Pricing and Hedging of Illiquid Asset Derivatives

在这项工作中，我们考虑了所谓的非流动性资产衍生品的定价和套期保值，其中标的资产是未交易的，如天气衍生品或保险，提供了在统一框架下制定和解决这些问题的方法，并使用真实数据进行了实证分析。首先，我们讨论以天气衍生品作为基准的情况，其中标的指数由温度(可能对交易所市场交易有用)或风速(可能用于风电交易)定义。特别是，我们提出了基于风速预测误差的天气衍生品来对冲风电发电量预测误差造成的损失，并举例说明了所提衍生品的套期保值效果。然后，我们建立了未定权益的最小方差套期保值问题，并利用加性模型给出了该问题的解。文中还给出了一种用最小市场风险值来计算非流动性资产衍生品价格的方法。最后，我们将我们提出的技术应用于套期保值欧式期权的收益，在欧式期权中，标的指数由使用几只流动性交易的股票的市场指数给出。我们还展示了如何使用协整的股票对构建最优投资组合，并演示了涉及从日经225股票中选择的一些股票对的案例研究。

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.