An SGBM-XVA demonstrator: a scalable Python tool for pricing XVA

Abstract

In this work, we developed a Python demonstrator for pricing total valuation adjustment (XVA) based on the stochastic grid bundling method (SGBM). XVA is an advanced risk management concept which became relevant after the recent financial crisis. This work is a follow-up work on Chau and Oosterlee in (Int J Comput Math 96(11):2272–2301, 2019), in which we extended SGBM to numerically solving backward stochastic differential equations (BSDEs). The motivation for this work is basically two-fold. On the application side, by focusing on a particular financial application of BSDEs, we can show the potential of using SGBM on a real-world risk management problem. On the implementation side, we explore the potential of developing a simple yet highly efficient code with SGBM by incorporating CUDA Python into our program.

Towards control of dam and reservoir systems with forward–backward stochastic differential equations driven by clustered jumps

“…A massive computational architecture will then be needed. 41 Another numerical issue to be considered in future is the choice of basis. This is a key issue when computing BSDEs and related stochastic optimization models.…”

“…Using a soft‐computing technique 85 or a penalization method 86 may mitigate the singularity, but convergence with respect to penalty and hyper parameters have to be carefully analyzed. A massive computational architecture will then be needed 41 …”

“…37,38 The stochastic maximum principle, by contrast, reduces resolving a control problem to solving a system of forward-backward stochastic differential equations (FBSDEs) applicable to higher dimensions. [39][40][41] Another difference between the two approaches is that simulating both control and controlled dynamics is naturally carried out in the latter, while they must be addressed separately in the former. We focus on the maximum principle because our interests are in both optimal control and controlled dynamics.…”

“…They invoke the symmetry E = B, J = C, K = G. In summary, the system of ODEs to be solved contains nine equations subject to the homogenous terminal condition 0 at t = T, which are (33)- (41). The proof is then completed.…”

“…These equations can only reasonably manage problems having one or two state variables 34–36 unless a special approximation technique to deal with the curse of dimensionality is used 37,38 . The stochastic maximum principle, by contrast, reduces resolving a control problem to solving a system of forward–backward stochastic differential equations (FBSDEs) applicable to higher dimensions 39–41 . Another difference between the two approaches is that simulating both control and controlled dynamics is naturally carried out in the latter, while they must be addressed separately in the former.…”