Security Pricing: II. Numerical Methods," Papers cond-mat/9901279, arXiv.org.
    7. Longstaff, Francis A & Schwartz, Eduardo S, 2001. "Valuing American Options by Simulation: A Simple Least-Squares Approach," University of California at Los Angeles, Anderson Graduate School of Management qt43n1k4jb, Anderson Graduate School of Management, UCLA.
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