This paper presents an extensive test of the Libor Market on the Euro Cap and Swaption market. The deterministic LIBOR market model prices OTC cap exactly and prices OTC swaptions with errors well below two basis points. Tests for the hedging performance show that the deterministic LIBOR market...

SABR stochastic volatility model is appealing for modeling smile and skew of option prices. Hagan, who first proposed this model, derived a closed form approximation for european options and showed that it provides consistent and stable hedges. Here I prove a new exact closed formula for the...

In this paper, we introduce an extension to the LIBOR Market model that is suitable to incorporate both sudden market shocks as well as changes in the overall economic climate into the interest rate dynamics. This is achieved by substituting the simple diffusion process of the original LIBOR...

A Markovian Projection is investigated for the Local Stochastic Volatility Libor Market Model. An approximation based on the Log Normal process is introduced. In this approximation, the Markovian Projection is fitted to the CEV model rather than to Displaced Diffusion. The relationship with a...

In this paper we outline the European interest rate swaption pricing formula from first principles using the Martingale Representation Theorem and the annuity measure. This leads to an expression that allows us to apply the generalized Black-Scholes result. We show that a swaption pricing...

We propose a term structure of forward rates driven by a kernel-correlated Levy random field under the HJM framework. The kernel-correlated Levy random field is composed of a kernel-correlated Gaussian random field and a centered Poisson random measure. We shall give a criterion to preclude...

Regulators and central banks are defining-through mathematical formulae-the market microstructure for the calculation of fixings for LIBOR interest rate swaps in terms of the relevant swap rates that reference the Risk-Free Rate that will replace a particular LIBOR post its cessation. The...

The credit valuation adjustment (CVA) of OTC derivatives is an important part of the Basel III credit risk capital requirements and current accounting rules. Its calculation is not an easy task - not only it is necessary to model the future value of the derivative, but also the probability of...

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...

A callable leveraged constant maturity swap (CMS) spread note allows the holder to benefit from future changes in the spread between two swap interest rates. The issues retains the right to call the note at pre-specified times in the future. The note is priced via Monte Carlo simulation using...