Near Real-Time Risk Simulation of Complex Portfolios on Heterogeneous Computing Systems with OpenCL
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1 Near Real-Time Risk Simulation of Complex Portfolios on Heterogeneous Computing Systems with OpenCL Javier Alejandro Varela, Norbert Wehn Microelectronic Systems Design Research Group University of Kaiserslautern, Germany Javier Alejandro Varela, Norbert Wehn Near Real-Time Risk Simulation of Complex Portfolios on Heterogeneous Computing Systems with OpenCL. In Proceedings of IWOCL 17, Toronto, Canada, May 16-18, 2017, 10 pages. DOI:
2 Summary I. Overview: Portfolio Risk II. OpenCL + Workload Allocation III. Algorithmic Optimizations / Numerical Scheme IV. Minimizing Device Global Memory V. Conclusion 2
3 Summary I. Overview: Portfolio Risk II. OpenCL + Workload Allocation III. Algorithmic Optimizations / Numerical Scheme IV. Minimizing Device Global Memory V. Conclusion 3
4 Portfolio Composition: Overview: Portfolio Risk Stocks (S 1, S 2 ) Corporate Bond Foreign Currency Options: European Asian (on S 1 ) What is the RISK at which this portfolio is exposed? European Barrier (on S 2 ) American Vanilla (on S 1 ) American 2D Max (on S 1,S 2 ) Cash (no simulation required) 4
5 Overview: Portfolio Risk What is Value-at-Risk (VaR)? I am α percent certain there will not be a loss of more than VaR USD in the next N days (Hull, Options Futures and Other Derivatives). VaR of level α Portfolio loss function L α - quantile Var α L t+n inf l R P L t+n > l Loss empirical distribution function F L l P L t+n > l where α is as high as 95%, 99%, 99.5%. Industry standard (Basel II and Basel III) What is Expected Shortfall (ES or cvar)? ES α L t+n 1 1 α α (1 α) = inf l R F L l α 1 Var γ L t+n dγ 5
6 Overview: Portfolio Risk How to compute Value-at-Risk (VaR)? 1. Historical simulation: describes future changes based on empirical distribution of observed past data. 2. Variance-Covariance method: first-order approximation of the loss function L. assumes normally distributed returns. 3. Monte Carlo (MC) method: simulates the loss function L. Does not rely on historical data. No need for approximation. No assumption of a normal distribution. Computationally intensive problem Heterogeneous problem (many different algorithms involved) Exploit OpenCL 6
7 Overview: Portfolio Risk Portfolio Simulation: External Internal Stocks (S 1, S 2 ) Corporate Bond Foreign Currency Options: European Asian (on S 1 ) European Barrier (on S 2 ) American Vanilla (on S 1 ) American 2D Max (on S 1,S 2 ) Cash (no simulation required) Two Models: Black-Scholes (BS) Heston t t + N 7
8 Overview: Portfolio Risk 252 steps (1008 steps for european Barrier) External Internal 32k paths 32k paths 1 step (BS model) 4 steps (Heston model) t t + N Single-precision floating point operations 8
9 Sequence of steps: Overview: Portfolio Risk Asset 1 Asset N P&L portf Sorted P&L portf Simulated Scenarios (.h 1 ) + + (.h N ) Portf. value - today = Sorting (ascending order) VaR ES (mean) where: h i = holding of Asset i (for i=1,,n) 9
10 Summary I. Overview: Portfolio Risk II. OpenCL + Workload Allocation III. Algorithmic Optimizations / Numerical Scheme IV. Minimizing Device Global Memory V. Conclusion 10
11 OpenCL + Workload Allocation Asset 1 Asset N P&L portf Sorted P&L portf Simulated Scenarios (.h 1 )+ +( Portf..h N ) - value = today Sorting (ascending order) VaR ES (mean) where: h i = holding of Asset i (for i=1,,n) SuperMicro Superserver 7048GR-TR Intel Xeon E v3 CPU (Host) OpenCL Devices: CPU Xeon PHI (dual-socket motherboard) Intel Xeon E v3 Intel Xeon Phi 7120P Individual OpenCL Command Queues GPU 0 GPU 1 (shared PCIe link) Nvidia K80 11
12 OpenCL + Workload Allocation ILP formulation (Matlab s intlinprog) min x f T. x subject to x i are integers A. x b A eq. x b eq lb x lu Set of Kernels: K = k Stocks2Corr, k Bond, k F.Currency, Set of Devices: D = d CPU, d PHI, d GPU0, Binary decision variables: x k,d, where: 0 x k,d 1 Total runtime: x T, where: 0 x T 12
13 OpenCL + Workload Allocation ILP formulation (continued) Constraints: Single assignment of each kernel among all devices: k K, d D x k,d = 1 Device runtime: d D, k K t k,d. x k,d x T 0 Device global memory: d D, m k,d. x k,d M d k K Cost function: f T. x = x T 13
14 OpenCL + Workload Allocation Workload Allocation with ILP 1) Profile each kernel on every device 2) ILP CPU (Host) OpenCL Devices: CPU Xeon PHI GPU 0 GPU 1 14
15 OpenCL + Workload Allocation Kernels Runtime CPU (Host) OpenCL Devices: CPU Xeon PHI GPU 0 GPU 1 15
16 Summary I. Overview: Portfolio Risk II. OpenCL + Workload Allocation III. Algorithmic Optimizations / Numerical Scheme IV. Minimizing Device Global Memory V. Conclusion 16
17 Algorithmic Optimizations Random Numbers Reuse Approach Nested MC-Based Risk Measurement of Complex Portfolios: Acceleration and Energy Efficiency S. Desmettre, R. Korn, J. Varela, N. Wehn. Risks Vol. 4, no. 4, pages 36, October, (All parameters in the internal simulation remain constant) Incorrect Different option prices Correct 17
18 Algorithmic Optimizations Paths-Reuse Approach (+Normalization) (Note: All parameters in the internal simulation remain constant) 18
19 Algorithmic Optimizations Paths-Reuse: European-style Options 0Path Values [USD] Normalized S0=1 Kernel P1 Internal Simulation Maturity Maturity Max Value / Path Min Value / Path Simulation Steps Extracted Stochastic Information Option Price [USD] Kernel P2 Information-Reuse Approach 19
20 Algorithmic Optimizations Paths-Reuse: American-style Options Kernel P1 Internal Simulation 0Path Values [USD] Normalized S0=1 Simulation Steps Maturity Option price [USD] Kernel P2 Backward Step-By-Step Decision Process (Regression) 20
21 Algorithmic Optimizations Runtime: Paths-/Info-Reuse (under BS model) 4.5x 6.8x 1. RNs-reuse 2. Info-reuse 3. Paths-reuse 1000x 1000x European Options American Options 21
22 Algorithmic Optimizations Runtime: Paths-/Info-Reuse (under BS model) 9.2x 12.0x 1. RNs-reuse 2. Info-reuse 3. Paths-reuse 1500x 2500x European Options American Options 22
23 Numerical Scheme Interpolation: Kernel: AmericanVanillaBT AmericanVanillaLS P1 P2 Fast, accurate and inelegant valuation of American options. Adriaan Joubert and L.C.G. Rogers In Proceedings of the Numerical Methods Workshop at the Isaac Newton Institute, April 1995, L.C.G. Rogers and D. Talay (Eds.). CambridgeS. Kernel: Interpolate 1D Option Price [USD] Extension: American2DMax P1 P2 Interpolate 2D Option Price [USD] 23
24 Numerical Scheme Runtime: Interpolation (American-style Options) 10000x 1. RNs-reuse 2. Interpolation+Paths-reuse 3. Interpolation+Surface Load&Transfer 1000x
25 Summary I. Overview: Portfolio Risk II. OpenCL + Workload Allocation III. Algorithmic Optimizations / Numerical Scheme IV. Minimizing Device Global Memory V. Conclusion 25
26 Minimizing Device Global Memory Device Global Memory Cost (Kernels) 26
27 Minimizing Device Global Memory Autoaggregation Asset 1 Asset N P&L portf Sorted P&L portf Simulated Scenarios (.h 1 )+ +( Portf..h N ) - value = today Sorting (ascending order) VaR ES (mean) CPU (Host) where: h i = holding of Asset i (for i=1,,n) OpenCL Devices: CPU Xeon PHI Device global memory Accum. Minimizes Host workload Minimizes data transfers via PCIe GPU 0 GPU 1 Single output vector per device 27
28 Summary I. Overview: Portfolio Risk II. OpenCL + Workload Allocation III. Algorithmic Optimizations / Numerical Scheme IV. Minimizing Device Global Memory V. Conclusion 28
29 I. Overview: Portfolio Risk II. Conclusion Simulated Scenarios Asset 1 OpenCL + Workload Allocation (.h 1 )+ +( Asset N P&L portf Portf..h N ) - value = today Sorting (ascending order) Sorted P&L portf VaR ES (mean) CPU (Host) OpenCL Devices: CPU Xeon PHI GPU 0 GPU 1 III. Algorithmic Optimizations / Numerical Scheme 4.5x 6.8x 10000x 1000x 1000x 1000x IV. Minimizing Device Global Memory Portability (Numerical Results) 29
30 Questions? Thanks for your attention 30
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