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NO‐ARMAGEDDON MEASURE FOR ARBITRAGE‐FREE PRICING OF INDEX OPTIONS IN A CREDIT CRISIS
Author(s) -
Morini Massimo,
Brigo Damiano
Publication year - 2011
Publication title -
mathematical finance
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.98
H-Index - 81
eISSN - 1467-9965
pISSN - 0960-1627
DOI - 10.1111/j.1467-9965.2010.00444.x
Subject(s) - numéraire , economics , index (typography) , arbitrage , measure (data warehouse) , rational pricing , financial economics , stochastic game , econometrics , microeconomics , capital asset pricing model , computer science , database , world wide web
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.