MA310 Half Unit
Mathematics of Finance and Valuation
This information is for the 2016/17 session.
Teacher responsible
Dr Johannes Ruf
Availability
This course is available on the BSc in Business Mathematics and Statistics, BSc in Mathematics and Economics, BSc in Mathematics with Economics and BSc in Statistics with Finance. This course is available as an outside option to students on other programmes where regulations permit. This course is available with permission to General Course students.
Prerequisites
MA313 Probability for Finance is required
Course content
Main mathematical ideas in the modelling of asset price evolution and the valuation of contingent claims (e.g., calls, puts); discrete methods will dominate. Introductory treatment of the BlackScholes continuoustime model. This course introduces a range of mathematical concepts and techniques of modern finance. It considers discrete and continuous time models for the price dynamics of actively traded assets. It develops the basic principles of riskneutral valuation of contingent claims, such as call and put options. The course contains some elements of stochastic analysis such as Brownian motion, stochastic integration, stochastic change of variable formula, change of probability measures. These analytic tools are used for the pricing of contingent claims in stochastic models of financial markets. Specific topics studied include: oneperiod and multiperiod binomial tree models; the Black and Scholes model; selffinancing replicating portfolios; martingales and conditional expectation; Itô calculus; riskneutral valuation of call and put options in the absence of arbitrage; the Black and Scholes formula; option deltas, gammas, vegas, and other sensitivities.
Teaching
22 hours of lectures and 10 hours of classes in the LT.
Formative coursework
Written answers to set problems will be expected on a weekly basis.
Indicative reading
Lecture notes will be provided. Background texts: T Bjork, Arbitrage Theory in Continuous Time, Oxford Finance, 2004; A Etheridge, A Course in Financial Calculus, CUP, 2002; M Baxter & A Rennie, Financial Calculus, CUP, 1996; P Wilmott, S Howison & J Dewynne, The Mathematics of Financial Derivatives, CUP, 1995; J Hull, Options, Futures and Other Derivatives, 6th edition, PrenticeHall, 2005. D Lamberton & B Lapeyre, Introduction to stochastic calculus applied to finance, 2nd edition, Chapman & Hall, 2008. S E Shreve, Stochastic Calculus for Finance. Volume I: The Binomial Asset Pricing Model; Volume II: ContinuousTime Models. Springer, New York, 2004.
Assessment
Exam (100%, duration: 2 hours) in the main exam period.
Key facts
Department: Mathematics
Total students 2015/16: 8
Average class size 2015/16: 8
Capped 2015/16: No
Value: Half Unit
PDAM skills
 Selfmanagement
 Problem solving
 Application of information skills
 Communication
 Application of numeracy skills
 Specialist skills
Course survey results
(2013/14  2015/16 combined)
1 = "best" score, 5 = "worst" scoreThe scores below are average responses.
Response rate: 100%
Question 
Average  

Reading list (Q2.1) 
2.4  
Materials (Q2.3) 
2.2  
Course satisfied (Q2.4) 
2.1  
Lectures (Q2.5) 
2  
Integration (Q2.6) 
1.7  
Contact (Q2.7) 
2  
Feedback (Q2.8) 
2  
Recommend (Q2.9) 
