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Mean-Reverting Stochastic Processes, Evaluation of Forward Prices and Interest Rates

Author

Listed:
  • Makhankov, V. G.
  • Aguero-Granados, M. A.

Abstract

We consider mean-reverting stochastic processes and build self-consistent models for forward price dynamics and some applications in power industries. These models are built using the ideas and equations of stochastic differential geometry in order to close the system of equations for the forward prices and their volatility. Some analytical solutions are presented in the one factor case and for specific regular forward price/interest rates volatility. Those models will also play a role of initial conditions for a stochastic process describing forward price and interest rates volatility. Subsequently, the curved manifold of the internal space i.e. a discrete version of the bond term space (the space of bond maturing) is constructed. The dynamics of the point of this internal space that correspond to a portfolio of different bonds is studied. The analysis of the discount bond forward rate dynamics, for which we employed the Stratonovich approach, permitted us to calculate analytically the regular and the stochastic volatilities. We compare our results with those known from the literature.

Suggested Citation

  • Makhankov, V. G. & Aguero-Granados, M. A., 2009. "Mean-Reverting Stochastic Processes, Evaluation of Forward Prices and Interest Rates," MPRA Paper 18750, University Library of Munich, Germany, revised 19 Nov 2009.
    • Handle: RePEc:pra:mprapa:18750
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    References listed on IDEAS

    as
    1. Vasicek, Oldrich, 1977. "An equilibrium characterization of the term structure," Journal of Financial Economics, Elsevier, vol. 5(2), pages 177-188, November.
    2. Hilliard, Jimmy E. & Reis, Jorge, 1998. "Valuation of Commodity Futures and Options under Stochastic Convenience Yields, Interest Rates, and Jump Diffusions in the Spot," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 33(1), pages 61-86, March.
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    More about this item

    Keywords

    : Stochastic Differential Geometry; Mean-Reverting Stochastic Processes and Term Structure of Specific (Some) Economic/Finance Instruments;

    JEL classification:

    • A12 - General Economics and Teaching - - General Economics - - - Relation of Economics to Other Disciplines
    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • C23 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Models with Panel Data; Spatio-temporal Models
    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium

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