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Computational Methods in Financial Mathematics

  • Summer schools
  • Department of Mathematics
  • Application code SS-ME200
  • Starting 2021
  • Short course: Open
  • Location: Houghton Street, London

Derivative pricing, investment decisions and financial risk management rely on stochastic models describing financial markets. In these models, quantities of interest such as the price of a financial product often need to be approximated using computational methods. This is a hands-on course in which such methods are introduced and implemented. A particular focus of the course is on Monte Carlo methods, i.e., simulation methods to approximate integrals and expectations of random variables.

Based on the binomial tree model, the fundamental ideas underlying the theory of risk-neutral pricing are introduced. In this context, expressions of option prices as suitable expectations of random variables are derived. It is then shown how these expectations can be evaluated using computational methods.

The course also develops the students’ computational skills. Indeed, each time a new computational method is introduced, students implement and apply it to relevant examples during supervised programming sessions. To enable students to do this, the course contains an introduction to programming in Python and its applications in financial mathematics.

The course is largely self-contained and reviews the necessary mathematical concepts. No prior programming experience is expected.

Session: One - Applications closed
Dates: 21 June – 9 July 2021 
Lecturers: Professor Johannes Ruf and Professor Luitgard Veraart 

Programme details

Key facts

Level: 200 level. Read more information on levels in our FAQs

Fees:  Please see Fees and payments

Lectures: 36 hours 

Classes: 18 hours

Assessment*: Two written examinations

Typical credit**: 3-4 credits (US) 7.5 ECTS points (EU)

*Assessment is optional

**You will need to check with your home institution

For more information on exams and credit, read Teaching and assessment

Prerequisites

Calculus at lower undergraduate level and an introductory course in probability or statistics.

Programme structure

The topics that this course will cover:

  • Methods for generating samples from a given probability distribution
  • Monte Carlo estimation
  • Variance reduction techniques
  • The binomial asset pricing model and the concept of no-arbitrage
  • The Black-Scholes option pricing model as a limit of the binomial model
  • Application of Monte Carlo methods to pricing financial derivatives
  • Introduction to programming in Python

Course outcomes

Students are provided with both the mathematical foundations and the programming skills to analyse and price financial derivatives numerically. 

Teaching

The LSE Department of Mathematics is internationally recognised for its teaching and research. Located within a world-class social science institution, the department aims to be a leading centre for Mathematics in the Social Sciences. The Department of Mathematics was submitted jointly to REF 2014 with LSE's Department of Statistics: 84% of the research outputs of the two departments were classed as either world-leading or internationally excellent in terms of originality, significance and rigour.

The Department has more than doubled in size over the past few years, and this growth trajectory reflects the increasing impact that mathematical theory and mathematical techniques are having on subjects such as economics and finance, and on many other areas of the Social Sciences.

On this three week intensive programme, you will engage with and learn from full-time lecturers from the LSE’s mathematics faculty.

Reading materials

The main reading material will be the detailed handouts distributed at the beginning of the course. Optionally, the following books might also be helpful:

-   S. M. Ross, Simulation, Academic press, 5th edition, 2013.
-   R. W. Shonkwiler and F. Mendivil, Explorations in Monte Carlo Methods, Springer, 2009.
-   S. E. Shreve, Stochastic Calculus for Finance I: The Binomial Asset Pricing Model, Springer, 2005.

**Course content, faculty and dates may be subject to change without prior notice

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