On securitization and equilbrium pricing in incomplete markets

在过去的几十年里，出现了一系列新的金融产品，其中一些是写在非流通下属身上的。这些金融产品是一种称为证券化的过程的产物，该过程将不可交易的风险转化为可交易的金融证券。因此，其结果是一种新的金融产品，可以被视为将不可交易风险转移到金融市场的工具。不可交易风险的一个例子是天气风险，这影响了许多企业。随之而来的自然问题是：这种金融产品的公平价格应该是多少？一种可能性是均衡价格。均衡价格是市场出清的价格，即市场参与者在金融产品的需求与供应相等的情况下采取最优行动的价格。均衡定价得到了广泛的研究，特别是在完全市场(完全风险转移是可能的市场)。在现实中，市场是不完整的(原因有很多：流动性不足、交易限制、特殊风险等)。这使得分析变得更加复杂。在这个项目中，我们重点研究了对市场参与者的投资组合施加风险限制的模型，并分析了特殊风险对均衡价格的影响。通过实施风险限制来减少风险敞口是新的风险管理规则(巴塞尔协议I和巴塞尔协议II)的一部分。特殊风险是指由于特定证券和/或市场参与者的独特情况而导致价格变化的风险。尽管在不完全市场中有均衡定价的例子，但仍然需要一个更好的数学框架来描述和计算均衡价格。该项目的智力优势是数学和金融框架，它允许对均衡价格进行数字计算。此外，它还建议应如何设计金融产品，以便有效地减轻和转移风险。该项目更广泛的影响是，所提出的方法可以推广到其他金融经济模型。更具体地说，我们的方法可以用来分析不完全市场范式下资产收益率与总消费之间的关系。

Over the last few decades an array of new financial products have emerged, some of them written on non-tradable underlings. These financial products are the output of a process called securitization that transforms non-tradable risks into tradable financial securities. Thus, the result is a new financial product which can be regarded as a vehicle to transfer non-tradable risk to financial markets. One example of non-tradable risk is weather risk and this affects many businesses. The natural question which arises is: What should be the fair price to be charged for such a financial product? One possibility is the equilibrium price. Equilibrium prices are the prices for which the market clears, that is the market participants act optimally in such a way that the demand for the financial product equal the supply. Equilibrium pricing has been widely studied especially in complete markets (markets in which perfect risk transfer is possible). In reality markets are incomplete (for many reasons: illiquidity, trading constraints, idiosyncratic risk etc.) and this renders the analysis more complicated. In this project we focus on models where risk limits are imposed on market participants portfolios and we analyze the effect of idiosyncratic risk on equilibrium prices. Reducing the risk exposure by imposing risk limits is part of the new risk management regulations (Basel I and II accords). Idiosyncratic risk is the risk of price change due to the unique circumstances of a specific security and/or market participants. Although there are available examples of equilibrium pricing in incomplete markets, there is still need for a better mathematical framework for characterizing and computing the equilibrium prices. The project intellectual merit is the mathematical and financial framework which allows for numerical computation of equilibrium prices. Further it suggests how the financial products should be designed in order to be efficient in mitigating and transferring risk. The broader impact of this project is that the method proposed can be extended to other financial economic models. More specifically our methodology can be used to analyze the relationship between rates of assets return and aggregate consumption in incomplete market paradigms.