基于半定规划的Libor市场模型风险管理方法
Risk-Management Methods for the Libor Market Model Using Semidefinite Programming
摘要：
当利率动态被描述的Libor市场模型在BGM97中，我们展示了一些必要的风险管理结果可以从校准程序的对偶。特别是，如果目标是最大化另一个互换的价格，我们证明了最优对偶变量描述的对冲投资组合的意义上的\cite{Avel96}。在一般情况下，协方差矩阵对所有市场运动场景的局部灵敏度可以直接从最优对偶解计算。我们还展示了如何半定规划可以用来管理伽玛暴露的投资组合。
英文摘要：
When interest rate dynamics are described by the Libor Market Model as in BGM97, we show how some essential risk-management 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 \cite{Avel96}. 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.
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