On securitization and equilbrium pricing in incomplete markets

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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.