Stochastic String Models with Continuous Semimartingales

31 Pages Posted: 19 May 2014 Last revised: 19 Mar 2017

See all articles by Alberto Bueno-Guerrero

Alberto Bueno-Guerrero

IES Francisco Ayala

Manuel Moreno

University of Castilla-La Mancha

Javier F. Navas

Universidad Pablo de Olavide

Date Written: November 6, 2014

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

Suggested Citation

Bueno-Guerrero, Alberto and Moreno Fuentes, Manuel and Navas, Javier F., Stochastic String Models with Continuous Semimartingales (November 6, 2014). Available at SSRN: https://ssrn.com/abstract=2438601 or http://dx.doi.org/10.2139/ssrn.2438601

Alberto Bueno-Guerrero (Contact Author)

IES Francisco Ayala ( email )

Av Francisco Ayala, 0
Granada, 18014
Spain

Manuel Moreno Fuentes

University of Castilla-La Mancha ( email )

Cobertizo San Pedro Martir s/n
Toledo, Toledo 45071
Spain

Javier F. Navas

Universidad Pablo de Olavide ( email )

Ctra. de Utrera, Km.1
41013 Seville
Spain

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