# Mathematical Finance & Financial Data Science Seminar

#### The Adaptive Curve Evolution Model for Interest Rates

**Speaker:**
Matthias Heymann, Goldman Sachs, Model Risk Management

**Location:**
Warren Weaver Hall 1302

**Date:**
Tuesday, April 2, 2019, 5:30 p.m.

**Synopsis:**

In this talk, the speaker presents the key results from his recent book of the same title. The ACE model—in its original form developed by Gregory Pelts and now carefully rephrased, refined, and made more accessible by Matthias Heymann—is the first to combine all of the most desirable analytical properties in one interest rate model: It is low-dimensional (with any dimension n ∈ ℕ\{2}), complete (i.e., it models all tenors), arbitrage-free, highly flexible (it provides 2n+1 discrete parameters, plus the functional noise parameter σ(x,t)), and time homogeneous if desired, and it imposes a lower bound on rates; moreover, it has the rare feat of being unspanned (i.e., its bond price function does not depend on σ), which simplifies calibration.

While its original derivation relied on an arsenal of compelling tools borrowed from theoretical physics (in particular, Einstein's Special Theory of Relativity), the model's form presented in this talk will only require basic mathematical skills.

**Bio – Matthias Heymann**

Matthias Heymann has a Ph.D. in mathematics (2002–07, Courant Institute of Mathematical Sciences, NYU) and did a postdoc in the Duke University Mathematics Department (2007–10). Specializing in probability theory, during his academic career he made contributions related to Wentzell–Freidlin theory, i.e., the study of maximum likelihood transition curves in stochastic dynamical systems with small noise. One of his most notable publications is his monograph "Minimum Action Curves in Degenerate Finsler Metrics — Existence and Properties," published in Springer's "Lecture Notes in Mathematics" series.

Since 2010 he has been working as a quantitative analyst at Goldman Sachs. During this time he started his work on the ACE model, which eventually turned into his second book, whose results are presented in this talk.