1 ProActive Parallel Suite for Finance Abhijeet Gaikwad Viet_Dung Doan Mireille BOSSY Francoise BAUDE INRIA Sophia-Antipolis France.

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ProActive Parallel Suite for Finance

Abhijeet Gaikwad

Viet_Dung Doan

Mireille BOSSY

Francoise BAUDE

INRIA Sophia-AntipolisFrance

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Outline

Grid computing in the financial industry

Objectives PicsouGrid – Framework for parallelizing financial algorithms

Background

Gridified Algorithms Building the optimal exercise boundary (Ibanez and Zapatero 2002) Continuation/Exercise regions classification (Picazo 2002)

Conclusion and Perspectives

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Compute Intensive Financial Applications

Investment banks and security firms

Financial Portfolio Management Risk Management Option Pricing Algorithmic trading of equity options and hedge funds Advanced analytics

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Grid computing in the financial industry

Cluster computing Fixed configuration, homogeneous system

Nightly volume computing, batch processing Data mining, back office applications ... (ex. Datasynapse)

Daily trading Interest rate securities, option contracts, future contracts ...

Undeveloped daily trading areas : Time constraint problems Fault tolerance problems Distributed and parallel single complex option pricing algorithms

Particularly algorithms using Monte Carlo methods Opportunities to parallelize

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Objectives

From cluster computing to grid computing Scalability: multi-site network of 1000+ cores Heterogeneity: support a diverse set of resources Load balancing: adapt computational load depending on available resources. Fault tolerance: recover from faults such as network partitions or failed

processes/systems. Rationalisation of resources to lower costs Ease of Provisioning, deployment and data distribution, Interoperability,

debugging, testing, monitoring, and more...

Common pricing solutions Performance comparison: Java and C/C++ implementation Parallelize algorithms: produce efficient parallel versions of common pricing

algorithms. Open-source algorithms: produce option pricing algorithms which can be used by

external parties

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Background (1)

ProActive A Java Grid middle-ware library Project OASIS – INRIA Sophia Antipolis, UNSA, CNRS, France Provides a simplified asynchronous, parallel, distributed development

environment. Grid'5000

~3500 CPUs distributed in 9 sites across France, for research in Grid Computing, e-Science and Cyber-infrastructures

Site Sophia 148 cores, AMD Opteron 246, 2.0GHz Heterogeneous desktop grid at INRIA Sophia Antipolis: P4 (Bi-2GHz),P4

(3.6GHz), P4 (Core 2, 2.4GHz).

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Background (2)

Option trading Call option: allows holder to purchase an asset at a fixed price in the future Put option: allows holder to sell an asset at a fixed price in the future

Option pricing European: fixed future exercise date American: can be exercised any time up to expiry date

Option type: standard, basket, barrier Black-Scholes Model: one, multil-dimension Parameters

Spot price of the underlying : S, Strike price : K, Constant interest rate : r, Volatility rate : sigma, Maturity date : T, number of time step : m

For multidimensional underlying assets or complex options: → numerical simulations are required.

Monte Carlo methods Easy to parallelize and distribute

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High Dimensional American Option Pricing

There are many efficient grid-based methods for options with early exercise features.

Only practical in relatively low dimensions (upto 10) Suffer from “The Curse of Dimensionality”

For high dimensional problems Monte Carlo methods are the only approach.

Early exercise feature make Monte Carlo more complicated because, typically one has to determine the early exercise strategy as part of the problem

Main Theme: If the optimal early exercise boundary is known a priori, then an American option becomes equivalent to a barrier option and can be easily be valued using Monte Carlo

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PicsouGrid V1. architecture

reserveworkers

ClientServe

r

Sub-Server

Sub-Server

Worker

ProActive Worker

DB

ProActive

ProActive

ProActive

JavaSpacevirtual sharedmemory (to

v3)

option pricing requestMC simulation packetheartbeat monitorMC result

PicsouGrid Deployment and Operation

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PicsouGrid V2.

Bag-of-tasks architecture General Algorithm Tasks Simulation tasks

ProActive Monte Carlo API Abstraction of Server/Sub-servers from the previous-version Experimental Parallel Random Generator

SSJ - A Java Library for Stochastic Simulation

Gridified Bermudan/American Option pricing algorithm Ibanez/Zapatero

Optimal Exercise Boundary Approach Picazo

Continuation and Exercise region classification

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Optimal Exercise Boundary Approach (1)Overview

Proposed by Ibanez and Zapatero in 2002 Time backward computing Base on the property that at each opportunity date:

There is always an exercise boundary The boundary is a point (1 dimension) and a

curve (high-dimension) where the exercise values match the continuation values

Exercise when the underlying price reaches the boundary

Estimate the optimal exercise boundary F(X) at each opportunity through a regression. F(X) is a quadratic or cubic polynomial

Advantages: Provides the optimal exercise rule Possible to compute the greeks Possible to use straightforward Monte Carlo

simulation

Optimal exercise boundary

Exercise point

Underlying price

trajectory

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Optimal Exercise Boundary Approach (2)Description of the sequential algorithm

Maximum basket of d underlying American put Step 1 : compute the exercise boundary

At each opportunity, make a grid of J good lattice points

Compute the optimal boundary points Need N2 paths of simulations Need n iterations to converge

Regression Compute for all opportunity date

Step 2 : simulate a straightforward Monte Carlo simulation (easy to parallelize) N = nbMC

Complexity

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Distributed approach: For step 1

Divide the computation of J optimal boundary points by J independent tasks

Do the sequential regression on master node

For step 2 Divide N paths by nb1 small

independent packets Breakdown in computational time

Benchmarks See next slide

Optimal Exercise Boundary Approach (3)Parallel approach for high-dimensional option (I.Muni Toke, 2006)

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Optimal Exercise Boundary (5) – Benchmarks

Maximum of 5 assets, Call option

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Continuation and Exercise region Classification (1)Overview

Proposed by Picazo in 2002 Time backward computing Base on the property that at each opportunity date:

Classify the continuation values to have the characterization of the waiting zone and the exercise zone

Compute the characterization of the decision boundary F(x) through the classification boosting algorithms (ex. Adaboost, Logistic boost).

F(x) = a0 + a1X1 + a2X2 + ... + anXn

Advantages: Classification is easier to solve than a regression. Possible to use straightforward Monte Carlo

simulation.

Regression

Classification

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Standard American and basket American Asian put. Step 1 : compute the characterization of the

boundary at each opportunity date Simulate N1 paths of the underlying, denote xi

with i = (1,.., N1 ) With each xi, simulate N2 paths of simulations to

compute the difference between the exercise and the continuation values, denote yi.

Classification with the training set (xi,yi) Need n iterations to converge

Step 2 : simulate a straightforward Monte Carlo simulation (easy to parallelize) N = nbMC

Complexity

Continuation and Exercise region Classification (2)Description of the sequential algorithm

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Distributed approach For step 1

Divide N1 paths by nb small independents packets

Parallelize the classification process

Discuss more later For step 2

Divide N paths by nb1 small independents packets

Breakdown computational time

Benchmarks See next slide

Continuation and Exercise region Classification (3)Toward a parallel classification

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Continuation and Exercise region Classification (4)

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Continuation and Exercise region Classification (5)

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Conclusion and Perspectives

PicsouGrid: Many more computational finance algorithms have already been developed and need

to be similarly benchmarked:

Barrier, Basket American (Longstaff-Schwartz, Ibanez-Zapatero and Picazo)

American option

Implementations of parallel approaches

Experimentations and benchmarks over large-scale grids

Improve the implementations and the benchmarks “Continuous” operation of option pricing, rather than “one-shot”

Improve modularization/Componentization of finance algorithms

Efficient Scheduling of Bag-of-Tasks

Middleware really is critical: need to provide end users and application developers with reliable, consistent, and easy to use

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Thank you

Questions?