The Malliavin calculus, a functional analytic approach
نویسندگان
چکیده
منابع مشابه
Weak approximations. A Malliavin calculus approach
We introduce a variation of the proof for weak approximations that is suitable for studying the densities of stochastic processes which are evaluations of the flow generated by a stochastic differential equation on a random variable that may be anticipating. Our main assumption is that the process and the initial random variable have to be smooth in the Malliavin sense. Furthermore, if the inve...
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We derive and analyze Monte Carlo estimators of price sensitivities (“Greeks”) for contingent claims priced in a diffusion model. There have traditionally been two categories of methods for estimating sensitivities: methods that differentiate paths and methods that differentiate densities. A more recent line of work derives estimators through Malliavin calculus. The purpose of this article is t...
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Within the last ten years there have been many published and unpublished contributions on how to apply Malliavin calculus in the context of mathematical finance. The purpose of this paper is on one side to give the mathematical background for the application of Malliavin calculus in the framework of the Heston stochastic volatility model, and on the other side to provide an applicable formula f...
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Acknowledgements I enjoyed the help and support from numerous friends and faculty members during whilst writing this thesis. My greatest debt however, goes to my supervisor, Professor Tony Dooley, who initiated me to the fantastic field of Malliavin calculus. With his incredible breadth and depth of knowledge and intuition, he guided me to structure and clarify my thought and suggested valuable...
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This article is an introduction to Malliavin Calculus for practitioners. We treat one specific application to the calculation of greeks in Finance. We consider also the kernel density method to compute greeks and an extension of the Vega index called the local vega index.
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ژورنال
عنوان ژورنال: Journal of Functional Analysis
سال: 1981
ISSN: 0022-1236
DOI: 10.1016/0022-1236(81)90011-2