Managing new type of risks - Electricity, weather, and insurance risks and their derivatives-

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In this research project, we developed basic theories for managing new types of risks such as electricity, weather, and insurance. The main results that we obtained so far are as follows.The first is the derivation of pricing formula for "Edokko Options." The Edokko Option is a generalization of the alpha-percentile (or quintile) option. This formula gives us the price of an option whose payoff is determined by the frequency that the underlying asset price is less than a certain critical value in a certain period of time. We may apply this formula to price a weather derivatives whose payoff depends on the number of rainy days in a certain period of time e.g., between June 1 and July 31.The second is the analysis of optimal portfolio strategies in incomplete markets with price jump. Electricity prices sometimes jump, which is called price "spikes" and is an important characteristics of this market. Our second result provides a way to manage such discontinuous "jump" risks. This analysis enables us to calculate the premium of the insurance for such jump risks.The third is the analysis of liquidity of financial products to trade new (and not well known) risks. Taking CAT insurance futures and reinsurance markets as an example, we analyzed how the asymmetric information about the risks between the seller and the buyers affects the trade of the products. We obtain conditions under which new risks eventually can be traded as securities.