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Valuation of caps and swaptions under a stochastic string model

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  • Bueno-Guerrero, Alberto
  • Moreno, Manuel
  • Navas, Javier F.

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.

Suggested Citation

  • Bueno-Guerrero, Alberto & Moreno, Manuel & Navas, Javier F., 2020. "Valuation of caps and swaptions under a stochastic string model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 559(C).
    • Handle: RePEc:eee:phsmap:v:559:y:2020:i:c:s0378437120305744
    DOI: 10.1016/j.physa.2020.125103
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    References listed on IDEAS

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    Cited by:

    1. Lloyd P. Blenman & Alberto Bueno-Guerrero & Steven P. Clark, 2022. "Pricing and Hedging Bond Power Exchange Options in a Stochastic String Term-Structure Model," Risks, MDPI, vol. 10(10), pages 1-17, September.
    2. Bueno-Guerrero, Alberto, 2022. "A Quantum Mechanics for interest rate derivatives markets," Chaos, Solitons & Fractals, Elsevier, vol. 155(C).

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    More about this item

    Keywords

    Stochastic string model; LIBOR market model; Black formula; Cap; Swaption;
    All these keywords.

    JEL classification:

    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

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