Total value adjustment for a stochastic volatility model. A comparison with the Black–Scholes model
نویسندگان
چکیده
• The total value adjustment (XVA) under the Heston model is studied for European and American options . Linear nonlinear partial differential equations have been deduced modelling XVA. Several numerical methods suitable boundary conditions are proposed in order to solve obtained PDEs A comparison with Black-Scholes made results. Expected exposures models also computed. Since 2007/2008 financial crisis, should be included when pricing derivatives. In present paper, derivative values of priced where we take into account counterparty risk. Whereas considering risk already dynamics [1], here novel contribution introduction stochastic volatility resulting a type equation solved. We derive modeling XVA assumed. For both options, linear problem deduced. obtain solution, appropriate considered. addition, method characteristics time discretization combined finite element spatial has implemented. expected exposure potential future computed compare current associated Black–Scholes model.
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ژورنال
عنوان ژورنال: Applied Mathematics and Computation
سال: 2021
ISSN: ['1873-5649', '0096-3003']
DOI: https://doi.org/10.1016/j.amc.2020.125489