Assessing the least squares Monte-Carlo simulation in the stochastic volatility model

Abstract

<P>THE LEAST SQUARES MONTE-CARLO METHOD APPROXIMATES THE OPTION VALUE USING A</P><P>LINEAR COMBINATION OF BASIS FUNCTIONS WITH BACKWARD INDUCTION TO ESTIMATE OPTIMAL</P><P>COEFFICIENTS IN EACH APPROXIMATION. LONGSTAFF AND SCHWARTZ (2001) HAVE GIVEN A</P><P>DETAILED ANALYSIS OF THE LSM APPROACH TO OPTION VALUATION. STENTOFT (2003) GIVES</P><P>A CLOSER EXAMINATION OF THE PERFORMANCE OF THE ALGORITHM IN THE SIMPLE BLACK-</P><P>SCHOLES CASE. IN THIS THESIS, WE TEST THE PERFORMANCE OF THE LSM METHOD IN PRICING</P><P>AMERICAN-STYLE OPTIONS IN THE STOCHASTIC VOLATILITY MODEL. WE SHOW THAT, WHEN</P><P>THE PRICES OF THE UNDERLYING ASSETS FOLLOW THE HESTON STOCHASTIC VOLATILITY MODEL,</P><P>THE LSM METHOD CAN BE IMPLEMENTED WELL IN PRICING AMERICAN OPTIONS AND THE</P><P>AMERICAN-BERMUDA-ASIAN OPTIONS ON ONE ASSET. HOWEVER, THE ESTIMATED RESULTS</P><P>USING DIFFERENT NUMBER OF BASIS FUNCTIONS CHANGE SIGNIFICANTLY, WHEN WE USE THIS</P><P>APPROACH TO PRICE THE MAXIMUM OPTIONS AND THE ARITHMETIC AVE