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

Journal Article


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Abstract


  • 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 View the MathML source. 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.

Publication Date


  • 2014

Citation


  • Goard, J. (2014). Exact and approximate solutions for options with time-dependent stochastic volatility. Applied Mathematical Modelling: simulation and computation for engineering and environmental systems, 38 (11-12), 2771-2780.

Scopus Eid


  • 2-s2.0-84900001621

Ro Full-text Url


  • http://ro.uow.edu.au/cgi/viewcontent.cgi?article=3292&context=eispapers

Ro Metadata Url


  • http://ro.uow.edu.au/eispapers/2283

Number Of Pages


  • 9

Start Page


  • 2771

End Page


  • 2780

Volume


  • 38

Issue


  • 11-12

Place Of Publication


  • 10.1016/j.apm.2013.11.006

Abstract


  • 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 View the MathML source. 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.

Publication Date


  • 2014

Citation


  • Goard, J. (2014). Exact and approximate solutions for options with time-dependent stochastic volatility. Applied Mathematical Modelling: simulation and computation for engineering and environmental systems, 38 (11-12), 2771-2780.

Scopus Eid


  • 2-s2.0-84900001621

Ro Full-text Url


  • http://ro.uow.edu.au/cgi/viewcontent.cgi?article=3292&context=eispapers

Ro Metadata Url


  • http://ro.uow.edu.au/eispapers/2283

Number Of Pages


  • 9

Start Page


  • 2771

End Page


  • 2780

Volume


  • 38

Issue


  • 11-12

Place Of Publication


  • 10.1016/j.apm.2013.11.006