Efficient Calibration and Greeks Estimation for a Panel of American Options Using a Stochastic Dynamic Program

Abstract

American-style options are financial derivatives that offer the flexibility of early exercise opportunities. This feature poses the difficulty of solving a dynamic optimization problem to determine the optimal exercise strategy. One significant advantage of the Stochastic Dynamic Program (SDP) is that its solution yields numerical approximations of option prices and sensitivities across the entire state-space partition. Through leveraging the homogeneity property, we efficiently value options with varying moneyness and maturity levels and conduct a calibration to market data. The methodology is versatile and applicable to various market dynamics, showcasing the substantial benefits of our SDP-based valuation method. This research proposes an efficient method for pricing a panel of American-style options integrating SDP to overcome computational challenges associated with the estimation of Greeks and efficient calibration to market data. A key contribution of this study is the analysis of the convergence of Greek estimates within the SDP framework, ensuring stability and accuracy. Additionally, we introduce a novel calibration method based on the Feynman-Kac Theorem, where the objective is to find a set of Greeks that satisfy the partial differential equation. This calibration method provides an alternative approach to standard calibration techniques.