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Valuation of a Swing Option in the Mean-Reverting Market Environment

Authors
Publisher
Elsevier B.V.
Publication Date
Keywords
  • Applied Mathematics
  • Modelling And Simulation
  • Probability Theory And Stochastic Processes
  • Applied_Mathematics/0208007
Disciplines
  • Economics
  • Mathematics

Abstract

We present the valuation of an operational swing option in the mean-reverting market environment. We consider such a swing option with the load for a customer being a time-dependent deterministic function of a random parameter. This random parameter can have various interpretations. In the special case of the identity load function, that is in the case of the load being equal to this random parameter, this random parameter can be interpreted as the load itself allowing for the modeling of the load directly. In the case of a general load function this random parameter can be interpreted, for example, as temperature allowing for the modeling of weather sensitive loads. In this regard, to be specific, in the case of a general load function, we will use temperature as an example of this random parameter throughout the article. We consider two cases when both power price and temperature follow mean-reverting geometric Brownian motions, and when power price follows mean-reverting geometric Brownian motions while temperature follows mean-reverting Brownian motion. In each of these cases we allow the volatilities, the correlation, the mean reversion rates, the equilibrium means, and the risk-free interest rate to depend on time. We also present analytic expressions for the value of the swing option in the following practically important cases of the load functions. If both power price and temperature follow mean-reverting geometric Brownian motions, we consider the load functions to be either power functions or linear combinations, discrete or continuous, of power functions. If power price follows mean-reverting geometric Brownian motion while temperature follows mean-reverting Brownian motion, we consider the load functions to be either exponential functions or linear combinations, discrete or continuous, of exponential functions, or polynomials. The derivation of these analytic expressions is based on the spectral method and the concept of an eigenclaim introduced earlier by the author. In order to value this swing option we explicitly value a European contingent claim with a general payoff in the mean-reverting market environment with a finite number of underlying securities and observable parameters. The prices of the underlying securities are assumed to follow mean-reverting geometric Brownian motions while the values of observable parameters are assumed to follow mean-reverting Brownian motions. The volatilities, correlations, the mean reversion rates, the equilibrium means, and the risk-free interest rate are allowed to be time-dependent.

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