1 ProActive Parallel Suite for Finance Abhijeet Gaikwad Viet_Dung Doan Mireille BOSSY Francoise...
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Transcript of 1 ProActive Parallel Suite for Finance Abhijeet Gaikwad Viet_Dung Doan Mireille BOSSY Francoise...
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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?