6:00 PM Seminar Begins

7:30 PM Reception

Hybrid Event

Fordham University

McNally Amphitheater

140 West 62nd Street

New York, NY 10023

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Abstract:

We present a semi-analytical approach for pricing American options including assets paying discrete or continuous dividends. Our method leverages the Generalized Integral Transform (GIT), which reframes the pricing problem - traditionally a complex partial differential equation with a free boundary - as a Volterra integral equation of the first kind. For transparency, we assume the underlying asset follows a time-inhomogeneous Geometric Brownian Motion, though the approach has been already extended to various pure diffusion or jump-diffusion models. By solving this integral equation, we can efficiently determine both the option price and the early exercise boundary while naturally accommodating the discontinuities introduced by discrete dividends. This methodology offers a powerful alternative to standard numerical techniques like binomial trees or finite difference methods, which often struggle with the jump conditions from discrete dividends, leading to a loss of accuracy or performance. Several examples demonstrate that the GIT method is both highly accurate and computationally efficient, as it bypasses the need for extensive computational grids or complex backward induction.

Bio:

Dr. Andrey Itkin is an Adjunct Professor in NYU's Department of Risk and Financial Engineering. With a PhD in the physics of liquids, gases, and plasma and a Doctor of Science in computational physics, he has authored several books and numerous publications spanning chemical physics, astrophysics, and computational and mathematical finance. Dr. Itkin has also held various research and managerial roles in the financial industry and is a member of several professional associations in finance and physics. He is also serving as Editor-in-Chief of the Review of Modern Quantitative Finance book series and on the Editorial Boards of the Journal of Derivatives and the International Journal of Computer Mathematics (2014-2024).