An Alternative Approach to Evaluate American Options Price Using HJM Approach

Abstract

Developments in finance industry and academic research has led to innovative financial products. This paper presents an alternative approach to price American options. Our approach utilizes famous \cite{heath1992bond} ("HJM") technique to calculate American option written on an asset. Originally, HJM forward modeling approach was introduced as an alternative approach to bond pricing in fixed income market. Since then, \cite{schweizer2008term} and \cite{carmona2008infinite} extended HJM forward modeling approach to equity market by capturing dynamic nature of volatility. They modeled the term structure of volatility, which is commonly observed in the market place as opposed to constant volatility assumption under Black - Scholes framework. Using this approach, we propose an alternative value function, a stopping criteria and a stopping time. We give an example of how to price American put option using proposed methodology.