Abstract
The sub-prime mortgage crisis of 2008 had a great effect on the financial market; it led to new market features and regulations. In particular, the dual curve feature has appeared in the over-the-counter market. As a result, the yield curve for computing forward values and the yield curve for discounting are no longer the same due to counterparty default risk. In addition, deleveraging regulation encourages financial institutions to invest in widely known simple products, typically at a single short rate. The classical Hull–White model, which is typically useful for simple interest rate products, is inadequate for the dual-curve situation. This study extends the Hull–White model with stochastic volatility to the dual-curve economy. Analytical solutions are derived for vanilla securities such as risk bearing zero bonds, bond options, and caplets. Our formulas facilitate the calibration of parameters by simultaneously fitting to the dual curves and the implied volatility surfaces.
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