Valuation of credit default swaps and swaptions (Q1776007)

This paper aims to develop a valuation framework for single-name credit derivatives that combine an arbitrary numeraire with a general conditional probability of survival arising from a subfiltration. The author starts from first financial principles and proceeds in a self-contained manner within a general probabilistic framework. New concepts and terminology are introduced to facilitate the discussion and to especially highlight the views on cash flow modelling and change of numeraire in presence of default. New concepts and results are presented for the evaluation of credit swaptions. A new formula on fractional recovery of a pre-default value is derived. The Black-Scholes formula for credit default swaptions is shown to serve as a least-squares approximation to the general case.