Piecewise linear double barrier options

Abstract

A piecewise linear double barrier option generalizes classical double barrier options because of its versatility in designing various double boundaries. This paper discusses how to price piecewise linear double barrier options. To this purpose, we derive the probability that an underlying process does not cross a given piecewise linear double barrier, where the underlying process follows the Brownian motion of piecewise constant drift. Using the established non-crossing probability, we provide the explicit pricing formulas of piecewise linear double barrier options and show how the shape of a double barrier affects the option prices through extensive numerical experiments.

The Boyle–Romberg Trinomial Tree, a Highly Efficient Method for Double Barrier Option Pricing

“…In [13], it is shown that the finite difference method for double barrier option pricing can be strongly enhanced by applying both a repeated Richardson extrapolation technique and a mesh optimization procedure in the Black-Scholes model. In [14,15], numerical methods are presented for pricing, respectively, double piecewise linear barrier options and step barrier options. The methods are based on probabilities that an underlying process does not cross the given barriers.…”