Total Value Adjustment of Multi-Asset Derivatives under Multivariate CGMY Processes

Counterparty credit risk (CCR) is a significant factor that financial institutions have to consider in today’s context, and the COVID-19 pandemic military conflicts worldwide heightened concerns about potential default risk. In this work, we investigate changes value of derivatives due counterparty risk, i.e., total adjustment (XVA). We perform XVA for multi-asset option based on multivariate Carr–Geman–Madan–Yor (CGMY) processes, which can be applied wider range derivatives, such as basket options, rainbow index options. For numerical methods, use Monte Carlo method combination with alternating direction implicit (MC-ADI) two-dimensional Fourier cosine expansion (MC-CC) find exposure make adjustments derivatives.