Matheus Grasselli: Calibration of Chaotic Models for Interest Rates

The Wiener chaos approach to interest rates was introduced a few years ago by Hughston and Rafailidis as an axiomatic framework to model positive interest rates, continuing a line of research started by the seminal Flesaker and Hughston model and including the elegant potential approach of Rogers and others. Apart from ensuring positivity, one appealing feature of the chaotic approach is its hierarchical way to introduce randomness into a model through different orders of chaos expansions. We propose a systematic way to calibrate Wiener chaos models to market data, and compare the performance of chaos expansions of different orders with popular interest rate models in the presence of interest rate derivatives of increased complexity.

This is joint work with Tsunehiro Tsujimoto.