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General approximation schemes for option prices in stochastic volatility models

Larsson, Karl LU (2012) In Quantitative Finance 12(6). p.873-891
Abstract
In this paper we develop a general method for deriving closed-form approximations of European option prices and equivalent implied volatilities in stochastic volatility models. Our method relies on perturbations of the model dynamics and we show how the expansion terms can be calculated using purely probabilistic methods. A flexible way of approximating the equivalent implied volatility from the basic price expansion is also introduced. As an application of our method we derive closed-form approximations for call prices and implied volatilities in the Heston [Rev. Financial Stud., 1993, 6, 327-343] model. The accuracy of these approximations is studied and compared with numerically obtained values.
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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Applied mathematical finance, Stochastic volatility, Option pricing, Stochastic applications
in
Quantitative Finance
volume
12
issue
6
pages
873 - 891
publisher
Taylor & Francis
external identifiers
  • wos:000304472100007
  • scopus:84861974857
ISSN
1469-7696
DOI
10.1080/14697688.2010.488244
language
English
LU publication?
yes
id
bdb59fbf-aa4c-400b-88e3-7d97a27b963e (old id 2911755)
date added to LUP
2012-07-23 13:42:43
date last changed
2017-01-01 04:18:48
@article{bdb59fbf-aa4c-400b-88e3-7d97a27b963e,
  abstract     = {In this paper we develop a general method for deriving closed-form approximations of European option prices and equivalent implied volatilities in stochastic volatility models. Our method relies on perturbations of the model dynamics and we show how the expansion terms can be calculated using purely probabilistic methods. A flexible way of approximating the equivalent implied volatility from the basic price expansion is also introduced. As an application of our method we derive closed-form approximations for call prices and implied volatilities in the Heston [Rev. Financial Stud., 1993, 6, 327-343] model. The accuracy of these approximations is studied and compared with numerically obtained values.},
  author       = {Larsson, Karl},
  issn         = {1469-7696},
  keyword      = {Applied mathematical finance,Stochastic volatility,Option pricing,Stochastic applications},
  language     = {eng},
  number       = {6},
  pages        = {873--891},
  publisher    = {Taylor & Francis},
  series       = {Quantitative Finance},
  title        = {General approximation schemes for option prices in stochastic volatility models},
  url          = {http://dx.doi.org/10.1080/14697688.2010.488244},
  volume       = {12},
  year         = {2012},
}