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

By V. G. Makhankov and M. A. Aguero-Granados

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

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Citations

  1. 1993.“Options, Futures, and other Derivative Securities”.
  2. (1968). Conditional Markov Processes and their Application to the Theory of Optimal Control”.
  3. (1992). Integrable Pseudospin Models in Condensed Matter”. Harwood Acad.
  4. (1984). Methods and Applications”. Part I, The Geometry of Surfaces, Transformations Groups, and Fields.
  5. (1999). Power Pricing – Making it Perfect”. Internet, Power: Continuing the electricity forward curve debate.
  6. (2001). Quantitative Finance”.
  7. Stochastic Differential Geometry in Finance Studies”.
  8. (1987). Stochastic Differential Geometry: an Introduction”.
  9. (1997). The Stochastic Behavior of Commodity Prices: Implications for Pricing and Hedging”.
  10. (1994). The Valuation of Commodity Contingent Claims”.
  11. (1998). Valuation of Commodity Futures and Options under Stochastic Convenience Yields, Interest Rates, and Jump Diffusions in the Spot”.