Valuation of caps and swaptions under a stochastic string model

Alberto Bueno-Guerrero, Manuel Moreno and Javier Navas

Physica A: Statistical Mechanics and its Applications, 2020, vol. 559, issue C

Abstract: We develop a Gaussian stochastic string model that provides exact closed-form expressions for the prices and hedging portfolios of caps and swaptions. Under certain conditions, our pricing expressions reduce to Black (1976) formulas. We also propose a stochastic string LIBOR market model that generalizes the models of Brace et al. (1997) and Longstaff et al. (2001a). We provide a possible explanation for some problems involved in the relative valuation of these derivatives. We also attain the observational equivalence of Kerkhof and Pelsser (2002) and prove that, in our setup, the models proposed by Brace et al. (1997) and Longstaff et al. (2001a) are more parsimonious than stated in the original papers.

Keywords: Stochastic string model; LIBOR market model; Black formula; Cap; Swaption (search for similar items in EconPapers)
JEL-codes: C02 G12 (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:559:y:2020:i:c:s0378437120305744

DOI: 10.1016/j.physa.2020.125103

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