Constant maturity swaps (CMS), CMS spreads and similar products are analyzed in multi-factor HJM models. For Gaussian models, which include some Libor Market Models and the G2 model, explicit approximated formula are provided. The approximations are done through two different approaches: an...

With the transitions to overnight benchmarks as the main benchmarks in some currencies, futures based on overnight rates are becoming more common. The most traded futures on overnight rates settle against compounded rates. The pricing of those futures requires some convexity adjustments with an...

This document contains implementation notes related to Bang and Daboussi (2022) . We have extended the original paper by allowing actual accrual factors (not all 1) and non-annual frequency on the fixed side. The note first describes the detailed formulas in this extended setting. In a second...

This note analyses derivative pricing in the context of a collateral rate switch during the life of a financial product or the existence of two overnight rates. In particular we analyse the impact of forward change of collateral, the impact on OISs when the collateral rate is different from the...

The Libor Market Model (LMM) describes the evolution of a yield curve through equations for a discrete set of forward rates. In the original version, the rate dynamic was log-normal. The rate dynamic has been extended. The main result presented here is a generic approximation that provides an...

The ISDA designed fallback for cash-settled swaptions with collateral discounting generates swap rate and term structure dependent exotics. To analyse precisely the fallback impact a full term structure of rates and volatility modelling is required. A recent paper Bang and Daboussi (2022)...

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...

Even if the name futures indicates a simple instrument, bond futures are complex. Several special features are embedded in the instrument. In particular the future is not written on one specific bond but on a basket of bonds, from which the short side can deliver the cheapest. This paper focuses...

Bond futures are liquid but complex instruments. Here they are analysed in a one-factor Gaussian HJM model. The in-the-model delta and out-of-the-model delta and gamma are studied. An explicit formula is provided for in-the-model delta. The out-of-the-model delta and gamma are equivalent to...