Theoretical and Empirical Studies on the Effect of Derivatives Trading on Economy

通过考虑期货收益的重复投资策略，推导出期货定价的理论公式。利用这一结果，我们对欧元-日元利率期货市场的价格形成进行了实证研究。我们发现：(1)利率期货价格包含了未来远期利率的信息；(2)当周期为5-7天时，实际价格与理论价格的变动是密切相关的；(3)实际价格与理论价格之间的差异在一天内被消除了相当一部分；同时，我们还构建了具有不同投资机会和异质投资者的证券市场的一般均衡模型。首先，我们分析了一个由短视投资者和长视投资者组成的经济模型，我们假设长视投资者的效用函数不取决于他自己的财富，而是取决于个人的总财富。这意味着，有远见的投资者是机构投资者，家庭将部分财富委托给他们进行投资。我们得到的结果是，在这个经济体中，短期利率的波动性必然比由同质投资者组成的经济体中的更大。其次，我们分析了一个由对数公用事业投资者和电力公用事业投资者组成的经济，其中平均投资收益服从平均回归过程。对于最简单的只存在电力公用事业投资者的情况，我们解析地推导出了均衡。其次，利用数值分析的方法，研究了一般情况下模型的平衡点。在此基础上，运用数值分析的方法，分析了衍生工具等新证券的引入所带来的资产种类增加对资产价格的影响。

By considering investment strategy duplicating payoff of futures, we derived a theoretical pricing formula of futures. Using this result, we investigated price formation of Euro-Yen Interest rate futures market empirically. We found (1) prices of interest rate futures contains information about forward rates in the future (2) when taking periods of five to seven days , movement of actual and theoretical prices are closely correlated (3) considerable part of discrepancy between actual and theoretical prices is eliminated within a day.Also, we constructed general equilibrium models of security market with varying investment opportunity and heterogeneous investors. First, we analyzed an economy consisting of myopic investors and long-sighted investors In this model, we assume the utility function of long-sighted investor did not depend on his own wealth, but on total wealth of individuals. This means the long-sighted investor is a institutional investor to which households entrust investment of some of their wealth. We got a result that volatility of short-term interest is necessarily greater in this economy than in an economy consisting of homogeneous investors. Second, we analyzed an economy consisting of log-utility investors and power-utility investors, in which mean return of investment follows a mean reverting process. For the simplest case where only power utility investors exist, we derived analytically the equilibrium. Next, by using numerical analysis, we investigated the equilibrium of the model for a general case. Furthermore, by using numerical analysis, the effect of increase in variety of assets which can be interpreted as introduction of new securities such as derivatives on asset prices was analyzed.