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Probability and Computational Finance Seminar
Raquel Gaspar
Technical University of Lisbon
Title: Convexity Adjustments for ATS models

Abstract: Practitioners are used to value a broad class of exotic interest rate derivatives simply by performing what is known as convexity adjustments (or convexity corrections). Convexity adjustments, however, are highly dependent on both the particular interest rate model one chooses and the exact payoff under analysis.

We start by exploiting the relations between various interest rate models and their connections to measure changes. As a result we classify convexity adjustments into \emph{forward adjustments} and \emph{swaps adjustments}.

We then focus on affine term structure (ATS) models and, in this context, conjecture convexity adjustments should be related of affine functionals. In the case of forward adjustments, we show how to obtain \emph{exact} formulas. Concretely for LIBOR in arrears (LIA) contracts, we derive the system of Riccatti ODE-s one needs to compute to obtain the exact adjustment. These ODE-s are very similar to the ones necessary to identify the ATS of bond prices. Based upon the ideas of \cite{SchraPelSwaps} we are also able to derive general swap adjustments useful, in particular, when dealing with constant maturity swaps (CMS).

Our approach bypasses the need for Taylor approximations or unrealistic assumptions. They include exact convexity adjustments previously derived, such as the adjustments associated with Gaussian models, but are far more general as they provide solutions for the entire ATS class of models.

Date: Monday, October 1, 2012
Time: 5:00 pm
Location: Wean Hall 6423
Submitted by:  Steve Shreve