The ACE model — in its original form developed by Gregory Pelts and now carefully rephrased, refined, extended, and made more accessible by Matthias Heymann in the present book — is the first to combine all of the most desirable analytical properties in one interest rate model.

It is low-dimensional (with the dimension n ∈  \ {2} of its state space coinciding with the one of the driving Brownian motion), complete (i.e., it models all tenors), arbitrage-free, highly flexible (it provides 2n+1 discrete parameters in addition to 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 can increase calibration leverage, and which allows the yield curve calibration to be separated from the calibration to caps, swaptions, and other interest rate derivatives.

In addition, we present an extension of the ACE model that covers the interest rates and bond prices of multiple currencies, along with each currency pair’s spot and forward exchange rates.

The book begins with an introduction that compiles a list of all of our desired model features, and that provides a detailed comparison with existing models. Part I of this book (“A Fast Track To ACE”), which is tailored to the reader who merely wishes to understand the ACE model well enough to use it in practice, then lays out all of the results in an easily understandable -based formulation, along with some straightforward proofs that require only standard knowledge in analysis, stochastic processes, and mathematical finance. Finally, Part II contains both a new quick derivation of the model equations, and separately the original derivation utilizing a variety of compelling non-standard mathematical techniques — carefully introduced along the way — that may well hold the key also to other financial modeling problems.

See the Finance page for further details.