Arrow -Debreu prices implicit in the term structure of interest rates: Theory and tests
The focus of this thesis is twofold. First, the development of a model for the determination of prices of Arrow-Debreu securities implicit in the term structure of interest rates. Second, the implementation of the model, both in a simulated environment and using market data, and the execution of tests of the various aspects thereof. In addition to the wealth of information contained in these prices, a further merit of identifying Arrow-Debreu prices is that complex state-contingent security valuation is significantly simplified. In particular, in an arbitrage-free environment, the price of a complex state-contingent security may be expressed as a weighted sum of Arrow-Debreu prices, where the weights correspond to the state-contingent payoffs of the complex security.
The model developed in this thesis exploits the information content in the current term structure to infer prices of Arrow-Debreu securities. In a complete, arbitrage-free framework, the value of a bond is modeled in terms of the pricing kernel and the transition density function of the spot interest rate process. The underlying concept for the implementation of the model is that a set of bond prices are taken from the current term structure and the transition density function is estimated from historical term structure data, using a nonparametric estimation technique. The pricing kernels are subsequently reverse engineered from the valuation expressions. The resulting pricing kernels maintain associated Arrow-Debreu prices that are unique, consistent with the initial term structure, and, furthermore, incorporate of the observed historical behavior of the term structure. In addition, the prices may be calibrated using the entire term structure of interest rates. The implementation of the model reveals that the Arrow-Debreu prices clearly manifest the characteristics of the underlying interest rate. The results indicate that the discretization of the interest rate process significantly affects the accuracy with which the prices embody the evolution of the term structure and exhibit the features of the interest rate process. Furthermore, the prices are considerably more sensitive to the transition density of the underlying interest rate than to a change in the term structure.
0310: Business community