Note on an extension of an asymptotic expansion scheme
type: Item
instance of: scholarly article
zbMATH Open document ID: 1303.91192
DOI: 10.1142/S0219024913500313
author: Akihiko Takahashi
author: Masashi Toda
published in: International Journal of Theoretical and Applied Finance
publication date: 2013-10-21T00:00:00Z
Mathematics Subject Classification ID: 91G60
Mathematics Subject Classification ID: 91G20
Mathematics Subject Classification ID: 65C30
Mathematics Subject Classification ID: 60H07
Mathematics Subject Classification ID: 60H10
zbMATH DE Number: 6217605
zbMATH Keywords: asymptotic expansion
zbMATH Keywords: option pricing
zbMATH Keywords: stochastic volatility model
zbMATH Keywords: CEV model
zbMATH Keywords: SABR model
zbMATH Keywords: Malliavin calculus
MaRDI profile type: Publication
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title: Note on an extension of an asymptotic expansion scheme
review text: This paper presents an extension of a general computational scheme for asymptotic expansions proposed in earlier works by the authors and coworkers. In the earlier works, a new method was developed for the computation of an arbitrary-order expansion with a normal benchmark distribution in a multidimensional diffusion setting. In particular, a new algorithm was proposed for calculating coefficients in an expansion by solving a system of ordinary differential equations. In the present note, by a change of variable technique, and by various ways of setting the perturbation parameters in the expansion, the authors provide the flexibility of setting the benchmark distribution around which the expansion is made and an automatic way for computation up to any order in the expansion. For instance, they introduce new expansions, called the log-normal expansion and the CEV expansion. They also show some concrete examples with numerical experiments, which imply that a high-order CEV expansion will produce a more precise and stable approximation for option pricing under the SABR model than other approximation methods such as the log-normal expansion and the well-known normal expansion.
reviewed by: Elisa Alòs
description: scientific article; zbMATH DE number 6217605