Proceedings of the ISCIE International Symposium on Stochastic Systems Theory and its Applications
Online ISSN : 2188-4749
Print ISSN : 2188-4730
第40回ISCIE「確率システム理論と応用」国際シンポジウム(2008年11月, 京都)
Simulation on multidimensional density functions through the Malliavin-Thalmaier formula and its application to finance
Arturo Kohatsu-HigaKazuhiro Yasuda
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2009 年 2009 巻 p. 342-347

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The Malliavin-Thalmaier formula was introduced in [4] for use in Monte-Carlo simulation. But when this formula is applied directly for computer simulation, we show that it is unstable. We propose an approximation of the Malliavin-Thalmaier formula. First we prove the central limit theorem to obtain the values of the parameters in Monte-Carlo simulations which achieves a prescribed error level. To prove it, we need the order of the bias and variance of the approximation error. Next we give an idea of the optimal approximation parameter and constants, which is often used in the kernel density estimation method. Finally we apply the Malliavin-Thalmaier formula and the approximated version to some models in finance and compare their results.
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© 2009 ISCIE Symposium on Stochastic Systems Theory and Its Applications
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