MA415 Half Unit
The Mathematics of the Black and Scholes Theory
This information is for the 2018/19 session.
Teacher responsible
Dr Albina Danilova and Dr Johannes Ruf
Availability
This course is compulsory on the MSc in Financial Mathematics. This course is available on the 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.
Prerequisites
Students must have completed September Introductory Course (Financial Mathematics and Quantitative Methods for Risk Management) (MA400).
Course content
This course is concerned with a mathematical development of the riskneutral valuation theory. 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 riskneutral probability measure of the corresponding discounted payoffs, pricing formulae for European put and call options, and the Black & Scholes PDE are derived. A class of exotic options is then considered. In particular, pricing formulas for lookback and barrier options are derived using PDE techniques as well as the reflection property of the standard Brownian motion. The course also introduces a model for foreign exchange markets and various foreign exchange options.
Teaching
20 hours of lectures and 20 hours of seminars in the MT.
The MA415 course has 30 compulsory hours of teaching with an additional 10 hours which are optional and reserved for covering advanced material and/or applications chosen by students. Students are strongly encouraged to attend the additional hours offered.
Indicative reading
N H Bingham and R Kiesel, RiskNeutral 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: Continuoustime Models: vol. 2, Springer
Assessment
Exam (100%, duration: 2 hours) in the summer exam period.
Key facts
Department: Mathematics
Total students 2017/18: 28
Average class size 2017/18: 28
Controlled access 2017/18: No
Value: Half Unit
Course survey results
(2014/15  2016/17 combined)
1 = "best" score, 5 = "worst" scoreThe scores below are average responses.
Response rate: 58%
Question 
Average  

Reading list (Q2.1) 
2.1  
Materials (Q2.3) 
1.6  
Course satisfied (Q2.4) 
1.8  
Integration (Q2.6) 
2  
Contact (Q2.7) 
2  
Feedback (Q2.8) 
2.1  
Recommend (Q2.9) 
