Tuesday, January 24th
5:45 PM Registration 6:00 PM Seminar Begins 7:30 PM Reception
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.
About the Series
The IAQF's Thalesians Seminar Series is a joint effort on the part of the IAQF (www.iaqf.org) and the Thalesians (www.thalesians.com). The goal of the series is to provide a forum for the exchange of new ideas and results related to the field of quantitative finance. This goal is accomplished by hosting seminars where leading practitioners and academics present new work, and following the seminars with a reception to facilitate further interaction and discussion.
