Evaluating the credit exposure of interest rate derivatives under the real-world measure

Takashi Yasuoka

Abstract

This paper examines the credit exposure evaluation properties of interest rate derivatives to manage counterparty credit risk, working with the real-world probability. We briefly introduce the Heath–Jarrow–Morton (HJM) model and the Hull–White (HW) model in connection with real-world modeling. In a backward-looking approach, a real-world model is constructed from a combination of interest rate model and historical data of forward rates. By using data from the Japanese London Interbank Offered Rate/swap markets and considering three sample periods, we construct a number of real-world models: specifically, the HW model, the one-factor HJM model, the three- factor HJM model and other variations. The exposure profiles of interest rate swaps are calculated from the forward-rate scenarios simulated by our real-world models. We compare the results of applying the above models, using three sample periods from the viewpoint of model validation. As a result, the potential future exposure profile under the real-world simulation reflects the volatility structure and the historical drift of the forward rates. In contrast, the risk-neutral model does not reflect the historical drift, but it does reflect the volatility structure.