Stochastic String Models with Continuous Semimartingales

Abstract

This paper reformulates the stochastic string model of Santa-Clara and Sornette (2001) using stochastic calculus with continuous semimartingales. We present some new results, such as: a) the dynamics of the short-term interest rate, b) the PDE that must be satisfied by the bond price, and c) an analytic expression for the price of a European bond call option. Additionally, we clarify some important features of the stochastic string model and show its relevance to price derivatives and the equivalence with a infinite dimensional HJM model to price European options.

Keywords: Stochastic calculus, Semimartingales, Stochastic strings, Derivatives pricing, Term structure, Interest rates

JEL Classification: C60, E43, G13