Pricing derivatives on graphics processing units using Monte Carlo simulation

2012 ◽  
Vol 26 (9) ◽  
pp. 1679-1697 ◽  
Author(s):  
L.A. Abbas-Turki ◽  
S. Vialle ◽  
B. Lapeyre ◽  
P. Mercier
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Graphics Processing Units ◽  
Graphics Processing

scholarly journals XVA PRINCIPLES, NESTED MONTE CARLO STRATEGIES, AND GPU OPTIMIZATIONS

2018 ◽  
Vol 21 (06) ◽  
pp. 1850030 ◽  
Author(s):  
LOKMAN A. ABBAS-TURKI ◽  
STÉPHANE CRÉPEY ◽  
BABACAR DIALLO
Keyword(s):  
Monte Carlo ◽  
Interest Rate ◽  
Outer Layer ◽  
Graphics Processing Units ◽  
Lower Layer ◽  
Credit Derivatives ◽  
Square Root ◽  
Root Number ◽  
Graphics Processing ◽  
Gpu Implementation

We present a nested Monte Carlo (NMC) approach implemented on graphics processing units (GPUs) to X-valuation adjustments (XVAs), where X ranges over C for credit, F for funding, M for margin, and K for capital. The overall XVA suite involves five compound layers of dependence. Higher layers are launched first, and trigger nested simulations on-the-fly whenever required in order to compute an item from a lower layer. If the user is only interested in some of the XVA components, then only the sub-tree corresponding to the most outer XVA needs be processed computationally. Inner layers only need a square root number of simulation with respect to the most outer layer. Some of the layers exhibit a smaller variance. As a result, with GPUs at least, error-controlled NMC XVA computations are doable. But, although NMC is naively suited to parallelization, a GPU implementation of NMC XVA computations requires various optimizations. This is illustrated on XVA computations involving equities, interest rate, and credit derivatives, for both bilateral and central clearing XVA metrics.

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