The Baruch Quantitative Finance Seminar provides a forum for Baruch faculty and students to present their research. Seminars are open to everyone who is interested. We meet on select Wednesday afternoons, typically from 2pm to 3pm in Baruch Vertical Campus Room 6-215.
Jim Gatheral, Presidential Professor, Department of Mathematics
September 24, 2014
Jim Gatheral, Baruch College
Title: Fractional Volatility Models
October 1, 2014
Feng Chen, Baruch College
Title: The Space-time Parallel Approach with Spectral Method and Parareal Method
Abstract:In large-scale scientific computing, the computational costs are high in both spatial and temporal dimensions. There is an increasing demand of new mathematical algorithms scalable on modern supercomputing architectures. In this presentation, I will introduce a high-order, space-time parallel framework for computationally complex disciplines. I first discuss recent efforts to develop spectral methods on graphics processing units (GPU). Then I will present the parallel-in-time approach to break the sequential bottleneck of the time direction.
October 8, 2014
Tai-Ho Wang, Baruch College
Title: Most likely path approximations
Abstract:We derive an exact Brownian bridge representation for the transition density in a local volatility model, which then leads to an exact expression for the transition density in terms of a path integral. In the time homogeneous case, we recover the heat kernel expansion by Taylor-expanding around the most-likely-path. Repeating the same procedure in the time inhomogeneous case leads to a new and natural approximation to the transition density which differs from the conventional heat kernel expansion. We show that by suitably approximating the path integral representation, we recover the results obtained in our previous work. Applying the same methodology to higher dimension models we obtain a Bessel bridge representation for the heat kernel in the hyperbolic space. In particular, the closed form expression in the case of 3 dimensional hyperbolic space is recovered. Extensions to fractional models will be briefly discussed.
October 22, 2014
Anja Richter, Baruch College
Title: Discrete Time Term Structure Theory and Consistent Recalibration Models
Abstract:We present theory and applications of forward characteristic processes in discrete time following a seminal paper of Jan Kallsen and Paul Krühner. More precisely we describe a rich, still tractable class of discrete time stochastic processes, whose marginal distributions are given at initial time and which are free of arbitrage. This means we can construct models with a pre-described (implied) volatility surface and quite general volatility surface dynamics. We finally describe the simulation and calibration of consistent recalibration models.