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Arbitrage-Free Pricing of Credit Index Options: The No-Armageddon Pricing Measure and the Role of Correlation after the Subprime Crisis

25 Pages Posted: 3 Jan 2008 Last revised: 22 Jun 2016

Damiano Brigo

Imperial College London - Department of Mathematics

Massimo Morini

Banca IMI; Bocconi University

Date Written: December 1, 2007

Abstract

In this work we consider three problems of the standard market approach to the pricing of credit index options: the definition of the index spread is not valid in general, the payoff considered leads to a pricing which is not always defined, and the candidate numeraire to define a pricing measure is not strictly positive, which would lead to an inequivalent pricing measure.

We give to the three problems a general mathematical solution, based on a novel way of modelling the flow of information through the definition of a new subfiltration. Using this subfiltration, we take into account consistently the possibility of default of all names in the portfolio, that is neglected in the standard market approach. We show that, while this mispricing can be negligible for standard options in normal market conditions, it can become highly relevant for different options or in stressed market conditions.

In particular, we show on 2007 market data that after the subprime credit crisis the mispricing of the market formula compared to the no arbitrage formula we propose has become financially relevant even for the liquid Crossover Index Options.

Keywords: credit option, subprime, correlation, market models, arbitrage

JEL Classification: C63,G13

Suggested Citation

Brigo, Damiano and Morini, Massimo, Arbitrage-Free Pricing of Credit Index Options: The No-Armageddon Pricing Measure and the Role of Correlation after the Subprime Crisis (December 1, 2007). Available at SSRN: https://ssrn.com/abstract=1080064 or http://dx.doi.org/10.2139/ssrn.1080064

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

Massimo Morini (Contact Author)

Banca IMI ( email )

Corso Matteotti 6
20121 Milano, 20100
Italy

Bocconi University ( email )

Via Sarfatti, 25
Milan, MI 20136
Italy

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