Integration by parts formula for locally smooth laws and applications to sensitivity computations

• 成果类型: Article
• 署名作者: Bally, Vlad; Bavouzet, Marie-Pierre; Messaoud, Marouen
• 署名单位: Universite Gustave-Eiffel; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Paris-Est-Creteil-Val-de-Marne (UPEC)
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/105051606000000592
• 发表日期: 2007
• 页码: 33-66
• 关键词: malliavin calculus; greeks; MARKET

摘要

We consider random variables of the form F = f(V-1,..., V-n), where f is a smooth function and Vi, i EN, are random variables with absolutely continuous law p(i) (y) dy. We assume that p(i), i = 1,..., n, are piecewise differentiable and we develop a differential calculus of Malliavin type based on a In pi. This allows us to establish an integration by parts formula E(delta i phi(F)G) = E(phi(F)H-i(F, G)), where H-i(F, G) is a random variable constructed using the differential operators acting on F and G. We use this formula in order to give numerical algorithms for sensitivity computations in a model driven by a Levy process.