Mathematical Finance & Financial Data Science Seminar

Looking Forward to Backward-Looking Rates: A Modeling Framework for Term Rates Replacing LIBOR

Speaker: Fabio Mercurio, Bloomberg & NYU Courant

Location: Warren Weaver Hall 1302

Date: Tuesday, February 4, 2020, 5:30 p.m.


In this talk, we define and model forward risk-free term rates, which appear in the payoff definition of derivatives and cash instruments, based on the new interest-rate benchmarks that will be replacing IBORs globally. We show that the classic interest-rate modeling framework can be naturally extended to describe the evolution of both the forward-looking (IBOR-like) and backward-looking (setting-in-arrears) term rates using the same stochastic process.

We then introduce an extension of the LIBOR Market Model (LMM) to backward-looking rates. This extension, which we call generalized forward market model (FMM), completes the LMM by providing additional information about the rate dynamics between fixing/payment times, and by implying dynamics of forward rates under the classic money-market measure.

Our FMM formulation is based on the concept of extended zero-coupon bonds, which proves to be very convenient when dealing with backward-looking setting-in-arrears rates. Thanks to this, not only the bonds themselves, but also the forwards and swap rates, along with their associated forward measures, can be defined at all times, even those beyond their natural expiries.

Bio – Fabio Mercurio

Fabio is global head of Quantitative Analytics at Bloomberg LP, New York. His team is responsible for the research on and implementation of cross-asset analytics for derivatives pricing, XVA valuations and credit and market risk. Fabio is also adjunct professor at NYU. He has jointly authored the book "Interest rate models: theory and practice" and published extensively in books and international journals, including 19 cutting-edge articles in Risk Magazine.  Fabio is the recipient of the 2020 Risk quant of the year award.