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 occurring in the stochastic differential equation driving the forward rates under a single pricing measure. The generic market model is particularly apt for pricing of Bermudan CMS swaptions, fixed-maturity Bermudan swaptions, and callable hybrid coupon swaps.market model, generic market models, generic drift terms, hybrid products, BGM model

Fast drift approximated pricing in the BGM model

This paper shows that the forward rates process discretized by a single time step together with a separability assumption on the volatility function allows for representation by a low-dimensional Markov process. This in turn leads to e±cient pricing by for example finite differences. We then develop a discretization based on the Brownian bridge especially designed to have high accuracy for single time stepping. The scheme is proven to converge weakly with order 1. We compare the single time step method for pricing on a grid with multi step Monte Carlo simulation for a Bermudan swaption, reporting a computational speed increase of a factor 10, yet pricing sufficiently accurate.BGM model, predictor-corrector, Brownian bridge, Markov processes, separability, Feynman-Kac, Bermudan swaption

Fast drift approximated pricing in the BGM model

This paper presents a method for fast drift approximated pricing in the BGM model (Brace, G¸atarek and Musiela, 1997). It is a significant addition to the predictor-corrector drift approximation method introduced by Hunter, Jäckel and Joshi (HJJ, 2001). HJJ use the drift approximation only to speed up their Monte Carlo by reducing it to single time-step simulation. We show that much more efficient numerical methods (e.g. finite differences) may be used at the cost of a minor additional assumption, separability. We also present a new drift approximation and propose a method to measure the accuracy of a drift approximation. This measure shows that our drift approximation is more accurate than the one of HJJ. We compare fast drift approximated pricing with Monte Carlo simulation for a Bermudan swaption, reporting a computational speed increase of a factor 10