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# Applied Math Seminar: Dan Pirjol (Stevens Institute of Technology)

## October 9 @ 4:15 pm - 5:15 pm

Title: The Hartman-Watson distribution: numerical evaluation and applications in mathematical finance

Abstract: The Hartman-Watson distribution appears in several problems of applied probability and financial mathematics. Most notably, it determines the joint distribution of the time-integral of a geometric Brownian motion and its terminal value. A classical result by Yor (1981) expresses it as a one-dimensional integral which is however difficult to evaluate numerically in the region of interest for financial applications. The talk gives an introduction to the HW distribution and presents an asymptotic expansion which can be used for an efficient numerical evaluation. Two applications from mathematical finance are discussed: Asian options pricing in the Black-Scholes model, and option pricing in the log-normal SABR model.