Results 1 
3 of
3
RiskManagement Methods for the Libor Market Model Using Semidefinite Programming
, 2003
"... When interest rate dynamics are described by the Libor Market Model as in Brace, Gatarek & Musiela (1997), we show how some essential riskmanagement results can be obtained from the dual of the calibration program. In particular, if the objetive is to maximize another swaption's price, we ..."
Abstract

Cited by 6 (0 self)
 Add to MetaCart
When interest rate dynamics are described by the Libor Market Model as in Brace, Gatarek & Musiela (1997), we show how some essential riskmanagement results can be obtained from the dual of the calibration program. In particular, if the objetive 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.
RiskManagement Methods for the Libor Market Model Using Semidefinite Programming ∗
, 2003
"... When interest rate dynamics are described by the Libor Market Model as in [BGM97], we show how some essential riskmanagement results can be obtained from the dual of the calibration program. In particular, if the objetive is to maximize another swaption’s price, we show that the optimal dual variab ..."
Abstract
 Add to MetaCart
When interest rate dynamics are described by the Libor Market Model as in [BGM97], we show how some essential riskmanagement results can be obtained from the dual of the calibration program. In particular, if the objetive is to maximize another swaption’s price, we show that the optimal dual variables describe a hedging portfolio in the sense of [AP96]. 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.
COMPARISON OF TWO METHODS FOR SUPERREPLICATION
"... Abstract. We compare two methods for superreplication of options with convex payoff functions. One method entails an overestimation of the unknown covariance matrix in the sense of quadratic forms. With this method the value of the superreplicating portfolio is given as the solution of a linear Bl ..."
Abstract
 Add to MetaCart
(Show Context)
Abstract. We compare two methods for superreplication of options with convex payoff functions. One method entails an overestimation of the unknown covariance matrix in the sense of quadratic forms. With this method the value of the superreplicating portfolio is given as the solution of a linear BlackScholes type equation. In the second method the choice of quadratic form is made pointwise. This leads to a fully nonlinear equation, the socalled BlackScholesBarenblatt equation, for the value of the superreplicating portfolio. In general, this value is smaller for the second method than for the first method. We derive estimates for the difference between the initial values of the superreplicating strategies obtained using the two methods. 1.