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Pricing vulnerable options with correlated credit risk under jump-diffusion processes when corporate liabilities are random. (English) Zbl 1418.60067

Summary: In this paper, we consider an improved model of pricing vulnerable options with credit risk. We assume that the vulnerable European options not only face default risk, but also face the rare shocks of the underlying assets and the counterparty assets. The dynamics of two correlated assets are modeled as a class of jump diffusion processes. Furthermore, we assume that the dynamic of the corporate liability is a geometric Brownian motion that is related to the underlying asset and the counterparty asset. Under this new framework, we give an explicit pricing formula of the vulnerable European options.

MSC:

60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
60J75 Jump processes (MSC2010)
60J70 Applications of Brownian motions and diffusion theory (population genetics, absorption problems, etc.)
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