Exact and approximate solutions for options with time-dependent stochastic volatility

In this paper it is shown how symmetry methods can be used to find exact solutions for European option pricing under a time-dependent 3/2-stochastic volatility model dv=kv(A(t)-v)dt+bv32dZ. This model with A(t) constant has been proven by many authors to outperform the Heston model in its ability to...

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Bibliographic Details
Published in:Applied mathematical modelling 2014-06, Vol.38 (11-12), p.2771-2780
Main Author: Goard, Joanna
Format: Article
Language:English
Subjects:
Option pricing
Stochastic volatility
Volatility model
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Summary:In this paper it is shown how symmetry methods can be used to find exact solutions for European option pricing under a time-dependent 3/2-stochastic volatility model dv=kv(A(t)-v)dt+bv32dZ. This model with A(t) constant has been proven by many authors to outperform the Heston model in its ability to capture the behaviour of volatility and fit option prices. Further, singular perturbation techniques are used to derive a simple analytic approximation suitable for pricing options with short tenor, a common feature of most options traded in the market.
ISSN:0307-904X
DOI:10.1016/j.apm.2013.11.006