Exact simulation of final, minimal and maximal values of Brownian motion and jump-diffusions with applications to option pricing

被引：6

作者：

Becker M. ^{[1
]}

机构：

[1] Saarland University, Campus C3 1

来源：

Computational Management Science | 2010年 / 7卷 / 1期

关键词：

Brownian motion; Double barrier options; Importance sampling; Jump-diffusions; Monte Carlo simulation;

D O I：

10.1007/s10287-007-0065-9

中图分类号：

学科分类号：

摘要：

We introduce a method for generating (W x,T (μ,σ),m x, T (μ,σ),M x,T (μ,σ)), where W x,T (μ,σ) denotes the final value of a Brownian motion starting in x with drift μ and volatility σ at some final time T, m x T (μ,σ) = inf 0 t T W x t (μ, σ) and M x T (μ,σ) = sup 0 t T W x,t (μ,σ). By using the trivariate distribution of (W x,T (μ, σ),m x,T (μ, σ),M x,T (μ,σ)), we obtain a fast method which is unaffected by the well-known random walk approximation errors. The method is extended to jump-diffusion models. As sample applications we include Monte Carlo pricing methods for European double barrier knock-out calls with continuous reset conditions under both models. The proposed methods feature simple importance sampling techniques for variance reduction. © 2007 Springer-Verlag.

引用

页码：1 / 17

页数：16

共 19 条

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