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The stochastic string model as a unifying theory of the term structure of interest rates

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

Abstract

We present the stochastic string model of Santa-Clara and Sornette (2001), as reformulated by Bueno-Guerrero et al. (2015), as a unifying theory of the continuous-time modeling of the term structure of interest rates. We provide several new results, such as: (a) an orthogonality condition for the volatilities in the Heath, Jarrow, and Morton (1992) (HJM) model, (b) the interpretation of multi-factor HJM models as approximations to a full infinite-dimensional model, (c) a result of consistency based on Hilbert spaces, and (d) a theorem for option valuation.

Suggested Citation

  • Bueno-Guerrero, Alberto & Moreno, Manuel & Navas, Javier F., 2016. "The stochastic string model as a unifying theory of the term structure of interest rates," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 461(C), pages 217-237.
    • Handle: RePEc:eee:phsmap:v:461:y:2016:i:c:p:217-237
    DOI: 10.1016/j.physa.2016.05.044
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    1. Bueno-Guerrero, Alberto & Moreno, Manuel & Navas, Javier F., 2015. "Stochastic string models with continuous semimartingales," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 433(C), pages 229-246.
    2. J. C. Arismendi-Zambrano & T. Ramos-Almeida & J. C. Reboredo & M. A. Rivera-Castro, 2020. "Identifying Statistical Arbitrage in Interest Rate Markets: A Genetic Algorithm Approach," Economics Department Working Paper Series n305-20.pdf, Department of Economics, National University of Ireland - Maynooth.
    3. Bueno-Guerrero, Alberto, 2022. "A Quantum Mechanics for interest rate derivatives markets," Chaos, Solitons & Fractals, Elsevier, vol. 155(C).
    4. 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).

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