Weak and strong Taylor methods for numerical solutions of stochastic differential equations

被引：10

作者：

Siopacha, Maria ^{[1
]}

Teichmann, Josef ^{[2
]}

机构：

[1] Raiffeisen Zentralbank Osterreich AG, Market Risk, A-1030 Vienna, Austria

[2] ETH, Dept Math, CH-8092 Zurich, Switzerland

来源：

QUANTITATIVE FINANCE | 2011年 / 11卷 / 04期

基金：

奥地利科学基金会;

关键词：

Stochastic volatility; LIBOR market models; Mathematical finance; Option pricing via simulation; Interest rate modelling; Interest rate derivatives; Malliavin calculus;

D O I：

10.1080/14697680903493573

中图分类号：

F8 [财政、金融];

学科分类号：

0202 ;

摘要：

We apply the results of Malliavin-Thalmaier-Watanabe for strong and weak Taylor expansions of solutions of perturbed stochastic differential equations (SDEs). In particular, we determine weight expressions for the Taylor coefficients of the expansion. The results are applied to LIBOR market models in order to find precise and quick algorithms. In contrast to methods such as Euler-Maruyama-Monte-Carlo for the full SDE, we obtain more tractable expressions for accurate pricing. In particular, we present a readily tractable alternative to 'freezing the drift' in LIBOR market models that has an accuracy similar to the Euler-Maruyama-Monte-Carlo scheme for the full LIBOR market model. Numerical examples underline our results.

引用

页码：517 / 528

页数：12

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