Student Project - Parallel Monte Carlo Simulations in Haskell

This project is about constructing a Monte Carlo simulation library in Haskell. The library should be structured to allow for different statistical distributions (e.g. the Gaussian normal and log-normal) and for parallel execution. Consideration should be given to parallel calculations such that each thread generates random numbers that are independent from the other threads’ calculations. The generator should be deterministic if given the same initialisation i.e. given the same so-called seed value - in other words given a certain seed value the generator simulates the same pseudo-random numbers.

Contact person

Jost Berthold (joint supervision with Sinan Gabel)

Notes

An estimate of an expected value of a function F can be obtained by generating/simulating values from the desired statistical distribution, and finding the mean of F applied to those values. This provides relatively easy access to valuing financial contracts.

A random walk can be created by recursively summing pseudo-random numbers.

Its use can vary widely but test cases will be directed towards valuing financial contracts.

Key topics

Functional programming, Haskell, Parallel computations.

Monte Carlo method (statistics), pseudo-random uniformly distributed numbers (reals, integers), Seed value (for the random generator).

Finance, Valuation.

Input

A (commercial) working Monte Carlo (non-parallel) simulation library written in Mathematica “Derivatives Expert IV for Mathematica” (relevant part is module/package 18). The library has accommodating examples, documentation and test files. A .pdf version of the documentation can be found at http://ifs.dk/DerivativesExpert/DerivativesExpertManual.pdf; see pages 309-326.

Gentle, J. E. Random Number Generation and Monte Carlo Methods, 2nd ed. Springer-Verlag, 2003.

http://en.wikipedia.org/wiki/Monte_Carlo_method

Prerequisites

Capable of writing small and middle sized applications in Haskell (GHC). Understand basic statistics.