28.1 THE MARKET PRICE OF RISK

We start by considering the properties of derivatives dependent on the value of a single variable θ. Assume that the process followed by θ is

dθθ=mdt+sdz(28.1)

where dz is a Wiener process. The parameters m and s are the expected growth rate in θ and the volatility of θ, respectively. We assume that they depend only on θ and time t. The variable θ need not be the price of an investment asset. It could be something as far removed from financial markets as the temperature in the center of New Orleans.

Suppose that f1 and f2 are the prices of two derivatives dependent only on θ and t. These can be options or other instruments that provide a payoff in the future equal to some function of θ. Assume that during ...

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