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Heat kernel methods in finance: the SABR model.

Пнд, 01/09/2012 - 15:01 — SomNambul
Authors: Carmelo Vaccaro
Subjects: Pricing of Securities
link: http://arxiv.org/abs/1201.1437
Abstract

The SABR model is a stochastic volatility model not admitting a closed form
solution. Hagan, Kumar, Leniewski and Woodward have given an approximate
solution by means of perturbative techniques. A more precise approximation was
obtained by Henry-Labord\`ere using the heat kernel expansion method. The
latter relies on deep and hard theorems from Riemannian geometry which are
almost totally unknown to people working in finance, who however are those
primarily interested in these results.

The goal of this report is to fill this gap and makes these topics
understandable to people with a basic knowledge of calculus and linear algebra.

Bi Shan

Втр, 01/10/2012 - 09:44 — Bi Shan

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