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...

We extend the short rate model of Vasicek (1977) to include jumps in the local mean. Conditions ensuring existence of a unique equivalent martingale measure are given, implying that the model is arbitrage-free and complete. We develop efficient numerical methods for computation of zero coupon...

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...

The pricing of the European cash-settled swaptions is analysed. The standard market formula results are compared to results obtained from different models. Significant discrepancies are observed, justifying the title

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...

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...

Libor derivative pricing has changed with the crisis; Libor is no longer one unambiguous curve as a large basis has appeared between different Libor tenors. A previous approach to derivative discounting is reviewed in the light of those changes. The valuation of so-called linear derivatives, the...

Libor derivative pricing has changed with the crisis; Libor is not anymore one unambiguous curve as a large basis has appeared between different Libor tenors. A previous approach to derivative discounting is reviewed at the light of those changes. The valuation of so called linear derivatives,...

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...

Derivative pricing is about cash flow discounting at the riskfree rate. This teaching has lost its meaning post the financial crisis, due to the addition of extra value adjustments (XVA), which also made derivatives pricing and valuation a very difficult task for investors. This article recovers...