(NY) - Tai-Ho Wang - Probability density of lognormal fractional SABR model

Probability density of lognormal fractional SABR model

Tai-Ho Wang

Seminar Program

5:45pm Registration
6:00pm Seminar
7:30pm Reception

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 Edgeworth style of expansion of the probability density for the fractional SABR model. 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.

Biography

Tai-Ho Wang holds a professorship in mathematics at Baruch College, City University of New York since 2012. His research in quantitative finance includes implied volatility asymptotics in small time, static arbitrage free bounds on basket options, optimal liquidation and execution in market impact models, and recently information dynamics in financial market.

Disclaimer

This a joint IAQF/Thalesians seminar, and not an instructional program of New York University.