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- Published on Sunday, 11 September 2005 20:00
- Written by Douglas Eadline
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One way clusters earn their keep is by helping to forecast and predict risk. Like forecasting the weather, timeliness is important, because yesterdays forecast is of no value if we get the answer tomorrow. Similarly, financial institutions need to do an almost real-time analysis on market derivatives to determine the Value At Risk (VAR) (see below). In the late eighties and early nineties, institutions realized that they could divide up the large portfolios of derivative positions and use parallel computers to perform VAR calculations thereby providing the almost real-time analysis they desired.

Many organizations found however, that the computing resources to perform these tasks are used only at certain times. Typically the risk determinations were done three times a day for three days during the trading period and then left idle the rest of the time. The was the need for very quick turn around on the {mosgoogle right} trading days, because federal regulation's require that financial institution "know" the amount of risk they own. Due to the nature of the work load, and the cost of a dedicated supercomputer, companies like Bear Stearns and Lehman Brothers started using clustered Sun workstations to run their derivative pricing and VAR calculations. This approach was developed in in the early 1990's and can be considered the first clusters on Wall Street.

One of the key issues with financial computing is often time to solution. Unlike a large scale simulation of an aircraft design that may take days to run, financial information usually is needed in real-time. Again like weather prediction, the more complex the model, the better the results, the longer it take to run, and the more difficult it it becomes to provide timely results. Clusters represent an affordable answer to the real-time nature of financial markets. As an aside, weather prediction on clusters can also be considered a financial application. Long term models of weather are of great interested to commodities traders.

Clusters continue to solve these types of "embarrassing parallel" problems, but they are not limited to this type of application. There are other areas that are not quite as simple to implement, but none the less useful to the financial market. Some of the more interesting applications are discussed below.

Value at Risk (VAR) is basically is the largest amount of money that an instrument (a derivative) can loose with a probability of X for a time period Y. Or put another way, a portfolio manager would like to know that a $30 million portion of portfolio has only a 1% chance that the loss will exceed the $30 million over the next month. These calculations typically are determined using Monte Carlo methods which are easily parallelized and run on clusters.

The NSE uses a Linux cluster to implement an advanced risk management system that enables on-line risk and position monitoring of members. If a trade crosses a Value at Risk (VAR) limit, the next trade will be automatically rejected. Such a monitoring process requires real-time throughput, high scalability, and the ability to work under high loads. In the course of normal trading, if a broker goes past his acceptable risk limits, his account is disabled in real-time and the system sends out alerts to the trading system and risk management team.

The software system used for doing VAR calculations is called *Prism* (Parallel Risk Management System). Prism is a cluster application that uses uses MPI to farm out jobs to worker nodes. The cluster uses a master/worker model and consists of a centralized head node that is connected via Fast Ethernet to the worker nodes. The initial system handled 50 trades/second but now accommodates the 500 trades/sec seen by the NSE. Each trade calls for two VAR computations. In order to handle the load, the NSE estimated the calculation of each VAR needed about 30 milliseconds for every computation (or trade). If the monitoring system was to be real-time, and scalable, then distributing the load was the only way to deliver this performance at a reasonable price. The head node used was a dual-CPU Intel Xeon running at 1 Ghz. This machine receives trade information and was designed to be fault tolerant so that data recovery is possible in case of a service outage. The worker machines were Intel PIII running at 800 Mhz. The workers do all the VAR computations and then send it back to the head node. The current system can be scaled up to 1,000 trades/second and the NSE believes it can continue to scale up the the cluster as the trade volume increases with faster machines and interconnects. Worker nodes can be easily added (or removed) thus providing another level of fault tolerance.

Due to the economics and unavailability of cluster technology, the PRISM system is probably the most cost effective monitoring system available today.

This type of *divide and conquer* problem is very effective in a cluster or distributed environment because there is no communication between the worker processes. It is very powerful for two reasons. First, it works transparently within a known desktop application (Excel) and second it is highly scalable. Scalability provides the ability to adding more worker nodes as the problem size to grows with no reduction in time to solution.

Kx has, in the past, demonstrated Kdb running on a Linux cluster consisting of 50 CPUs, 50 Gigabytes of RAM, and 300 GB of storage. They loaded 2 years of NYSE tick data (2.5 billion trades and quotes) onto the cluster and where able to archive a sub-second query response rate on all publicly traded stocks. In addition, multi-dimensional aggregations were produced in 5 to 20 seconds.

Quantlib offer tools that can be used for building your own applications. Some of the components include, Lattice methods, finite differences, Monte Carlo, Short-rate models, Currencies and FX (exchange) rates, and Instruments and pricers. There are also source code example applications using the Quantlib library.

This article was originally published in ClusterWorld Magazine. It has been updated and formated for the web. If you want to read more about HPC clusters and Linux you may wish to visit Linux Magazine.

Sidebar One: The Black-Scholes Formula |

You will ofter hear the Black-Scholes equation mentioned when people are discussing the finance markets. The Black-Scholes equation is the workhorse of the finance community and provides a method to determine how much a call option is worth at any given time. A call option is a contract between two parties that allows the buyer the right but not the obligation to buy an agreed quantity of a particular commodity or financial instrument at an agreed upon price for an agreed upon time. The power of the Black-Scholes model is that it lets you calculate the value of an option at any given time. Using Black-Scholes the price of the call option is based on a fraction of the stock's current price minus a fraction of the exercise price. These fractions depend on five factors; the price of the stock; the exercise price of the option; the risk-free interest rate; the time to maturity of the option, and volatility of the underlying stock price. The last factor is the only one that is unobservable. Financial institutions use the Black-Scholes and other methods to calculate the value of options from which they can understand the risk and set a price to help manage the portfolio. Using the Black-Scholes equation requires the solution of a set of partial differential equations by means of numerical integration. Depending on the number of assets taken into account, obtaining a solution can be highly computationally intensive. |

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Sidebar Two: Resources |

Computational Financial Derivatives Laboratory
The QuantNotes |

**Douglas Eadline** is the swinging Head Monkey at ClusterMonkey.net.