No‐Armageddon Measure for Arbitrage‐Free Pricing of Index Options in a Credit Crisis

21 Pages Posted: 23 Aug 2011

See all articles by Massimo Morini

Massimo Morini

Banca IMI; Bocconi University

Damiano Brigo

Imperial College London - Department of Mathematics

Date Written: October 2011

Abstract

In this work, we consider three problems of the standard market approach to credit index options pricing: the definition of the index spread is not valid in general, the considered payoff leads to a pricing which is not always defined, and the candidate numeraire for defining a pricing measure is not strictly positive, which leads to a nonequivalent pricing measure. We give a solution to the three problems, based on modeling the flow of information through a suitable subfiltration. With this we consistently take into account the possibility of default of all names in the portfolio, that is neglected in the standard market approach. We show on market inputs that, while the pricing difference can be negligible in normal market conditions, it can become highly relevant in stressed market conditions, like the situation caused by the credit crunch.

Keywords: credit index options, subfiltrations, credit crunch, default correlation, market models, arbitrage

Suggested Citation

Morini, Massimo and Brigo, Damiano, No‐Armageddon Measure for Arbitrage‐Free Pricing of Index Options in a Credit Crisis (October 2011). Mathematical Finance, Vol. 21, Issue 4, pp. 573-593, 2011. Available at SSRN: https://ssrn.com/abstract=1914915 or http://dx.doi.org/10.1111/j.1467-9965.2010.00444.x

Massimo Morini (Contact Author)

Banca IMI ( email )

Corso Matteotti 6
20121 Milano, 20100
Italy

Bocconi University ( email )

Via Sarfatti, 25
Milan, MI 20136
Italy

Damiano Brigo

Imperial College London - Department of Mathematics ( email )

South Kensington Campus
London SW7 2AZ, SW7 2AZ
United Kingdom

HOME PAGE: http://www.imperial.ac.uk/people/damiano.brigo

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