Application of simplest random walk algorithms for pricing barrier options
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.
Keywords
Cite
@article{arxiv.1211.5726,
title = {Application of simplest random walk algorithms for pricing barrier options},
author = {M. Krivko and M. V. Tretyakov},
journal= {arXiv preprint arXiv:1211.5726},
year = {2012}
}
Comments
It's a pre-publication which final version will appear as a chapter in Recent Developments in Computational Finance (Eds. T. Gerstner and P.E. Kloeden), 2013. [it has one picture and 22 pages]