Pricing multicallable range accruals with the Libor Market Model

Abstract

PurposeThe paper aims to propose a consistent and robust pricing/hedging methodology for callable fixed income structures with embedded caplet‐linked options.Design/methodology/approachA range of recently published (1997‐2003) works about the Libor Market Model (LMM) tackle the problems of modelling the forward curve with more than two factors and calibrating it to caps either/or to swaps. Other articles involve the pricing of Bermudan options using Monte Carlo simulation. In the form of case study, the very popular structure of multicallable range accrual bonds is used. A complete calibration methodology is described in detail, which links the structure's price to the market caps and swaptions prices as well as to the historical correlations between forward rates. We present the direct implementation of the Monte Carlo technique for this particular problem. Furthermore, we explore the application of the Longstaff–Schwartz least squares algorithm and its variations for the estimation of the expected value of continuation.FindingsThis paper suceeds in producing a consistent and robust pricing/hedging methodology for callable fixed income structures with embedded caplet‐linked options.Practical implicationsThe increased complexity of similar fixed income structures makes traditional approaches like Black–Derman–Toy or Hull‐White trees inadequate for the task of consistent pricing and hedging. Therefore, care must be taken to ensure consisted hedging across the different volatility markets.Originality/valueThis article explores variations and settings of the popular LMM and the Longstaff‐Scwartz algorithm that can be relatively consistent with both the cap and swaption volatility market. The framework is built using as a benchmark the most liquid fixed income structure so that it can be tested for robustness.