标题： 双资产期权定价 显示英文标题

标题： Option Pricing of Twin Assets

摘要： 如何对非交易资产的索赔进行定价和对冲在当今期权定价理论中变得越来越重要。 处理这些问题最常见的做法是使用另一个相似或“密切相关”的交易资产或指数来进行对冲。 隐含地，交易者假设在这里，交易资产和非交易资产之间的相关性越高，对冲效果越好。 这引发了这样一个问题，即\textquoteleft{}与\textquoteright{}的相关程度到底有多高。 在本文中，引入了孪生资产的概念，重点讨论两个资产相似的具体含义。 我们的研究结果表明，为了拥有非常相似的资产，例如相同的双胞胎，仅靠高相关性是不够的。 具体来说，指出了两个基本的相似性标准：i) 资产的变异系数，ii) 资产之间的相关性。 从这里，提出了一种衡量资产之间相似性水平的方法，并且其次开发了一个孪生资产的期权定价模型。 所提出的模型使我们能够使用其孪生资产来对一个非交易资产的期权进行定价，但这次我们知道所面临的确切误差水平。 最后，一些数值示例展示了孪生资产根据其相似性水平的表现，以及它们的潜在差异将如何转化为所提出的期权定价模型的 MAPE（平均绝对百分比误差）。 显示英文摘要

摘要： How to price and hedge claims on nontraded assets are becoming increasingly important matters in option pricing theory today. The most common practice to deal with these issues is to use another similar or "closely related" asset or index which is traded, for hedging purposes. Implicitly, traders assume here that the higher the correlation between the traded and nontraded assets, the better the hedge is expected to perform. This raises the question as to how \textquoteleft{}closely related\textquoteright{} the assets really are. In this paper, the concept of twin assets is introduced, focusing the discussion precisely in what does it mean for two assets to be similar. Our findings point to the fact that, in order to have very similar assets, for example identical twins, high correlation measures are not enough. Specifically, two basic criteria of similarity are pointed out: i) the coefficient of variation of the assets and ii) the correlation between assets. From here, a method to measure the level of similarity between assets is proposed, and secondly, an option pricing model of twin assets is developed. The proposed model allows us to price an option of one nontraded asset using its twin asset, but this time knowing explicitly what levels of errors we are facing. Finally, some numerical illustrations show how twin assets behave depending upon their levels of similarities, and how their potential differences will traduce in MAPE (mean absolute percentage error) for the proposed option pricing model.