Stochastic Interest Rates for Local Volatility Hybrids Models

Abstract

This paper studies the impact of stochastic interest rates for local volatility hybrids. Our research shows that it is possible to explicitly determine the bias between the local volatility of a model with stochastic interest rates and the local volatility of the same model, but with deterministic interest rates as a function between the correlation of the stochastic interest rates and the digital at the local strike. The paper will show that this bias can be expressed in a simpler form under the assumption of a diffusion of the stochastic interest rates, enabling us to compute a fast calibration for a hybrid model with stochastic interest rates. This bias leads to a decrease in the value of the local volatility as a result of the induced volatility caused by the stochastic drift. Numerical results illustrate the importance of the bias and confirm that some stochastic noise arises from the stochastic drift.