Random Switching Times Among Randomly Parameterized Regimes of Random Interest Rate Rate Scenarios

Most of the usual stochastic interest rate models are designed and calibrated to provide plausible behavior in expected value and variance, which are the raw material for …rst approximation pricing and hedging of …nancial instruments. Standards of practice and often regulators require actuaries to stress-test …nancial positions over long projection horizons against extreme interest rate paths. The behavior of extreme paths in the usual stochastic interest rate models is not nearly so plausible as the behavior of their expected values and variances. This paper proposes a new class of models that deliver more plausible extreme paths while preserving the usual expected value and variance behavior. Along the way we derive the closed form solution for the traditional mean-reverting lognormal process, including the drift compensation.