Hybrid Calibration Procedures for Term Structure Models

Calibration is the well-established methodology to fit a model to observed option price data. A calibrated model reflects the current market view on its future evolution, typically under the risk-neutral measure. On the other side, statistical estimation on the basis of historical data estimates a model on the basis of past movements (hence under the historical or actual measure). While calibration is more used in pricing and hedging of derivatives, statistical estimation is the standard tool for risk management. Both approaches have their advantages and drawbacks. Calibration, reflecting actual market views, is able to react very quickly on changes while statistical estimation provides more stability. The hybrid calibration procedure suggested here combines both approaches and therefore might serve for increasing stability in calibration on one side and providing a tool for risk management which is able to react quickly on recent market changes. The paper considers a termstructure model with credit risk on the basis of Gaussian random fields proposed in Schmidt. The risk-free model of Kennedy (1994) is a special case and thus the methodologies may also be applied to risk-free term structures. We also discuss a methodology suggested in Roncoroni and Guiotto (2000). The market for credit portfolio products increased tremendously, Especially in the last years, while the market for single-name credit derivatives did not grow in that speed. However, the recent turmoil caused by the U.S. subprime mortgage crisis changed the view on credit portfolio products and it is likely that singlename credit derivatives become increasingly important because of their transparency and the fact that the risk management of single-name derivatives is of course much simpler. We start by a number of pricing results on single-name credit risky securities, such as digitals, bonds with zero recovery and under certain recovery assumptions, European options on bonds, and credit default swaptions with a knock-out feature. Thereafter, different hybrid calibration procedures are discussed and illustrated. Finally, we compute some risk measures for the proposed model.