Here we present a yield curve interpolation method, one that’s based on conditioning a stochastic model on a set of market yields. The concept is closely related to a Brownian bridge where you generate scenario according to an SDE, but with the extra condition that the start and end of the scenario’s must have certain values. In this paper we use Gaussian process regression to generalization the Brownian bridge and allows for more complicated conditions. As an example, we condition the Vasicek spot interest rate model on a set of yield constraints and provide an analytical solution.
The resulting model can be applied in several areas:
- Monte Carlo scenario generation
- Yield curve interpolation
- Estimating optimal hedges, and the associated risk for non tradable products