Valuation of Credit Default Swaptions and Credit Default Index Swaptions

The paper provides simple and rigorous, albeit fairly general, derivations of valuation formulae for credit default swaptions and credit default index swaptions. Results of this work cover as special cases the pricing formulae derived previously by Jamshidian [Finance and Stochastics 8 (2004) 343–371], Pedersen [Quantitative Credit Research (2003)], Brigo and Morini (2005), and Morini and Brigo (2007). Most results presented in this work are completely independent of a particular convention regarding the specification of the fee and protection legs and thus they can also be used for valuation of other credit derivatives that exhibit similar features (for instance, options on CDO tranches). The main tools are a judicious choice of the reference filtration and a suitable specification of the risk-neutral dynamics for the pre-default (loss-adjusted) fair market spread