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A Self-Consistent Model for the Forward Price Dynamics


  • Vlad Makhankov



We consider mean-reverting stochastic processes and build a self- consistent model for forward price dynamics and their applications in power industries. This model with stochastic volatility of the forward price is built using the ideas and equations of stochastic differential geometry in order to close the system of equations for the forward price and its volatility. Stationary distributions for the forward price volatility are found analytically as well as the forward price curves in the one factor case. We consider two models for regular forward price volatility. 1)Pure exponential two parameter model with zero asymptotic. 2)Three parameter exponential model with non-zero asymptotic. The first model is a toy one although it can be used in the case of long terms, the second one is quite reliable for short terms. Those models will also play a role of initial conditions for a stochastic process described forward price volatility. We compare our results with those known from the literature.

Suggested Citation

  • Vlad Makhankov, 2003. "A Self-Consistent Model for the Forward Price Dynamics," Econometrics 0308005, EconWPA.
  • Handle: RePEc:wpa:wuwpem:0308005
    Note: Type of Document - Word; prepared on Word file; to print on HP LaserJet; pages: 25 ; figures: included 6 figures. Word for Windows document submitted via ftp

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    More about this item


    Forward price; volatility; stochastic; mean-reverting process;

    JEL classification:

    • C30 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - General
    • C31 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models; Quantile Regressions; Social Interaction Models
    • C50 - Mathematical and Quantitative Methods - - Econometric Modeling - - - General
    • C60 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - General

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