The Dynamics of the Forward Interest Rate Curve with Stochastic String Shocks

TL;DR

This paper introduces a novel class of interest rate models driven by stochastic string shocks, enabling flexible correlation structures among forward rates and facilitating bond price data fitting and option pricing.

Contribution

It develops stochastic partial differential equation-based models with stochastic strings that ensure continuous forward rate curves and versatile correlation patterns.

Findings

Models can replicate any correlation pattern among forward rates.

Interest rate options can be priced via simulation.

Perfect hedging requires trading bonds of all maturities.

Abstract

This paper offers a new class of models of the term structure of interest rates. We allow each instantaneous forward rate to be driven by a different stochastic shock, constrained in such a way as to keep the forward rate curve continuous. We term the process followed by the shocks to the forward curve ``stochastic strings'', and construct them as the solution to stochastic partial differential equations, that allow us to offer a variety of interesting parametrizations. The models can produce, with parsimony, any sort of correlation pattern among forward rates of different maturities. This feature makes the models consistent with any panel dataset of bond prices, not requiring the addition of error terms in econometric models. Interest rate options can easily be priced by simulation. However, options can only be perfectly hedged by trading in bonds of all maturities available.