  During the COVID-19 pandemic, many institutions have announced that their
counterparties are struggling to fulfill contracts.Therefore, it is necessary
to consider the counterparty default risk when pricing options. After the 2008
financial crisis, a variety of value adjustments have been emphasized in the
financial industry. The total value adjustment (XVA) is the sum of multiple
value adjustments, which is also investigated in many stochastic models such as
Heston and Bates models. In this work, a widely used pure jump L\'evy process,
the CGMY process has been considered for pricing a Bermudan option with various
value adjustments. Under a pure jump L\'evy process, the value of derivatives
satisfies a fractional partial differential equation(FPDE). Therefore, we
construct a method which combines Monte Carlo with finite difference of FPDE
(MC-FF) to find the numerical approximation of exposure, and compare it with
the benchmark Monte Carlo-COS (MC-COS) method. We use the discrete energy
estimate method, which is different with the existing works, to derive the
convergence of the numerical scheme.Based on the numerical results, the XVA is
computed by the financial
