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...

In this paper, we give a way to calculate a option implied volatility curve in closed form via the well known quadratic root formula. The closed form expression has 3 free parameters, which parsimoniously govern the assumed dynamics of implied volatility under forward swap measure. Preliminary...