Edgeworth expansion of stochastic trading timeEdgeworth expansion of stochastic trading time
Faculty of Applied Economics
Accountancy and Finance
Physica: A: theoretical and statistical physics. - Amsterdam
389(2010):16, p. 3179-3192
University of Antwerp
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) , 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.