Abstract
This paper follows an incomplete market pricing approach to analyze the evaluation of weather derivatives and the viability of a weather derivatives market in terms of hedging. A utility indifference method is developed for the specification of indifference prices for the seller and buyer of a basket of weather derivatives written on rainfall and temperature. The agent’s risk preference is described by an exponential utility function and the prices are derived by dynamic programming principles and corresponding Hamilton Jacobi-Bellman equations from the stochastic optimal control problems. It is found the indifference measure is equal to the physical measure as there is no correlation between the capital market and weather. The fair price of the derivative should be greater than the seller’s indifference price and less than the buyer’s indifference price for market viability and no arbitrage opportunities.
Highlights
In the context of climate change, rainfall and temperature are the major determinants of uncertainty affecting crop yield
Weather indexes are not tradable, the market is incomplete as the derivatives cannot be replicated by a self financing portfolio. This makes it impractical to apply no arbitrage pricing models to weather derivatives Alexandridis and Zapranis (2012); Benth and Benth (2007) as we cannot construct a risk free portfolio consisting of weather index and the derivative
The approach takes into account price risk, weather risks and all other risks in the financial capital market
Summary
In the context of climate change, rainfall and temperature are the major determinants of uncertainty affecting crop yield. A better understanding of the dynamics driving both the rainfall and temperature processes and possible hedging approaches provide a new way to transfer financial risks due to weather to financial markets where risk management strategies are available. This basket weather derivative enables the farmer to hedge risk due to rainfall and temperature variation at the same time in one transaction and to do it more cheaply rather than hedging rainfall and temperature independently.
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