Risk-Management Methods for the Libor Market Model Using Semidefinite Programming
16 Pages Posted: 12 Jul 2004
There are 2 versions of this paper
Risk-Management Methods for the Libor Market Model Using Semidefinite Programming
Risk-Management Methods for the Libor Market Model Using Semidefinite Programming
Date Written: February 25, 2003
Abstract
When interest rate dynamics are described by the Libor Market Model as in Brace, Gatarek & Musiela (1997), we show how some essential risk-management results can be obtained from the dual of the calibration program. In particular, if the objective is to maximize another swaption's price, we show that the optimal dual variables describe a hedging portfolio in the sense of Avellaneda & Paras (1996). In the general case, the local sensitivity of the covariance matrix to all market movement scenarios can be directly computed from the optimal dual solution. We also show how semidefinite programming can be used to manage the Gamma exposure of a portfolio.
Keywords: Market model, risk management, semidefinite programming
JEL Classification: C61, C63, G12
Suggested Citation: Suggested Citation
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