Speaker :
 Prof. TaiHo Wang (Baruch College, The City University of New York) 
Title :

Probability density of lognormal fractional SABR model 
Time :
 20170629 (Thu) 15:00  
Place : 
Seminar Room 722, Institute of Mathematics (NTU Campus) 
Abstract: 
Instantaneous volatility of logarithmic return in lognormal fractional SABR model is driven by the exponentiation of a correlated fractional Brownian motion. Due to the mixed nature of driving Brownian and fractional Brownian motions, probability density for such models are less known in the literature. We present in this talk a bridge representation for the joint density of the lognormal fractional SABR model in a Fourier space. Evaluating the bridge representation along a properly chosen deterministic path yields an expansion of the probability density for the fractional SABR model in Fourier space. A direct generalization of the representation to joint density at multiple times leads to a heuristic derivation of the large deviations principle for the joint density in small time. Approximation of implied volatility is readily obtained by applying the Laplace asymptotic formula to the call or put prices and comparing coefficients. The presentation is based on a joint work with Jiro Akahori and Xiaoming Song. 