Publication
Title
Edgeworth expansion of stochastic trading time
Author
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 DuruKleinert 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.
Language
English
Source (journal)
Physica: A: theoretical and statistical physics. - Amsterdam
Publication
Amsterdam : 2010
ISSN
0378-4371
Volume/pages
389:16(2010), p. 3179-3192
ISI
000279834400018
Full text (Publishers DOI)
Full text (publishers version - intranet only)
UAntwerpen
Faculty/Department
Research group
Publication type
Subject
Affiliation
Publications with a UAntwerp address
External links
Web of Science
Record
Identification
Creation 23.03.2011
Last edited 06.05.2017
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