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Finance, Economics, and Mathematics by Robert C. Merton, Oldrich A. Vasicek

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Chapter 30Pricing of Energy Derivatives

Unpublished memorandum, 2002.

It was shown in Geman and Vasicek (2001) (Chapter 29 of this volume) that the price c30-math-0001 of a forward contract maturing at T is subject to

1 equation

where c30-math-0003 are Wiener processes under a risk-neutral probability measure c30-math-0004 equivalent to P.

Integrating Eq. (1) from 0 to T and taking into account that c30-math-0005 yields

2 equation

Eq. (2) represents a complete specification of the forward/spot process. It is fully described by the forward contract volatilities, and it only includes processes whose stochastic properties under the measure P* are known. Therefore, the prices of energy derivatives and contingent claims can be calculated without recourse to the market prices of risk, which are not directly observable. In this sense, it is akin to the Heath/Jarrow/Morton (1992) model of interest rates (their Eq. (26)).

The price of any derivative contract (e.g., ...

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