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MA50298: Monte Carlo methods for finance

[Page last updated: 09 August 2024]

Academic Year: 2024/25
Owning Department/School: Department of Mathematical Sciences
Credits: 6 [equivalent to 12 CATS credits]
Notional Study Hours: 120
Level: Masters UG & PG (FHEQ level 7)
Period:
Semester 2
Assessment Summary: CWSI 25%, EXCB 75%
Assessment Detail:
  • Coursework (CWSI 25%)
  • Examination (EXCB 75%)
Supplementary Assessment:
Like-for-like reassessment (where allowed by programme regulations)
Requisites:
Learning Outcomes: Apply Monte Carlo methods to solve problems arising in Financial Mathematics. Interpret their results, and communicate any uncertainties in their results correctly.
Compare Monte Carlo methods with other computational methods, and evaluate which method would be more appropriate for a given problem.
Evaluate algorithmic efficiency of Monte Carlo methods for simulation.
Implement a range of Monte Carlo methods numerically, and analyse their results.


Synopsis: Monte Carlo methods are powerful and flexible methods allowing for the simulation of complex modelling situations. This course will develop the theory and practice of Monte Carlo-based numerical methods, and how they can be applied to a range of financial problems.

Aims: This course will develop the theory and practice of Monte Carlo-based numerical methods for applications in finance. Monte Carlo methods are powerful and flexible methods which permit simulation of complex modelling situations. In this unit we will see how these methods can be applied to a range of financial problems.

Skills: Problem Solving (T,F&A), Computing skills (T,F&A), Mathematical communication (T,F&A).

Content: Simulation of Random Variables, e.g. multi-variate Gaussian. Principles of Monte Carlo. Monte Carlo methods: variance reduction and control variates. Numerical simulation of SDEs (Euler-Maruyama, Milstein). Rare event simulation. Benefits of parallelisation for Monte Carlo methods. Optional topics from: Quasi-Monte Carlo methods. MCMC and Particle Filtering methods. Adjoint Monte Carlo methods for computing Greeks. Applications for Risk Management.

Course availability:

MA50298 is Compulsory on the following courses:

Department of Mathematical Sciences

Notes:

  • This unit catalogue is applicable for the 2024/25 academic year only. Students continuing their studies into 2025/26 and beyond should not assume that this unit will be available in future years in the format displayed here for 2024/25.
  • Courses and units are subject to change in accordance with normal University procedures.
  • Availability of units will be subject to constraints such as staff availability, minimum and maximum group sizes, and timetabling factors as well as a student's ability to meet any pre-requisite rules.
  • Find out more about these and other important University terms and conditions here.