------------------------------------------------------------------------------- [Image] [Image] [Image] Next: Electromagnetic Scattering Up: NYNET High Performance Previous: Multi Target Tracker ------------------------------------------------------------------------------- Financial Modeling Application Introduction and Problem description Financial modeling represents a promising industry application of high performance computing. In previous work, parallel stock option pricing models were developed for the Connection Machine-5 and DECmpp-12000 [5] [7], and later were ported on an IBM SP1 and a DEC Alpha cluster. These parallel models run approximately two orders of magnitude faster than sequential models on high-speed workstations. To further develop this application, a portable, workstation based, interactive visualization environment was developed for a heterogeneous computing environment. Application Visualization System (AVS) was used to integrate massively parallel processing, workstation based visualization, an interactive system control, and distributed I/O modules. Using a stock option price modeling application as a case study, we demonstrate a simple, effective and modular approach to coupling network-based concurrent modules into an interactive remote visualization environment. Two prototype simulation on-demand systems are developed, in which parallel option pricing models locally implemented on two system configurations (two meta machines): one with two MPP machines, a 32-node CM5 and a 8K-node DECmpp-12000 [6]; another with two distributed systems, an Ethernet-based IBM SP1 and a FDDI based network connecting a cluster of workstations [8], are coupled with an interactive graphical user interface over the NYNET ATM-based wide area network. Stock option pricing models are used to calculate a price for an option contract based on a set of market variables, (e.g. exercise price, risk-free rate, time to maturity) and a set of model parameters. Model price estimates are highly sensitive to parameter values for volatility of stock price, variance of the volatility, and correlation between volatility and stock price. These model parameters are not directly observable, and must be estimated from market data. Using optimization techniques for model parameter estimation holds great promise for improving model accuracy. We use a set of four option pricing models in this study. Simple models treat stock price volatility as a constant, and price only European (option exercised only at maturity of contract) options. More sophisticated models incorporate stochastic volatility processes, and price American contracts (option exercised at any time in life of contract) [3] [4]. These models are computationally intensive and have significant communication requirements. The four pricing models are: BS - the Black-Scholes constant volatility, European model; AMC - the American binomial, constant volatility model; EUS - the European binomial, stochastic volatility model; and AMS - the American binomial, stochastic volatility model. Detailed descriptions about these four modelis can be found in [3] [4] [5]. Analytic models are useful tools in the financial market, but require expert interpretation. To further evaluate and optimize pricing models to run in a parallel computing environment, we combine high performance computing modules for real-time pricing with real-time visualization of model results and market conditions, and a graphical user interface allowing expert interaction with pricing models. We envision a market expert using such a system to start and stop a set of models, adjust model parameters, and call optimization routines according to dynamically changing market conditions. System Configuration and Integration Two prototype systems for this application are developed and experimented on the NYNET. One focused on a meta computer consisting of two MPP machines, and the other on distributed workstation clusters. Configuration 1 - NYNET + CM-5 + DECmpp-12000 + Workstations Figure 4 is the system configuration of the first prototype interactive simulation-on-demand system for the option price modeling application, using an AVS/PVM framework proposed in [8] and utilizing the network infrastructure and distributed computing facility at NPAC. [Image] [Image] The AVS kernel runs on a SUN10 workstation which acts both as an AVS server to coordinate data-flow and top-level concurrent control among remote modules, and as a network gateway which links the NPAC in-house host machines locally networked by an Ethernet to the regional end-user through the NYNET. The ATM-based link is built around two Fore switches that operate at 155 Mbps (OC3c) while the wide area network portion of the network operates at OC48(2400 Mbps) speed. Our heterogeneous computing system for stock option pricing consists of four compute nodes, a home machine, and two file server machines. All workstations, including the front-ends of the DECmpp-12000 and CM-5, are connected by a 10MBit/second Ethernet based LAN. The four option pricing models run on remote compute nodes: BS model on a DEC5000, AMC model on a SUN4, EUS model on a CM-5 and AMS on a DECmpp-12000(SX). Each remote compute node has its own I/O capability. Our DECmpp-12000 is a massively parallel SIMD system with 8192 processors. Each RISC-like processor has a control processor, forty 32-bit registers, and 16 KBytes of RAM. All the processor elements are arranged in a rectangular two-dimensional grid and are tightly coupled with a DEC5000 front-end workstation. The theoretical peak performance is 650 Mflops DP. Our CM-5 is a parallel MIMD machine with 32 processing nodes. Each processing node consists of a SPARC processor for control, four proprietary vector units for numerical computation, and 32 MBytes of RAM. The control node of the CM-5 is a SUN4 workstation. The theoretical peak performance is 4 Gflops. Sequential compute nodes include a DEC5000 and a SUN4. The DEC5000 performs at 6.8 Mflops, and has 16 Mbytes memory. The SUN4 runs at 4.3 Mflops and has 32 Mbytes memory. The user interface runs on a remote SUN4. This machine combines user runtime input (model parameters, network configuration) with historical market databases stored on disk, and broadcasts this data to remote compute nodes. System synchronization occurs with each broadcast. An IBM RS/6000 is used as a file server for non-graphical output of model data. In this application, model prices calculated at remote compute nodes and corresponding market data are written to databases for later analysis. In summary, the heterogeneous computing system illustrated in Figure 4 provides distributed computing,distributed memory, and distributed input/output for the stock option pricing application. Our heterogeneous computing system integrates diverse functions-computation, visualization, and system control over a diverse set of hardware. We use a mix of programming languages on the remote compute nodes-Fortran77 on the DEC5000, C on the SUN4, CMFortran on the CM-5, and MPL (data parallel C) on the DECmpp-12000. AVS integrates visualization, networking functionality, and computation. At the operating system level, all remote modules are compiled and linked as stand-alone programs. Input and output ports are defined in modules by the programmer using specific library routines provided by AVS. Each module represents a process. Inputs and outputs between remote modules are implemented via socket connections. There are two source of input data: historical market data read from disk files, and runtime input of model parameters by the user through a GUI. Output from all four models is rendered in a graphics window, displayed numerically in a shell window, and written to a database by the file server. Figure 5 illustrates the GUI for managing user runtime input and output, and the system configuration. Runtime input includes user defined model parameters and system execution styles. Outputs include 2-dimensional displays of model and market prices calculated by the compute nodes. The system configuration includes choice of pricing models, network configurations and interface layouts. [Image] [Image] Pricing models are extremely sensitive to model parameters for implied volatility, variance of stock volatility and correlation between stock price and its volatility. These parameters may be read from data files (historical estimates), calculated just prior to running the pricing model (by optimization), or defined at run time (expert user). Configuration 2 - NYNET + IBM SP1 + DEC Alpha Farm + Workstations Figure 6 is the system configuration of the second prototype interactive simulation-on-demand system for the option price modeling application, using an AVS/PVM framework proposed in [8] and utilizing the network infrastructure and distributed computing facility at NPAC. [Image] [Image] The AVS kernel runs on a SUN10 workstation which acts both as an AVS server to coordinate data-flow and top-level concurrent control among remote modules, and as a network gateway which links the NPAC in-house host machines locally networked by an Ethernet to the regional end-user through the NYNET. The two parallel pricing models (EUS model and AMS model) are implemented in PVM and run respectively on a 8-node IBM SP1, networked by an Ethernet at the time of evaluation, and a 8-node DEC Alpha cluster inter-connected by a FDDI-based GIGAswitch. They are coupled under the proposed AVS environment with the other two sequential simple models(BS model and AMC model) running on a SUN4 and a DEC5000 workstation, respectively. The nodal processor of SP1 is IBM RISC/6000 processor running at 62.5 MHz and is one of the most powerful processors available. The DEC Alpha farm consists of 8 Alpha model 4000 workstations which are supported by a high performance networking backbone of a dedicated, switched FDDI segments. The GIGAswitch provides full FDDI bandwidth and low latency switching to every workstation in the farm. While displayed on the end-user's home machine, a user interface actually runs on a remote SUN4 which combines user runtime input (model parameters, network configuration) with historical market databases stored on disk, and broadcasts this data to remote compute nodes. Top-level system synchronization occurs with each broadcast. An IBM RS/6000 is used as a file server for non-graphical output of model data. In this application, model prices calculated at remote compute nodes and corresponding market data are written to databases for later analysis. All models output are graphically displayed on the end-user's home machine(a SUN10) in AVS graph viewers. Figure 5 gives the user interface showing the simulation control panel(left), model output windows(top) and the flow network(bottom). Performance Analysis The timings for one trade of the parallel option models on various models is given in the Table 2. Note: * The timing data is measured when the level of binomial tree is 17. * On MIMD machines, all the two models weakly depend on communication but solely depend on node performance of the parallel systems. But on SIMD machine, it also depends on communication. Different algorithms are used on MIMD (with explicit message passing paradigm) and on SIMD (with Fortran90 data parallel paradigm) systems. * EUS - EUropean Stocahstic volatility binomial model; * AMS - AMerican Stocahstic volatility binomial model. [Image] [Image] Conclusion The financial modeling application implemented on NPAC supercomputer facility and experimented over the NYNET gives a promising application of simulation-on-demand on the information superhighway which combines the high-performance computing at a supercomputer center like NPAC with high-bandwidth wide area network like NYNET for high-speed remote access and distributed computing. We are exploring new software framework in this area and plan to apply the integration technique described in this work to other InfoMall applications. We plan to add on top of the AVS framework a network user interface, Mosaic, a distributed hypermedia software from NCSA, to support InfoVision simulation-on-demand projects over the ATM-based wide area network. We believe that methodologies and tools for information integration will play a more and more important role with the adoption of HPCC technologies in industry. ------------------------------------------------------------------------------- [Image] [Image] [Image] Next: Electromagnetic Scattering Up: NYNET High Performance Previous: Multi Target Tracker ------------------------------------------------------------------------------- ------------------------------------------------------------------------------- ryadav@npac.syr.edu