MA415 Half Unit
The Mathematics of the Black and Scholes Theory
This information is for the 2025/26 session.
Course Convenor
Prof Mihail Zervos
Availability
This course is compulsory on the MSc in Financial Mathematics. This course is available on the MSc in Quantitative Methods for Risk Management, MSc in Statistics (Financial Statistics) and MSc in Statistics (Financial Statistics) (Research). This course is available with permission as an outside option to students on other programmes where regulations permit.
Requisites
Pre-requisites:
Students must have completed MA400 before taking this course.
Course content
This course develops the mathematical theory of risk-neutral valuation. In the context of the binomial tree model for a risky asset, the course introduces the concepts of replication and martingale probability measures. The mathematics of the Black & Scholes methodology follow. In particular, the expression of European contingent claims as expectations with respect to the risk-neutral probability measure of the corresponding discounted payoffs, pricing formulae for European put and call options, and the Black & Scholes PDE are derived. The course expands on PDE techniques for the pricing and hedging of several options. Implied volatilities as well as stochastic volatility models are then considered. The course also introduces the Black & Scholes model for foreign exchange markets and various foreign exchange options.
Teaching
10 hours of seminars and 20 hours of lectures in the Autumn Term.
Formative assessment
The main formative assessment will be in the form of weekly exercise sets, which will be discussed in the seminars. Some of the topics of these will be similar to what is expected in the summative assessment (exam).
Indicative reading
N H Bingham and R Kiesel, Risk-Neutral Valuation, Springer; T Björk, Arbitrage Theory in Continuous Time, Oxford; P J Hunt and J Kennedy, Financial Derivatives in Theory and Practice, Wiley; D Lamberton and J Kennedy, Introduction to Stochastic Calculus Applied to Finance, Chapman & Hall; D. Lamberton and B. Lapeyre, Introduction to Stochastic Calculus Applied to Finance, Chapman & Hall/Crc Financial Mathematics Series, 2nd edition, 2007; S E Shreve, Stochastic Calculus for Finance: Continuous-time Models: vol. 2, Springer
Assessment
Exam (100%), duration: 120 Minutes in the Spring exam period
Key facts
Department: Mathematics
Course Study Period: Autumn Term
Unit value: Half unit
FHEQ Level: Level 7
CEFR Level: Null
Total students 2024/25: 34
Average class size 2024/25: 17
Controlled access 2024/25: NoCourse selection videos
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