Risk-Management Methods for the Libor Market Model Using Semidefinite Programming

Posted: 10 Nov 2005

See all articles by Alexandre d'Aspremont

Alexandre d'Aspremont

Princeton University - Department of Operations Research and Financial Engineering

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Abstract

When interest rate dynamics are described by the Libor market model as in Brace et al (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 and 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: Libor market model, hedging portfolio, Avellaneda and Paras (1996), Brace et al (1997), semidefinite programming , Gamma exposure

Suggested Citation

d'Aspremont, Alexandre, Risk-Management Methods for the Libor Market Model Using Semidefinite Programming. Journal of Computational Finance, Vol. 8, No. 4, Summer 2005, Available at SSRN: https://ssrn.com/abstract=840444

Alexandre D'Aspremont (Contact Author)

Princeton University - Department of Operations Research and Financial Engineering ( email )

Princeton, NJ 08544
United States

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