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

2. 2 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

3. 3 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

4. 4 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

5. 5 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

6. 6 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).

7. 7 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

8. 8 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

9. 9 PicsouGrid V1. architecture reserve workers Client Server Sub- Server Worker ProActive Worker DB ProActive JavaSpace virtual shared memory (to v3) option pricing request MC simulation packet heartbeat monitor MC result PicsouGrid Deployment and Operation

10. 10 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 algorith m  Ibanez/Zapatero  Optimal Exercise Boundary Approach  Picazo  Continuation and Exercise region classification

11. 11 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

12. 12 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 N 2 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

13. 13  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 nb 1 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)

14. 14 Optimal Exercise Boundary (5) – Benchmarks  Maximum of 5 assets, Call option

15. 15 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) = a 0 + a 1 X 1 + a 2 X 2 +... + a n X n  Advantages:  Classification is easier to solve than a regression.  Possible to use straightforward Monte Carlo simulation. Regression Classification

16. 16  Standard American and basket American Asian put.  Step 1 : compute the characterization of the boundary at each opportunity date  Simulate N 1 paths of the underlying, denote x i with i = (1,.., N 1 )  With each x i, simulate N 2 paths of simulations to compute the difference between the exercise and the continuation values, denote y i.  Classification with the training set (x i,y i )  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

17. 17  Distributed approach  For step 1  Divide N 1 paths by nb small independents packets  Parallelize the classification process  Discuss more later  For step 2  Divide N paths by nb 1 small independents packets  Breakdown computational time  Benchmarks  See next slide Continuation and Exercise region Classification (3) Toward a parallel classification

18. 18 Continuation and Exercise region Classification (4)

19. 19 Continuation and Exercise region Classification (5)

20. 20 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

21. 21 Thank you Questions?