Edgeworth expansions of stochastic trading time

Marc Decamps and Ann De Schepper

Physica A: Statistical Mechanics and its Applications, 2010, vol. 389, issue 16, 3179-3192

Abstract: Under most local and stochastic volatility models the underlying forward is assumed to be a positive function of a time-changed Brownian motion. It relates nicely the implied volatility smile to the so-called activity rate in the market. Following Young and DeWitt-Morette (1986) [8], we propose to apply the Duru–Kleinert process-cum-time transformation in path integral to formulate the transition density of the forward. The method leads to asymptotic expansions of the transition density around a Gaussian kernel corresponding to the average activity in the market conditional on the forward value. The approximation is numerically illustrated for pricing vanilla options under the CEV model and the popular normal SABR model. The asymptotics can also be used for Monte Carlo simulations or backward integration schemes.

Keywords: Stochastic volatility; Fourier transform; Duru–Kleinert transformation; Edgeworth expansions (search for similar items in EconPapers)
Date: 2010
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:389:y:2010:i:16:p:3179-3192

DOI: 10.1016/j.physa.2010.04.014

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