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DRPS : Course Catalogue : School of Mathematics : Mathematics

Postgraduate Course: Derivative Pricing and Financial Modelling (MATH11057)

Course Outline
SchoolSchool of Mathematics CollegeCollege of Science and Engineering
Course typeStandard AvailabilityNot available to visiting students
Credit level (Normal year taken)SCQF Level 11 (Postgraduate) Credits15
Home subject areaMathematics Other subject areaFinancial Mathematics
Course website None Taught in Gaelic?No
Course descriptionThe aim of this course is to study the application of the Black-Scholes model to the range of derivative securities encountered in the market, and to the term structure of interest rates. The principle tool will be the equivalent martingale measure. Links between derivative prices and PDEs will be indicated but solution of PDEs will be covered elsewhere. Discrepancies between the Black-Scholes model and market data will be described, and alternative models presented.
Entry Requirements (not applicable to Visiting Students)
Pre-requisites Co-requisites
Prohibited Combinations Other requirements MSc Financial Mathematics students only.
Additional Costs None
Course Delivery Information
Delivery period: 2013/14 Semester 2, Not available to visiting students (SS1) Learn enabled:  No Quota:  None
Web Timetable Web Timetable
Course Start Date 13/01/2014
Breakdown of Learning and Teaching activities (Further Info) Total Hours: 150 ( Lecture Hours 40, Summative Assessment Hours 1.5, Programme Level Learning and Teaching Hours 3, Directed Learning and Independent Learning Hours 105 )
Additional Notes Examination takes place at Heriot-Watt University.
Breakdown of Assessment Methods (Further Info) Written Exam 100 %, Coursework 0 %, Practical Exam 0 %
No Exam Information
Summary of Intended Learning Outcomes
On completion of this course the student should be able to:
! demonstrate an understanding of the theoretical frameworks for pricing derivatives, including the Black-Scholes model;
! demonstrate an awareness of the differences between the real-world and the risk-neutral probability measures;
! derive the underlying theory for pricing bonds and interest-rate derivatives;
! show their critical understanding of the assumptions underlying common models of asset process and interest rates;
! show a conceptual understanding of the processes in pricing derivative securities to enable the wider application of knowledge in different and new contexts;
! calculate approximate prices for European and American-style derivatives using the binomial model;
! use the Black-Scholes formula to tackle appropriate problems;
! demonstrate how to price and hedge simple equity derivatives contracts;
! demonstrate how the Greeks can be used to manage the risk in a portfolio of derivatives;
! apply the main models for the term-structure of interest rates for pricing bonds and interest-rate;
! find problem solutions in groups;
! plan and organize self-study and independent learning;
! use programming tools in the application of pricing methods;
! communicate effectively problem solutions to peers.
Assessment Information
See 'Breakdown of Assessment Methods' and 'Additional Notes' above.
Special Arrangements
MSc Financial Mathematics students only.
Additional Information
Academic description Not entered
Syllabus The Black-Scholes PDE.
Extension of the Black-Scholes model to stocks paying dividends, foreign exchange and derivatives on futures; futures prices under the risk-neutral measure; market price of risk.
Hedging and the Greeks; portfolio insurance.
The term-structure of interest rates: spot rates, forward rates and the yield curve.
Discrete-time interest-rate models.
Continuous-time interest-rate models: Vasicek, Cox-Ingersoll-Ross, pricing interest rate derivatives; the Heath-Jarrow-Morton approach; other no-arbitrage models.
Transferable skills Not entered
Reading list Etheridge, A. (2002). A Course in Financial Calculus. CUP.
Cairns, A.J.G. (2003). Interest Rate Models: An Introduction. Princeton University Press.
Hull, J.C. (2002). Options, Futures and Other Derivatives (5th Edition). Prentice-Hall.
Lamberton, D. & Lapeyre, B. (1996). Introduction to Stochastic Calculus Applied to Finance. Chapman & Hall.
Bingham, N.H. & Kiesel, R. (2004). Risk-Neutral Valuation. Pricing and Hedging of Financial Derivatives. Springer.
Study Abroad Not entered
Study Pattern Not entered
Course organiserDr Sotirios Sabanis
Tel: (0131 6)50 5084
Course secretaryMrs Kathryn Mcphail
Tel: (0131 6)50 4885
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