ABSTRACT

This paper presents a simple yet powerful simulation-based approach for approximating the values of prices and Greeks (ie, derivatives with respect to the underlying spot prices, such as delta, gamma, etc) for American-style options. This approach is primarily based upon the least squares Monte Carlo (LSM) algorithm and is thus termed the modified LSM (MLSM) algorithm. The key to this approach is that with initial asset prices randomly generated from a carefully chosen distribution, we obtain a regression equation for the initial value function, which can be differentiated analytically to generate estimates for the Greeks. Our approach is intuitive, easy to apply, computationally efficient and, most importantly, provides a unified framework for estimating risk sensitivities of the option price to underlying spot prices. We demonstrate the effectiveness of this technique with a series of increasingly complex but realistic examples.