Bounding Bermudan Swaptions in a Swap-rate Market Model

Generic market models

Currently, there are two market models for valuation and risk management of interest rate derivatives, the LIBOR and swap market models. In this paper, we introduce arbitrage-free constant maturity swap (CMS) market models and generic market models featuring forward rates that span periods other than the classical LIBOR and swap periods. We develop generic expressions for the drift terms occurr...

Implications for Hedging of the choice of driving process for one-factor Markov-functional models

In this paper, we study the implications for hedging Bermudan swaptions of the choice of the instantaneous volatility for the driving Markov process of the one-dimensional swap Markov-functional model. We find that there is a strong evidence in favour of what we term “parametrization by time” as opposed to “parametrization by expiry”. We further propose a new parametrization by time for the dri...

Pricing Bermudan Swaptions in the LIBOR Market Model

Choice of Interest Rate Term Structure Models for Assets and Liability Management

This paper compares the pricing and hedging performance of the LMM model against two spot-rate models, namely Hull-White and Black-Karasinski, and the more recent Swap Market Model from an Asset-Liability-Management (ALM) perspective. In contrast to previous studies in the literature, our emphasis here is on ALM and we use hedging performance on Bermudan swaptions to proxy risk management outco...

Libor Market Model with Stochastic Volatility

In this paper we extend the standard LIBOR market model to accommodate the pronounced phenomenon of implied volatility smiles/skews. We adopt a multiplicative stochastic factor to the volatility functions of all relevant forward rates. The stochastic factor follows a square-root diffusion process, and it can be correlated to the forward rates. For any swap rate, we derive an approximate process...