An Alternative Approach to Evaluate American Options Price Using HJM Approach

TL;DR

This paper introduces an innovative method leveraging the HJM approach to price American options, incorporating dynamic volatility modeling to improve valuation accuracy over traditional methods.

Contribution

It extends the HJM framework from bond to equity markets, proposing a new valuation function, stopping criteria, and demonstrating its application to American put options.

Findings

Effective in capturing dynamic volatility effects

Provides an alternative valuation framework for American options

Demonstrates practical implementation with an example

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.