A simple and fundamental question in derivatives pricing is how (contingent) cash-flows should be discounted. As cash can generally not be invested at Libor, the Libor curve is probably not the right discounting curve, even for Libor derivatives. The impact on derivative pricing of changing the...

The twin brothers Libor Market and Gaussian HJM models are investigated. A simple exotic option, floor on composition, is studied. The same explicit approach is used for both models. Using an approximation the LLM price is obtained without Monte Carlo simulation. The results of the approximation...

The original Libor Market Model (LMM) has been extended to several dynamics (or local volatilities) for the underlying Libor rates. The main result presented here is a generic approximation that provides an explicit swaptions price for local volatilities LMM. The approximation is base on an...

With the generalisation of Variation Margin (VM) collateral, the derivative world is not driven anymore by discrete cash flows but by continuous dividend. Due to practical constraints, the VM is paid with a one day delay. This delay reduces significantly the effectiveness of the margin process...

We propose an approach for the dynamical estimation of initial margins. We determine initial margins at future points in time by computing a risk measure of the modelled price increment over a margin period of risk. As an example, we produce the initial margin process for interest rate swap...

In the framework of the Libor Market Model (LMM) an explicit pricing formula is obtained for European swaptions. The LLM used is a displaced diffusion also called Bond Market Model (BMM). The results are similar to the one obtained for the Gaussian HJM. The extension to bond futures and...

An approximation approach to Constant Maturity Swaps (CMS) pricing in the separable one-factor Gaussian LMM and HJM models is presented. The approximation used is a Taylor expansion on the swap rate as a function of a random variable which is intuitively similar to a (short) rate. This approach...

An exotic option (floor on rolled deposit) is studied in the shifted log-normal Libor Market (LMM) and Gaussian HJM models. The shifted log-normal LMM exhibits a controllable volatility skew. An explicit approach is used for both models. Using approximations the price in the LMM is obtained...

A simple and fundamental question in derivatives pricing is the way (contingent) cash-flows should be discounted. As cash can not be invested at Libor the curve is probably not the right discounting curve, even for Libor derivatives. The impact on derivative pricing of changing the discounting...

A simple exotic option (floor on rolled deposit) is studied in the shifted log-normal Libor Market (LMM) and Gaussian HJM models. The shifted log-normal LMM exhibits a controllable volatility skew. An explicit approach is used for both models. Using approximations the price in the LMM is...