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ARBITRAGE‐FREE BILATERAL COUNTERPARTY RISK VALUATION UNDER COLLATERALIZATION AND APPLICATION TO CREDIT DEFAULT SWAPS
Author(s) -
Brigo Damiano,
Capponi Agostino,
Pallavicini Andrea
Publication year - 2014
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.1467-9965.2012.00520.x
Subject(s) - collateralization , credit risk , credit derivative , credit default swap , business , valuation (finance) , counterparty , arbitrage , default risk , itraxx , credit valuation adjustment , financial system , financial economics , actuarial science , economics , finance , credit reference
We develop an arbitrage‐free valuation framework for bilateral counterparty risk, where collateral is included with possible rehypothecation. We show that the adjustment is given by the sum of two option payoff terms, where each term depends on the netted exposure, i.e., the difference between the on‐default exposure and the predefault collateral account. We then specialize our analysis to credit default swaps (CDS) as underlying portfolios, and construct a numerical scheme to evaluate the adjustment under a doubly stochastic default framework. In particular, we show that for CDS contracts a perfect collateralization cannot be achieved, even under continuous collateralization, if the reference entity’s and counterparty’s default times are dependent. The impact of rehypothecation, collateral margining frequency, and default correlation‐induced contagion is illustrated with numerical examples.