Numerix Pricing with CUDA. Ghali BOUKFAOUI Numerix LLC

Transcription

1 Numerix Pricing with CUDA Ghali BOUKFAOUI Numerix LLC

2 What is Numerix? Started in 1996 Roots in pricing exotic derivatives Sophisticated models CrossAsset product Excel and SDK for pricing Expanded into wide range of products Around 200 people Distributed around the world

3 Option Value Option Value Exotic Derivatives Put and Call options are vanilla Fungible Heavily traded Custom structured products are exotic Bespoke Path dependent No market Underlying Value Underlying Value

4 Object Oriented Approach in Numerix CrossAsset

5 Pricing Architecture: Deal User specified deal structure Script for payoff Event schedules Indexes for data Value at a point in time; Data Parallel; Specified at run time; Customer proprietary. PRODUCTS DISCOUNTING callfloata, callfloatg NONDISCOUNTING geommean, arithmean, count END PRODUCTS PAYOFFSCRIPT IF ISACTIVE(InDates) THEN IF ISFIRST(InDates) THEN geommean = 1 END IF geommean *= XYZ arithmean += XYZ count += 1 IF ISLAST(InDates) THEN arithmean = arithmean / count geommean = POW(geomMean, 1.0 / count) callfloata = MAX(XYZ - arithmean, 0) callfloatg = MAX(XYZ - geommean, 0) END IF END IF END PAYOFFSCRIPT

6 Pricing Architecture: Model Numerix Models Interest rate Equities FX Rates Credit Hybrid Representation of SDE; Calibrate to market at model creation; Roll from t 1 to t 2 during runtime; SP500 USD/JPY USD

7 Pricing Architecture: Pricer 15 Brings it together Deal Model Method Quality Does simulation PDE MC Tree Produces prices. IF ISLAST(InDates) THEN arithmean = arithmean / count geommean = POW(geomMean, 1.0 / count) callfloata = MAX(XYZ - arithmean, 0) callfloatg = MAX(XYZ - geommean, 0) Price= Quality=10 Method=Forward MC

8 Pricing Architecture: Report Sensitivity to market changes: Chock market quotes Reprice Finite differences: Delta Gamma Can be hundreds of pricings FX::INST::EUR/USD::FWD::RATE::1d FX::INST::EUR/USD::FWD::RATE::2d FX::INST::EUR/USD::FWD::RATE::1w FX::INST::EUR/USD::FWD::RATE::2w FX::INST::EUR/USD::FWD::RATE::1m FX::INST::EUR/USD::FWD::RATE::2m FX::INST::EUR/USD::FWD::RATE::6m FX::INST::EUR/USD::FWD::RATE::1y FX::INST::EUR/USD::FWD::RATE::2y Market Data

9 Scale of Computation Single pricing: seconds; Many pricings for a given deal (Risk calculation); Many deals (or many policies); Using clusters is common; Enormous amount of calculation for a limited time

10 path Pricing with Slices CrossAsset uses slices A value on each MC path A given point in time. [or PDE point, tree node] Many thousands of paths Script calculate slices. Models propagate slices. Simple ops for MC Usually 10K to 1M elements time

11 Slice Encapsulates GPU Operations on slices Add, subtract, multiply Exp, pow Ops on slice object performs ops on GPU. Launches kernels CPU can go on Synchronize on reductions n= p=0x0ff39a82 CPU GPU

12 CUDA Calls for Operations Script is sequence of data parallel ops gm = pow(gm, 1.0 / n) tmp=pow(gm,x) gm=tmp Ultimate variables are discounted and passed to the result object; Model operations are data parallel by nature; Each operation type is a CUDA kernel; tmp n= p=0x0ff39a82 pow CPU GPU n= p=0x0ff5989 copy gm

13 Transparent Copy Not always data parallel Sometimes CPU more efficient Sometimes code just not ported to GPU. Copy to CPU for element-wise ops Copy to GPU for data parallel ops n= p=0x0ff39a82 CPU GPU

14 Sobol Sequences Sobol Sequences Improves MC convergence NVIDIA provides calls Use NVIDIA direction vectors Generate our own on GPU Modified Sobol sequences on CPU Feeds into path generation on GPU CPU Direction vectors GPU Sobol Sequences

15 Overview User specified script to specify the bespoke deal; Numerix models to propagate IR, FX, EQ, Credit or other Market Variables; Monte Carlo with Sobol sequences; SDK, Excel interfaces Same results with and without GPU

16 speedup Speedups Some cases provide significant speedup Complex scripts >10K paths Simple EQ model Forward Monte Carlo >10x speedup Speedup Customer paths

17 Pricing time (seconds) Speedups Some cases work well Complex scripts >10K paths Hybrid Model Sobol on CPU >3x speedup GPU CPU Paths

18 Next Steps Simultaneous Kernels. Many simultaneous pricings for risk reports Queue OP 1 OP 2 CPU Queue OP 1 OP 2 Queue OP 1 OP 2 Launch kernels for each OP 3 OP 3 OP 3 Use one SM per kernel OP N OP N OP N Smaller number of paths per simulation GPU SM SM SM

19 Next Steps Larger blocks of code for kernels. Recognize multiple operations. Compile whole script to CUDA. Compile on the fly? Database of compiled scripts? PRODUCTS DISCOUNTING callfloata, callfloatg NONDISCOUNTING geommean, arithmean, count END PRODUCTS PAYOFFSCRIPT IF ISACTIVE(InDates) THEN IF ISFIRST(InDates) THEN geommean = 1 END IF geommean *= XYZ arithmean += XYZ count += 1 IF ISLAST(InDates) THEN arithmean = arithmean / count geommean = POW(geomMean, 1.0 / count) callfloata = MAX(XYZ - arithmean, 0) callfloatg = MAX(XYZ - geommean, 0) END IF END IF END PAYOFFSCRIPT