Real-World Versus Risk-Neutral Measures in the Estimation of an Interest Rate Model with Stochastic Volatility

Abstract

In this paper, we consider a jump-diffusion two-factor model which stochastic volatility to obtain the yield curves efficiently. As this is a jump-diffusion model, the estimation of the market prices of risk is not possible unless a closed form solution is known for the model. Then, we obtain some results that allow us to estimate all the risk-neutral functions, which are necessary to obtain the yield curves, directly from data in the markets. As the market prices of risk are included in the risk-neutral functions, they can also be obtained. Finally, we use US Treasury Bill data, a nonparametric approach, numerical differentiation and Monte Carlo simulation approach to obtain the yield curves. Then, we show the advantages of considering the volatility as second stochastic factor and our approach in an interest rate model.