Various drift approximations for the displaced-discussion LIBOR market model in the spot measure are compared. The advantages, disadvantages and implementation choices for each of predictor-corrector and the Glasserman-Zhao method are discussed. Numerical tests are carried out and we conclude...

We study 20 different implementation methodologies for each of 11 different choices of parameters of binomial trees and investigate the speed of convergence for pricing American put options numerically. We conclude that the most effective methods involve using truncation, Richardson...

Power numeraires are defined. They are applied to the Black-Scholes model and the drift of the stock is derived. It is also shown how to use them to derive formulas for power options with barriers. A reinterpretation of contour-shifting in the context of characteristic function pricing is given....

Stochastic volatility, local volatility and stochastic interest rates are three of the most important extensions to the standard Black-Scholes framework. Although much work has been done on models incorporating one or two of these extensions, very little has been done on the combination of all...

The problem of developing sensitivities of exotic interest rates derivatives to the observed implied volatilities of caps and swaptions is considered. It is shown how to compute these from sensitivities to model volatilities in the displaced diffusion LIBOR market model. The example of a...

We present a fast method to price and hedge CMS spread options in the displaced-diffusion co-initial swap market model. Numerical tests demonstrate that we are able to obtain sufficiently accurate prices and Greeks with computational times measured in milliseconds. Further, we find that CMS...

Sensitivity analysis, or so-called 'stress-testing', has long been part of the actuarial contribution to pricing, reserving and management of capital levels in both life and non-life assurance. Recent developments in the area of derivatives pricing have seen the application of adjoint methods to...

We present a new class of upper bounds for the Monte Carlo pricing of Bermudan derivatives. This class contains both the additive and multiplicative upper bounds as special cases. We also see that the hypothesis that the pay-off is positive for the multiplicative upper bound is unnecessary. The...