Pricing American Options by Exercise Rate Optimization

TL;DR

This paper introduces a new Monte Carlo-based method for pricing American options by optimizing randomized exercise rates, which simplifies the computation and improves flexibility over traditional methods that determine optimal exercise regions.

Contribution

The novel approach optimizes exercise rates of randomized strategies, providing a differentiable objective function and demonstrating efficiency and flexibility across various models and option types.

Findings

Efficient pricing of American options in multiple models.

Flexible method applicable to various option types.

Improved convergence with fewer discretization steps.

Abstract

We present a novel method for the numerical pricing of American options based on Monte Carlo simulation and the optimization of exercise strategies. Previous solutions to this problem either explicitly or implicitly determine so-called optimal exercise regions, which consist of points in time and space at which a given option is exercised. In contrast, our method determines the exercise rates of randomized exercise strategies. We show that the supremum of the corresponding stochastic optimization problem provides the correct option price. By integrating analytically over the random exercise decision, we obtain an objective function that is differentiable with respect to perturbations of the exercise rate even for finitely many sample paths. The global optimum of this function can be approached gradually when starting from a constant exercise rate. Numerical experiments on vanilla put options in the multivariate Black-Scholes model and a preliminary theoretical analysis underline the efficiency of our method, both with respect to the number of time-discretization steps and the required number of degrees of freedom in the parametrization of the exercise rates. Finally, we demonstrate the flexibility of our method through numerical experiments on max call options in the classical Black-Scholes model, and vanilla put options in both the Heston model and the non-Markovian rough Bergomi model.