A numerical approach to obtain the yield curves with different risk-neutral drifts

Abstract

In this paper we consider the possible dependence of the market price of risk on time and interest rates. This fact gives as a result that the risk-neutral drift, which is one of the coefficients of the pricing equation, also depends on time and interest rates. Then, we estimate the risk-neutral drift directly from the slope of the yield curve. This approach is very accurate as we show with a numerical experiment. In order to obtain the term structure we also propose a suitable finite difference method, which converges to the true solution. Finally, we obtain and compare the yield curves with data from the US Treasury Bill market.