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Derivatives Pricing under Bilateral Counterparty Risk
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  and Duffie and Singleton . The probabilistic valuation formulas derived under this framework cannot be usually used for practical pricing due to their recursive path-dependencies. Instead, finite-difference methods are used to solve the quasi-linear partial differential equations that equivalently represent the claim value function. By imposing restrictions on the dynamics of the risk-free rate and the stochastic intensities of ...