Risk Minimizing Hedging of Liabilities
Dr Harry Zheng, Department of Mathematics, Imperial College

Abstract:
Duration is a useful tool in hedging liabilities. Macaulay duration is a well-known one but is criticized for its stringent assumptions. Many other durations have been suggested to accommodate more general type of shifts. Unfortunately, hedging is achieved only against assumed type of rate change. In this talk we introduce a risk (maximum loss) minimizing measure which is applicable to any pattern of changes. We discuss different hedging strategies and compare their performances with US T-bond and STRIPS data. We use a multi-stage linear programming model to select the optimal portfolio that minimizes the hedging loss and transaction cost. We also extend the measure to credit-risky and option-embedded bonds, the uncertainty of timing and amount of cash flows of these securities is characterized by risk-neutral survival probabilities derived from the market.