Skew Brownian motion discretization: A lattice approach for financial and actuarial applications

The biases introduced in option pricing by the Black-Scholes model have led to the exploration of alternative models that more accurately capture the dynamics of the underlying stock price. Among others, a skew Brownian motion characterized by a skew-normal distribution is one of the candidates useful to the scope. It is defined by combining a standard Brownian motion and an independent reflecting Brownian motion. In this study we propose a lattice-based discretization of a skew Brownian motion that allows the valuation of American-style contingent claims, other than European options for which explicit-form formulae are already available. At the best of the authors' knowledge, this contribution represents one of the first attempts to provide a model that is able to price American-type derivatives under a skew Brownian motion, and it is useful not only in financial but also in actuarial applications where such claims are embedded in several structured insurance policies, e.g., equity-linked policies with surrender options.