The Adaptive Curve Evolution Model for Interest Rates

The ACE model - in its original form developed by Gregory Pelts and now carefully rephrased, refined, 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=1,3,4,5... of its state space coinciding with the one of the driving Brownian motion), complete (i.e., it models all tenors), consistent (i.e., arbitrage-free), highly flexible (it provides 2n+1 discrete parameters in addition to the functional noise parameter sigma(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 sigma), 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.Chapter 1 explains all of our desired model features and provides a detailed comparison with other models. Chapter 2 ("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, lays out all of the results in an easily understandable R n-based formulation, along with some straightforward proofs that require only standard knowledge in analysis, stochastic processes, and mathematical finance. Finally, Chapters 3-6 contain the actual derivation of the model equations, 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