Ekaterina Gonina, Jike Chong, N.R. Satish*, Mikhail Smelyanskiy*, Kurt Keutzer, Department of EECS, University of California, Berkeley

This research is supported in part by an Intel Ph.D. Fellowship. This research also supported in part by Microsoft (Award #024263 ) and Intel (Award #024894) funding and by matching funding by U.C. Discovery (Award #DIG07-10227).

Parallel Computing Lab

ASPA

Market Conditions

Portfolio Pricer Value at Risk

Strategy

Trade

Instrument Models

Market Price Feed

- Input Data (general parameter information) - Algorithms/Routines

- Input Data (specific to user)

Quantitative Finance High Level Overview

•  Analytical

•  Monte Carlo •  Random Number generator

•  Result aggregation

•  Implicit & Explicit Finite Difference

•  Discretization

•  Convergence criteria

•  Iterative method (implicit)

Pricer and Value-at-Risk Estimator Customizable Parameters Structural Patterns: •  Iterative refinement •  MapReduce •  Pipe-and-filter

Computational Patterns: •  Dense Linear Algebra •  Sparse Linear Algebra •  Structured Grids •  Monte Carlo

Monte Carlo Based Value-at-Risk Analysis

Intra-day Risk Analysis In collaboration with Matthew Dixon, University of California, Davis

Potential Future Exposure Analysis In collaboration with the Center for Innovative Financial Technologies, UC Berkeley

Time S

teps

Trades

Path

Phase 1: Collect reporting

time steps of interest

Input: all trade types

and their parameters

Phase 2: Generate

market data for all time steps

Phase 3: Estimate instrument value for all

trades on reporting time step

Path

Time S

teps

Time S

teps

Path

Time S

teps

Time S

teps

Phase 4: Aggregating

value of all trades

Phase 5: Find PFE based on all path

•  Billions of instrument value must be priced overnight

•  Challenge lies in developing software architectures that are efficient, scalability, and maintainable

•  Working with one of the top financial data provider to architect their risk analytics engine

TypicalMonteCarloSimula3onSimula3onofmarketVaRop3mizedfor

Manycoreresourcehierarchy

(2)...

(3)...

(4)

(1)...

NumberofScenariostoSimulate

(3)

(4)

(1)(2)

Performance optimized using a three-levels approach comprised of problem reformulation, module selection and implementation styling.

148x speedup on same platform

DataAssimila3on

UniformRandomNumberGenera3on

(URNG)

(1)

ParameterDistribu3on

Transforma3on

(2)

InstrumentPricing

(3) (4)

With the proliferation of algorithmic trading,

derivative usage and highly leveraged hedge funds,

Value-at-Risk is an increasingly important metric

for financial institutions.

Typical four-step process in Monte Carlo simulation, each step can be customized with alternative implementations. Important computation pattern in Our Pattern Language.

NumberofScenariostoSimulate

Finite-Difference Methods for Option Pricing An Option is a tradable financial security whose value depends on the value of the underlying asset.

Task of Option Pricing is to find the price of the option given the underlying asset and market conditions

60-

Black-Scholes equation Heat Diffusion Equation

•  S-underlying asset price

•  V – option price

•  Sigma - volatility

•  R – riskless rate of return

•  Use the heat equation to solve the PDE using finite-difference methods

•  Discretization & Stencil computation

Crank-Nicolson Method In collaboration with N.R. Satish and Mikhail Smelyansky

Throughput Computing Lab, Intel

•  Half-step implicit, half-step explicit method

•  Gauss-Seidel iterative solver for implicit

•  Explicit data dependency

Market Parameters •  Starting Stock Price •  Volatility

Option Type •  American/European •  Payoff function

Discretization Parameters •  Number of timesteps •  Number of points

Input

Output

Option Values

For n timesteps: 1. Forward half-step

2. Backward half-step (Gauss-Seidel Solver)

Until Convergence

Pricing Routine

60%-90% of computation

Parallelization & Results Evaluated on Core i7 and Larrabee* SIMD-Level

•  Unroll the Gauss-Seidel iteration loop

•  Reuse registers

•  Efficient gather/scatter

Core-level

Embarrassingly-parallel – map one option per core

A, B, C.. = each an iteration operating on a vector of 4 values

Before Parallelization

After Parallelization

Neh

alem

La

rrab

ee

Nehalem Larrabee*

1 Option 2.13x 6.08x

128 Options 5.7x 25.95x

Speedup

Core Scaling