# Mathematical Finance & Financial Data Science Seminar

#### Determining Prices and Trading Strategies in FBSDE Models in Quantitative Finance with Deep Learning

**Speaker:**
Bernhard Hientzsch, Corporate Model Risk, Wells Fargo

**Location:**
Online 1302

**Date:**
Tuesday, April 27, 2021, 5:30 p.m.

**Synopsis:**

This talk will explore the application of deep learning in solving many pricing and risk modeling problems for common instruments which can be posed as Forward Backward Stochastic Differential Equations. The framework, referred to as DeepBSDE, employs deep neural networks to learn the appropriate controls required to achieve the target final value (payoff), in a forward version minimizing hedge P&L and in a backward version minimizing variance from conditional expectation of actually needed initial wealth. The framework can efficiently handle high-dimensional settings and nonlinear pricing problems in straightforward generic fashion where other approaches become intractable or overly complex. It naturally observes and minimizes appropriate characteristics of the corresponding trading strategy. This talk will present a quick overview of FBSDE models, the DeepBSDE approaches including their computational graphs, detailed visualizations of both versions for a risk-neutral linear example, application to a nonlinear example featuring differential rates, advantages against traditional approaches, and an extension of the forward version to the barrier option case. We will see that the methods provide comparable or better results than PDE methods for the nonlinear pricing example and better behaved P&L for the barrier option case.

**Speaker Bio**

Dr. Bernhard Hientzsch is a quantitative manager working in model risk R&D at Wells Fargo. He leads a group that concentrates on capital markets pricing and risk modeling and has managed, led and worked on a wide range of projects within that area. Previously, he was a postdoctorate researcher at New York University and self-employed. He received his Ph.D. in applied mathematics from the Courant Institute of Mathematical Sciences at NYU.

**Notes:**