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DEGREE REGULATIONS & PROGRAMMES OF STUDY 2023/2024

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DRPS : Course Catalogue : School of Mathematics : Mathematics

Undergraduate Course: Simulation (MATH10015)

Course Outline
SchoolSchool of Mathematics CollegeCollege of Science and Engineering
Credit level (Normal year taken)SCQF Level 10 (Year 4 Undergraduate) AvailabilityAvailable to all students
SCQF Credits10 ECTS Credits5
SummaryCourse for final year students in Honours programmes in Mathematics and/or Statistics.

Random number generation, basic Monte Carlo, variance reduction techniques, simulating Brownian paths,
Strong and weak approximations of solutions to SDEs,
Euler's approximations, Milstein's scheme,
Order of accuracy of the approximations,
Higher order schemes, accelerated convergence
Weak approximations of SDEs via numerical solutions of PDEs
Option price sensitivities (Greeks).
Course description Not entered
Entry Requirements (not applicable to Visiting Students)
Pre-requisites Students MUST have passed: Several Variable Calculus and Differential Equations (MATH08063) AND Fundamentals of Pure Mathematics (MATH08064) AND ( Probability (MATH08066) OR Probability with Applications (MATH08067))
Co-requisites Students MUST also take: Probability, Measure & Finance (MATH10024)
Prohibited Combinations Students MUST NOT also be taking Stochastic Differential Equations (MATH10085)
Other requirements None
Information for Visiting Students
Pre-requisitesNone
High Demand Course? Yes
Course Delivery Information
Not being delivered
Learning Outcomes
On completion of this course, the student will be able to:
  1. Understand Monte Carlo methods and variance-reduction techniques.
  2. Simulate random numbers from standard distributions.
  3. Numerically price some basic options.
  4. Demonstrate familiarity with numerical schemes for simulating solutions of SDEs.
  5. Apply simple higher order schemes.
Reading List
None
Additional Information
Course URL https://info.maths.ed.ac.uk/teaching.html
Graduate Attributes and Skills Not entered
KeywordsSim
Contacts
Course organiserDr Lukasz Szpruch
Tel: (0131 6)50 5742
Email: L.Szpruch@ed.ac.uk
Course secretaryMrs Alison Fairgrieve
Tel: (0131 6)50 5045
Email: Alison.Fairgrieve@ed.ac.uk
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