Effective parameters for stochastic volatility models

Zaizhi Wang ()
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Zaizhi Wang: Pricing Partners, Postal: Paris Cybervillage, 204 Rue de Crimée, 75019 PARIS, FRANCE, http://www.pricingpartners.com/

Journal of Financial Transformation, 2009, vol. 26, 108-115

Abstract: This paper tackles the issue of approximated formula for stochastic models with time dependent model parameters, using an averaging principle. The objective is to find a similar model but with constant parameters that is the closest to our initial process, along the same lines as the proof by Gyöngy (1986) for general stochastic processes. We extend previous results found by Piterbarg (2005) for the particular case of the SABR model [Hagan et al. (2002)]. The resulting formula can be evaluated very quickly, solving the implied Riccati equations. We compare the approximation with exact solution of the corresponding partial differential equation using an ADI method. Numerical results show that the approximation works well for short term maturities.

Keywords: Stochastic models; time dependent model parameters; ADI method (search for similar items in EconPapers)
JEL-codes: G12 G21 G31 (search for similar items in EconPapers)
Date: 2009
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Persistent link: https://EconPapers.repec.org/RePEc:ris:jofitr:1398

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