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

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

Discovering a Dihydrofluorescein Analogue as a Promising Fluorescence Substrate to HRP

Horseradish peroxidase (HRP) combined with its fluorescence substrates is attracting increasing attention for biochemical analysis. Amplex red is the most widely used fluorescence substrate to HRP;however, it suffers from some drawbacks, such as nonspecific responsiveness toward carboxylesterases. Discovering a new small molecular fluorescence substrate with improved sensitivity and selectivity for HRP is thus desired. Herein, three dihydrofluorescein derivatives (DCFHs) are presented to serve as HRP substrates through fluorescence turn-on methods. The most promising one, 2,7-dichloro-9-(2-(hydroxymethyl)phenyl)-9H-xanthene-3,6-diol (DCFH-1), exhibited excellent sensitivity in the detection of HRP. Moreover, DCFH-1 does not respond to carboxylesterase, thus holding advantages over Amplex red. In the further study, the detection reagent in the commercial ELISA kits was replaced with DCFH-1 to establish a new fluorescence ELISA, which works very well in the quantification of inflammatory cytokine biomarkers from in vitro models.

Total value adjustment of Bermudan option valuation under pure jump Lévy fluctuations.

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 the Heston [B. Salvador and C. W. Oosterlee, Appl. Math. Comput. 391, 125489 (2020)] and Bates [L. Goudenège et al., Comput. Manag. Sci. 17, 163-178 (2020)] models. In this work, a widely used pure jump Lévy process, the Carr-Geman-Madan-Yor process has been considered for pricing a Bermudan option with various value adjustments. Under a pure jump Lévy process, the value of derivatives satisfies a fractional partial differential equation (FPDE). Therefore, we construct a method that combines Monte Carlo with a finite difference of FPDE to find the numerical approximation of exposure and compare it with the benchmark Monte Carlo simulation and Fourier-cosine series method. We use the discrete energy estimate method, which is different from the existing works, to derive the convergence of the numerical scheme. Based on the numerical results, the XVA is computed by the financial exposure of the derivative value.