Journal of Risk Model Validation

Risk.net

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

Takashi Yasuoka

  • This paper studies the credit-exposure evaluation of interest rate derivatives working with the real-world probability.
  • From the viewpoint of model validation, we compare the results from applying the real-world model and the risk-neutral model.
  • The PFE profile under the real-world simulation reflects the volatility structure and the historical drift of the forward rates.
  • The risk-neutral model does not reflect the historical drift, but reflect the volatility structure.

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.

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