Pricing and Hedging of Illiquid Asset Derivatives

点击翻译按钮获取中文摘要

In this work, we consider pricing and hedging of the so-called illiquid asset derivatives in which the underlying assets are untraded such as weather derivatives or insurances, provide the methodology to formulate and solve these problems in a unified framework, and demonstrate empirical analysis using real data. First, we discuss the case of weather derivatives as a benchmark, where the underlying index is defined by the temperature (which may be useful for exchange market trades) or the wind speed (which may be used with wind power trades). In particular, we propose weather derivatives based on prediction errors of the wind speed to hedge the loss caused by prediction errors of the wind power output, and illustrate the hedge effect of the proposed derivatives. Then, we formulate a minimum variance hedging problem for contingent claims whose underlyings are untraded using liquidly traded assets, and provide a solution using additive models. A methodology for computing the prices of illiquid asset derivatives using the minimum market price of risk martingale measure is also demonstrated. Finally, we apply our proposed technique for hedging the payoff of European options in which the underlying index is given by a market index using several liquidly traded stocks. We also show how to construct an optimal portfolio using cointegrated pairs of stock and demonstrate case studies involving a number of pairs chosen from Nikkei 225 stocks.