Esscher transform
To derive an expression for future rainfall prices in Eq. (1), we need to take into account
risk preferences of investors. This is traditionally given by a MPR charged for issuing the
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derivative. The MPR is an important parameter of the equivalent martingale measure.
For this, we first need to specify the risk-neutral probability Q. We say that Q P such
that all tradable assets in the market are martingales after discounting. In the Black and
Scholes model, the unique equivalent martingale measure could be obtained by changing
the drift in the Brownian motion.
The market for rainfall derivatives and for