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

在这个研究项目中，我们发展了管理诸如电力、天气和保险等新型风险的基本理论。到目前为止，我们得到的主要结果如下。首先是“易多科期权”定价公式的推导。Edokko期权是alpha-百分位（或五分位）期权的泛化。这个公式给出了一种期权的价格，它的收益取决于在一定时期内标的资产价格低于某一临界值的频率。我们可以将此公式应用于天气衍生品的定价，其收益取决于特定时间段（例如，6月1日至7月31日之间）的雨天数量。第二部分分析了不完全市场中具有价格跳跃的最优投资组合策略。电力价格有时会跳涨，这被称为价格“峰值”，是这个市场的一个重要特征。我们的第二个结果提供了一种管理这种不连续的“跳跃”风险的方法。这种分析使我们能够计算出这种跳跃险的保险费。第三是分析金融产品的流动性，以交易新的（不为人所知的）风险。以CAT保险期货和再保险市场为例，分析了买卖双方风险信息不对称对产品交易的影响。我们获得了一些条件，在这些条件下，新的风险最终可以作为证券进行交易。

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.