A Conditional Valuation Approach for Path-Dependent Instruments

18 Pages Posted: 26 Sep 2005

See all articles by Steven H. Zhu

Steven H. Zhu

Bank of America; MIT Sloan School of Management; Brown University - Division of Applied Mathematics

Dante Lomibao

Morgan Stanley

Date Written: August 2005

Abstract

Credit exposure is the amount a bank can potentially lose in the event that one of its counterparties default. The measurement of exposure on derivative contracts is very important because it is used not only to set up the trading limits but also as an essential input to the bank's economic and regulatory capital calculation. The new Basel guideline has recommanded for a more forward-looking approach (in contrast to the tradtional loan-based method) to the treatment of counterparty exposure to the bank's trading book. We present a value-at-future methodology for calculating the exposures of derivative instruments across the future times. The standard valuation models used to price the instruments for mark-to-market are not applicable for calculating exposure on path-dependent instruments whose value at the future time may depend on either some event at an ealier time or in some cases on the entire path leading to the future date. For such path-dependent instruments, we propose in this paper the notion of conditional valuation, which is based on probabilistic conditional expectation techniques. Using the properties of the Brownian bridges, we show that analytic solutions are readily availabe for the exposure or value-at-future on a number of path-dependent instruments such as barrier options, average options, variance swaps and swap-settled swaptions.

Keywords: Credit risk, Derivative pricing, Brownian bridge and Conditional valuation

JEL Classification: G13

Suggested Citation

Zhu, Steven H. and Lomibao, Dante, A Conditional Valuation Approach for Path-Dependent Instruments (August 2005). Available at SSRN: https://ssrn.com/abstract=806704 or http://dx.doi.org/10.2139/ssrn.806704

Steven H. Zhu (Contact Author)

Bank of America ( email )

Bank of America Tower
One Bryant Park
New York, NY 10036
United States

MIT Sloan School of Management ( email )

100 Main Street
Cambridge, MA 02142
United States

Brown University - Division of Applied Mathematics ( email )

Providence, RI 02912
United States

Dante Lomibao

Morgan Stanley ( email )

1585 Broadway
New York, NY 10036
United States

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