High-performance numerical pricing methods

The Aurora Financial Management System developed at the University of Vienna is a decision support tool for portfolio and asset liability management. An investor chooses a portfolio of various assets or asset classes, in such a way that some objective 9], including a risk measure, is maximized, subject to uncertainty of future markets' development and additional constraints (e.g. budget restrictions). The system is based on pricing models for nancial instruments, and a multivariate Markovian birth-and-death model for liabilities. The core of the system is a large scale linear optimization problem whose solution is the main outcome of the tool. In this paper we discuss the parallelization of a major computational kernel from this system utilizing HPF+, an extended version of HPF. In Section 1.1 we give a brief overview of numerical pricing methods. In Section 2 we describe the parallelization of the backward induction algorithm using HPF+. This is followed by a brief description of proposed HPF extensions for clusters of SMPs in Section 3. Section 4 presents experimental results of the kernel on a Beowulf cluster and on a vector parallel supercomputer, followed by conclusions in Section 5. Since the investor in the nancial planning problem bases his decision (whether to buy, sell or keep a contract) on the prices for diierent instruments, the nancial management system contains a pricing module which determines prices at speciic times and states of the economic environment. It computes prices of diierent classes of nancial instruments. In particular it performs the pricing of derivative and interest rate dependent products. A derivative is a nancial instrument whose value depends on other, so called underlying securities (e.g. stock options). We concentrate on the pricing of interest rate dependent products, whose payments depend on actual or past interest rates (e.g. variable coupon bonds). The pricing problem can be stated as follows: what is the price today of an instrument which will pay some cash ows in the future, which depend the development of interest rates? For simple cases analytical formulas are available, but in general numerical techniques have to be applied. Products, whose cash ows depend on a value of a nancial variable in the past (path dependent products), are priced with Monte Carlo simulation techniques (see 5],,7]). Instruments without path