Representation of Zero Coupon Bond Prices in Terms of Two-Parameter Brownian Martingales Hayri Körezlioğlu
While considering the representation of zero coupon bond prices in terms of the random fields approach developed by Kennedy and Goldstein, this work treats the case where these random fields are generated by a Brownian sheet. Most works using random fields are based on the extention of the Heath-Jarrow-Morton Model and establish the compatibility condition between drift and diffusion terms under the risk neutral probability. The main purpose of this work is to start from models expressed in terms of the working probability (the historical probability) by presenting the adequate representation theorem for the Radon-Nikodym density of the risk neutral probability, and then to look for the compatibility condition under the historical probability by using the techniques of stochastic calculus for two-parameter Brownian martingales.