Essays on capital markets
This dissertation is comprised of three essays. The first essay is an empirical examination into determining which spot rate processes are well suited to capturing the dynamics of the term structure of interest rates. The second essay explores a relatively new 'Price Deflator' approach to modeling the term structure of interest rates. The final essay shows how one can recover the market's attitude towards risk from the prices of S&P 500 options.
In the first essay, a one factor partial equilibrium model of the term structure is presented. The model shows that changes in the short-term rate are a function of the yield curve at the origin, the market price of risk, and a diffusion coefficient equal to the change in volatility of bond returns. The results for the U.S. using Euro-currency yield data show that the square root volatility process is the best model. Also, it appears that the market price of risk should be allowed to vary with the level of interest rates.
The second essay shows that any model of the term structure is in essence a model of the behavior of the marginal utility of consumption of the representative investor, which we refer to as the price deflator. Here, the instantaneous risk-free interest rate is shown to be equal to the expected growth rate of the price deflator. We also obtain solutions for price deflators that are implied by some common spot rate processes and demonstrate how the approach can be used within a Monte Carlo framework to price an interest rate contingent claim.
In the third essay, the insights of Varian (1988) are used to derive the Pratt-Arrow measures of absolute and relative risk aversion. The results indicate that during the sample period option traders displayed increasing absolute risk aversion and increasing relative risk aversion. We also track the markets risk aversion over time by creating a "Risk Aversion Index." For the six month period between June and November 1995 we find that the market's risk appetite gradually increased.
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