We derive a partial integro differential equation (PIDE) which relates the price of a calendar spread to the prices of butterfly spreads and the functions describing the evolution of the process. These evolution functions are the forward local variance rate and a new concept called the forward...

We consider risk-neutral valuation of a contingent claim under bilateral counterparty risk in a reduced-form setting similar to that of Duffie and Huang [1996] and Duffie and Singleton [1999]. The probabilistic valuation formulas derived under this framework cannot be usually used for practical...