Application of simplest random walk algorithms for pricing barrier options

TL;DR

This paper evaluates a simple first-order random walk algorithm for barrier option pricing, demonstrating its effectiveness and versatility across different contract structures without needing trigger probability estimates.

Contribution

It introduces and tests a universal, easy-to-implement algorithm based on the weak Euler approximation for barrier option pricing, avoiding complex trigger probability calculations.

Findings

Effective for various barrier options including multi-asset derivatives

Does not require trigger probability estimation

Applicable to different barrier types and contract structures

Abstract

We demonstrate effectiveness of the first-order algorithm from [Milstein, Tretyakov. Theory Prob. Appl. 47 (2002), 53-68] in application to barrier option pricing. The algorithm uses the weak Euler approximation far from barriers and a special construction motivated by linear interpolation of the price near barriers. It is easy to implement and is universal: it can be applied to various structures of the contracts including derivatives on multi-asset correlated underlyings and can deal with various type of barriers. In contrast to the Brownian bridge techniques currently commonly used for pricing barrier options, the algorithm tested here does not require knowledge of trigger probabilities nor their estimates. We illustrate this algorithm via pricing a barrier caplet, barrier trigger swap and barrier swaption.