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**1 - 4**of**4**### Financial modeling on the Cell Broadband Engine

- In Proceedings of the 22 nd IEEE International Symposium on Parallel and Distributed Processing
, 2008

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### Parallel computation in econometrics: A simplified approach

- College, University of Oxford
, 2004

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### Abstract Valuation of Mortgage–Backed Securities in a Distributed Environment

"... Valuation of Mortgage–Backed Securities, regarded as integration in high–dimensional space, can be readily performed using the Monte Carlo method. The Quasi–Monte Carlo method, by utilizing low– discrepancy sequences, has been able to achieve better convergence rates at computational finance prob-le ..."

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Valuation of Mortgage–Backed Securities, regarded as integration in high–dimensional space, can be readily performed using the Monte Carlo method. The Quasi–Monte Carlo method, by utilizing low– discrepancy sequences, has been able to achieve better convergence rates at computational finance prob-lems despite analysis suggesting that the improved convergence comes into effect only at sample sizes growing exponentially with dimension. This may be attributed to the fact that the integrands are of low effective dimension and quasi–random sequences ’ good equidistribution properties in low dimensions allow for the faster convergence rates to be attained at feasible sample sizes. The Brownian bridge discretization is traditionally used to reduce the effective dimension although an alternate choice of discretization can produce superior results. This paper examines the standard Brownian bridge rep-resentation and offers a reparametrization to further reduce dimension. The performance is compared both in terms of improvement in convergence and reduced effective dimensionality as computed using ANOVA decomposition. Also, porting of the valuation algorithm to a distributed environment using Microsoft.NET is presented.

### PARAMETERIZED SHIFT REGISTER RANDOM NUMBER GENERATORS

"... Random numbers are crucial in many different fields, including simulation, sampling, numerical analysis, computer programming, decision making, aesthetics, and recreation [1]. A good random number generator should produce successive values that are independent and uniformly distributed. In addition, ..."

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Random numbers are crucial in many different fields, including simulation, sampling, numerical analysis, computer programming, decision making, aesthetics, and recreation [1]. A good random number generator should produce successive values that are independent and uniformly distributed. In addition, it should generate a full period and be efficiently computable. A shift register is a finite machine and a type of a classical sequential logic circuit mainly used for storage of digital data. It is an arrangement of t tubes in a row with a 0 or 1 on each tube, and shifts the contents of each tube to the next tube. If no input was made to the first tube, then at the end of t shifts, all tubes will have a 0 in them [2]. In this thesis we present an efficient way of using a shift register to generate sequences of pseudo-random numbers that are uniform and have maximal period. The implementation of this shift register is based on polynomial arithmetic.