On Pricing Risky Loans and Collateralized Fund Obligations

19 Pages Posted: 28 Jan 2010 Last revised: 30 Jan 2011

See all articles by Ernst Eberlein

Ernst Eberlein

University of Freiburg

Hélyette Geman

University of London - Economics, Mathematics and Statistics

Dilip B. Madan

University of Maryland - Robert H. Smith School of Business

Date Written: July 7, 2009

Abstract

Loan spreads are analysed for two types of loans. The first takes losses at maturity only; the second one follows the formulation of CFOs (Collateralized Fund Obligations), with losses registered over the lifetime of the contract. In both cases, the implementation requires the choice of a process for the underlying asset value and the identification of the parameters. The parameters of the process are inferred from the option volatility surface by treating equity options as compound options with equity itself being viewed as an option on the asset value with a strike set at the debt level following Merton (1974). Using data on General Motors stock during the year 2002/2003, we show that the use of spectrally negative Lévy processes is capable of delivering realistic spreads without inflating debt levels, deflating debt maturities or deviating from the estimated probability laws.

Keywords: first passage times, Merton compound option model, spectrally negative process

JEL Classification: G1, G12, G13

Suggested Citation

Eberlein, Ernst and Geman, Helyette and Madan, Dilip B., On Pricing Risky Loans and Collateralized Fund Obligations (July 7, 2009). Robert H. Smith School Research Paper No. RHS 06-145, Available at SSRN: https://ssrn.com/abstract=1540810 or http://dx.doi.org/10.2139/ssrn.1540810

Ernst Eberlein

University of Freiburg ( email )

Department of Mathematical Stochastics
Eckerstrasse 1
D-79104, Freiburg
Germany
++49 761 203 5660 (Phone)
++49 761 203 5661 (Fax)

Helyette Geman

University of London - Economics, Mathematics and Statistics ( email )

Malet Street
London, WC1E 7HX
United Kingdom

Dilip B. Madan (Contact Author)

University of Maryland - Robert H. Smith School of Business ( email )

College Park, MD 20742-1815
United States
301-405-2127 (Phone)
301-314-9157 (Fax)

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