No Arbitrage Pricing and the Term Structure of Interest Rates

Abstract: This dissertation provides an introduction to the concept of no arbitrage pricing and probability measures. In complete markets prices are arbitrage-free if and only if there exists an equivalent probability measure under which all asset prices are martingales. This is only a slight generalization of the classical fair game hypothesis. The most important limitation of this approach is the requirement of free and public information. Also in order to apply the martingale representation theorem we have to limit our attention to stochastic processes that are generated by Wiener or Poisson processes. While this excludes branching it does include diusion processes with stochastic variances.The result is a non-linear arbitrage pricing theory for nancial assets in general and for bonds in particular. Discounting of future cash ows is performed with zero coupon bonds as well as with short term interest rates (roll-over). In the presence of bonds discounting is an ambiguous operation unless an explicit intertemporal numeraire is dened. However, with the proper denitions we can dispense with the traditional expectations hypothesis about the term structure of interest rates. Arbitrage-free bond prices can be found simply from the fact that these are assets with a nite life and a xed redemption value.