Makhankov, V. G. and Aguero-Granados, M. A. (2009): Mean-Reverting Stochastic Processes, Evaluation of Forward Prices and Interest Rates.
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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.
|Item Type:||MPRA Paper|
|Original Title:||Mean-Reverting Stochastic Processes, Evaluation of Forward Prices and Interest Rates|
|Keywords:||: Stochastic Differential Geometry, Mean-Reverting Stochastic Processes and Term Structure of Specific (Some) Economic/Finance Instruments|
|Subjects:||A - General Economics and Teaching > A1 - General Economics > A12 - Relation of Economics to Other Disciplines
C - Mathematical and Quantitative Methods > C0 - General > C02 - Mathematical Methods
C - Mathematical and Quantitative Methods > C2 - Single Equation Models; Single Variables > C23 - Models with Panel Data; Longitudinal Data; Spatial Time Series
C - Mathematical and Quantitative Methods > C6 - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling > C62 - Existence and Stability Conditions of Equilibrium
|Depositing User:||Maximo Aguero|
|Date Deposited:||20. Nov 2009 05:35|
|Last Modified:||14. Feb 2013 07:33|
Clewlow C., and Ch. Strickland. 1999. “Power Pricing – Making it Perfect”. Internet, Power: Continuing the electricity forward curve debate.
Cortazar, G., and E. Schwartz. 1994. “The Valuation of Commodity Contingent Claims”. The Journal of Derivatives V.1, No 4: 27-39.
Dubrovin B, Fomenko A., and Novikov S. “Modern Geometry. Methods and Applications”. Part I, The Geometry of Surfaces, Transformations Groups, and Fields. Springer, Heidelberg 1984.
Hillard J. and Reis J. 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, 33, #1, pp.61-86.
Hull, J.C. 1993.“Options, Futures, and other Derivative Securities”. Prentice Hall, New Jersey.
Kendal W. 1987. “Stochastic Differential Geometry: an Introduction”. Acta Applicandae Mathematica, 9, pp. 29-60.
Makhankov V., Taranenko Yu., Gomez C., and Jones R.1995. “Geometrical Setting of the Term Structure of Interest Rate”. LA-UR-95-449. Los Alamos National Laboratory, Los Alamos, USA.
Makhankov, V.G.1997. “Stochastic Differential Geometry in Finance Studies”. In “Nonlinear Dynamics, Chaotic and Complex Systems”, Eds. E. Infeld, R. Zelazny and A. Galkowski, Cambridge University Press.
Makhankov V and Pashaev O. 1992. “Integrable Pseudospin Models in Condensed Matter”. Harwood Acad. Publishers GmbH, London.
Schwartz E. 1997. “The Stochastic Behavior of Commodity Prices: Implications for Pricing and Hedging”. The Journal of Finance, Vol. LII (3), pp. 923-73.
Stratonovich R. 1968. “Conditional Markov Processes and their Application to the Theory of Optimal Control”. Elsevier, N.Y.
Vasicek O. 1977. “An Equilibrium Characterization of the Term Structure”. Journal of Financial Economics, 5, pp. 177-88.
Wilmott P. 2001. “Quantitative Finance”. J. Willey & Sons