关键词 > MMF1928F/STA2503F
MMF1928F / STA 2503F: Pricing Theory / Applied Probability for Mathematical Finance
发布时间：2022-09-25
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MMF1928F / STA 2503F:
Pricing Theory / Applied Probability for Mathematical Finance
OUTLINE:
This course focuses on stochastic analysis and financial theory as it applies to derivative products. A working knowledge of basic probability theory, stochastic calculus, knowledge of ordinary and partial differential equations and familiarity with the basic financial instruments is assumed. The tentative topics covered in this course include, but are not limited to:
Arbitrage Strategies and replicating portfolios 
Multi‐ period model (Cox, Ross, Rubenstein) 
European, Barrier, and American options 
Change of Measure and Numeraire assets
2. Continuous Time Limit
Random walks and Brownian motion
Geometric Brownian motion
Black‐Scholes pricing formula
Martingales and measure change
3. Equity derivatives
Puts, Calls, and other European options in Black‐
Scholes
American contingent claims
Barriers, Look‐ Back, and Asian options
4. The Greeks and Hedging
Delta, Gamma, Vega, Theta, and Rho
Delta and Gamma neutral hedging
Time‐ based and move‐ based hedging
5. Interest rate derivatives
Short rate and forward rate models
Bond options, caps, floors, swaptions
6. Foreign Exchange models 
Cross currency options 
Quantos
Spot and forward price models
7. Stochastic Volatility Models
The Heston model
Volatility options
TEXTBOOKS:
The following are recommended (but not required) textbooks for this course: 
Stochastic Calculusfor Finance II : Continuous Time Models, Steven Shreve, Springer 
Options, Futures and Other Derivatives, John Hull, Princeton Hall
Two additional books that you may find useful are:
Arbitrage Theory in Continuous Time, Tomas Bjork, Oxford University Press 
Financial Calculus: An Introduction to Derivative Pricing, Martin Baxter and Andrew Rennie
In addition, you will receive a pdf booklet consisting of notes for the course. This is for your own consumption and is not to be distributed outside of this class.
Item
#
% of Grade
Quizzes are written tests that assess basic knowledge of the material they are typically 30 minutes long and will be conducted at the start (4:10 pm sharp) of tutorials. They will occur approximately every two weeks.
Projects are real world inspired problems that are based on the theory. They will be handed out approximately once every 4 weeks. You will be required to understand the theory, formulate an approach to the problem, implement the numerics in matlab, R, or Python, interpret the results, and write‐ up a short report. Reports are not simply a printout of the numerical results, or bullet point answers, but should be a formalized report (written in proper academic English) containing an abstract, introduction, model setup, methodology/theory, and discussion/interpretation of results. Pay close attention to how well the results are presented both verbally and graphically – this will form part of the assessment of your work.
I strongly suggest you use LaTeX for preparing your reports, however, word processors such as Microsoft Word are acceptable. In either case, documents are to be converted to PDF before uploading to the course website.
The exam is a 4‐ hour written test assessing deeper knowledge of the material. The exact date of the exam will be scheduled later – but it will fall within the usual exam period. Do NOT book your holiday flights until all your exams dates are confirmed.
MISSED QUIZZES / EXAM / LATE PROJECT POLICY:
In case of a missed quiz, you will be allowed to sit a 15‐ minute verbal makeup quiz on the missed material.
In case of a missed exam, you will be allowed to sit a 90‐ minute verbal makeup examination covering the content of the course tested on the written exam.
Late projects will be penalized 10% of the maximum grade for every part of a 24 hour period that it is late.
TUTORIALS:
Your TA is Steven Campbell, a Ph.D. candidate in the Department of Statistical Sciences focusing on research in Financial Mathematics. Tutorials will consist of the TA going through examples and answering questions on class content, and, when there is a quiz scheduled, the quiz will be conducted during the first part of the tutorial.
OFFICE HOURS:
Office hours will be held on Tuesday’s at a time to be decided on the first lecture.
