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The Potential Future Exposure of Path-dependent Instruments: Comment on Lomibao-Zhu's approach

by Chuang Yi of the Royal Bank of Canada

July 30, 2010

Abstract: Lomibao and Zhu (2005) proposed a conditional valuation approach for simulating the Expected Exposure (EE) profile of path-dependent instruments. Since their approach simulates Value at Future (VaF) instead of future Mark-to-Market (MtM) value, it is inappropriate to use for generating the Potential Future Exposure (PFE) pro le. In this article, we propose a new and simple methodology to correctly simulate the PFE pro le of path-dependent instruments. We also suggest a modified Lomibao-Zhu (LZ) approach to improve their simulation algorithm. For the numerical example on an up-and-out call option, we nd that the LZ approach underestimates the upper quantiles and overestimates the lower quantiles of the PFE.

Keywords: Potential Future Exposure, Expected Exposure, Path-dependent Instruments, Counterparty Credit Risk, First Passage Time.

Previously titled: "Future Mark-to-Market Value of Path-dependent Instruments"

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