Matthias Heymann

Biography – Finance

Math Ph.D.   •   Risk/Data Analyst   •   Financial Modeler   •   12 years experience (Goldman, Millennium)   •   Book Author

During his academic career (Ph.D. in mathematics from New York University, Assistant Research Professor at Duke University), Matthias Heymann specialized in probability theory, publishing works on both pure and applied topics.

He then started as an Associate in the Corporate Treasury group at Goldman Sachs, where he helped develop their new ALM (Asset and Liability Management) platform. Following his promotion to Vice President, he moved to the Model Risk Management team, where he validated a variety of risk models (including VaR and default risk) in the context of CCAR and DFAST.

During this time he also started his work on the Adaptive Curve Evolution Model for Interest and FX Rates, which he eventually published as a book.

He then joined the newly formed Risk Informatics group at Millennium, whose mandate was to provide analytical support for other groups’ projects, such as the firm’s transition to a new interest rate infrastructure, or the documentation of the equity factor model.

The Adaptive Curve Evolution Model for Interest & FX Rates

The Adaptive Curve Evolution Model
for Interest & FX Rates

Summary   •   Uses & Properties   •   Model Comparison   •   History   •   Model Equations

Summary

What is the ACE Model? The ACE Model is a powerful new model for interest rates (and in its optional multi-currency extension, also for currency exchange rates) developed by Gregory Pelts and Matthias Heymann. It is defined in the form of an unusually flexible short rate model, with a groundbreaking set of properties.

What does its name mean? In general, interest rate models provide probabilistic equations for the future evolution of the interest rate (i.e., yield) curve, so they are curve evolution models. This specific model has special properties that allow it to be more easily adapted (i.e., calibrated) to the large variety of interest rate derivative prices found on the market.

What is in the book? See its back cover text on the Books page, or in the excerpt (click on the Excerpt button below), which also contains the full table of contents.

Where can I get the book? Hard- and softcover prints are available on Amazon — click on the Order button below.

Uses & Properties

Uses:

  • Computing prices of illiquid interest rate (and in its extension, currency exchange rate) derivatives, in line with those observed for liquid instruments
  • More powerful replacement for other interest rate models (Hull–White, CIR, HJM, LMM, etc.) for any use

Core Advantage: Combines the speed of short rate models with the flexibility of LMM

Properties:

  • The first ever interest rate model to combine all of the most desirable analytical properties:
    • Low-dimensionality
    • Completeness
    • No arbitrage
    • Parametric flexibility
    • Time-homogeneity (if desired)
    • Lower bound on rates
    • Unspanned volatility (significantly facilitates calibration)
  • Full multi-currency support, including FX spot & forward rates, without increasing the state space dimension
  • For a detailed comparison to other models, see the book’s Introduction, which is included in the excerpt linked above.

Model Comparison

History

The original form of the ACE interest rate model was developed by Gregory Pelts in 2011–2012 within Goldman Sachs’ Derivative Analysis group, with both the model’s derivation and its final equations being based on tools and notation from theoretical physics.

In 2014–18, Matthias Heymann made the model more accessible with the first edition of his book, which lays out Pelts’ original derivation in detail, teaches all the necessary methods along the way, and eventually translates the model into a new, much simpler -based format. It also includes a short independent -based proof (but not derivation) of these equations.

In 2020, he released a second edition that extends the model to cover the interest rates of multiple currencies, along with their exchange rates.

Finally, in 2024, he published a third edition that also includes a new -based derivation of his equations.

Model Equations (Single Currency Model)

Model Equations
(Single Currency Model)

Model Equations (Multi-Currency Model)

Model Equations
(Multi-Currency Model)

Skill Set

Value Proposition   •   Technical & Analytical Skills   •   Software  •   Languages

Value Proposition: Technically adept mathematician whose combination of analytical insight, creativity, attention to detail, and a diverse skill set will be a unique and valuable asset for any team of financial modelers or developers. Twelve years of experience in the finance industry; experienced programmer; great academic track record (two book publications); excellent scientific problem solving and writing skills; dedicated mentor with great talent in explaining complicated concepts to non-mathematicians.

Technical Skills: Python, Rust, SQL, Slang, MatLab, R, Swift, Objective C, AWS, LaTeX, HTML, WordPress

Analytical Skills: Mathematical Finance, Probability Theory, Statistics, Machine Learning & AI, Numerical Analysis, Functional Analysis, ODE, PDE, SDE, Theoretical Physics

Software: MS Office, Affinity Suite (graphics work, publishing), DaVinci Resolve (video editing), Cubase (audio editing)

Languages: German (native), English (fluent), Italian (basic)