Abstract

HJM one-factor models (including Hull White) have many applications within finance. The risk neutral measure is one of the most common measures to use with HJM models. Since the risk neutral numeraire (money market account) and bond are driven by the same Brownian motion it is frequently assumed that the log correlation between these assets is perfect over an arbitrary interval. Our paper proves that the log correlation over is not perfect and we calculate the correct correlation for one factor HJM models. Finally using Monte Carlo Simulation we demonstrate our correlations are correct and using perfect correlation can lead to significant erroneous results.

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