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

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

Rolling Adjoints: Fast Greeks along Monte Carlo scenarios for early-exercise options

In this paper we extend the stochastic grid bundling method (SGBM), a regress-later based Monte Carlo scheme for pricing early-exercise options, with an adjoint method to compute in a highly efficient manner sensitivities along the paths, with reasonable accuracy. With the ISDA standard initial margin model being adopted by the financial markets, computing sensitivities along scenarios is required to compute quantities like the margin valuation adjustment

Rolling Adjoints: Fast Greeks along Monte Carlo scenarios for early-exercise options

In this paper we extend the Stochastic Grid Bundling Method (SGBM), a regress-later Monte Carlo scheme for pricing early-exercise options, with an adjoint method to compute in a highly efficient manner the option sensitivities (the “Greeks”) along the Monte Carlo paths, with reasonable accuracy. The path-wise SGBM Greeks computation is based on the conventional path-wise sensitivity analysis, however, for a regress-later technique. The resulting sensitivities at the end of the monitoring period are implicitly rolled over into the sensitivities of the regression coefficients of the previous monitoring date. For this reason, we name the method Rolling Adjoints, which facilitates Smoking Adjoints [M. Giles, P. Glasserman, Smoking adjoints: fast Monte Carlo Greeks, Risk 19 (1)(2006)88–92] to compute conditional sensitivities along the paths for options with early-exercise features

Stochastic grid bundling method for backward stochastic differential equations

In this work, we apply the Stochastic Grid Bundling Method (SGBM) to numerically solve backward stochastic differential equations. The SGBM algorithm is based on conditional expectations approximation by means of bundling of Monte Carlo sample paths and a local regress-later regression within each bundle. The basic algorithm for solving backward stochastic

GPU acceleration of the Seven-League Scheme for large time step simulations of stochastic differential equations

Monte Carlo simulation is widely used to numerically solve stochastic differential equations. Although the method is flexible and easy to implement, it may be slow to converge. Moreover, an inaccurate solution will result when using large time steps. The Seven League scheme, a deep learning-based numerical method, has been proposed to address these issues. This paper generalizes the scheme regarding parallel computing, particularly on Graphics Processing Units (GPUs), improving the computational speed

GeantV: Results from the prototype of concurrent vector particle transport simulation in HEP

Full detector simulation was among the largest CPU consumer in all CERN experiment software stacks for the first two runs of the Large Hadron Collider (LHC). In the early 2010's, the projections were that simulation demands would scale linearly with luminosity increase, compensated only partially by an increase of computing resources. The extension of fast simulation approaches to more use cases, covering a larger fraction of the simulation budget, is only part of the solution due to intrinsic precision limitations. The remainder corresponds to speeding-up the simulation software by several factors, which is out of reach using simple optimizations on the current code base. In this context, the GeantV R&D project was launched, aiming to redesign the legacy particle transport codes in order to make them benefit from fine-grained parallelism features such as vectorization, but also from increased code and data locality. This paper presents extensively the results and achievements of this R&D, as well as the conclusions and lessons learnt from the beta prototype.Comment: 34 pages, 26 figures, 24 table