Advanced Financial Models

Michael Tehranchi

Michaelmas 2019


Mon, Wed, Fri at 11am in MR9
The official course
description
Lecture notes
Lecture
notes. For more details on stochastic calculus,
you can see these
notes.
Examples classes
Fridays 2 to 3pm in MR14, beginning Fri 25 Oct.
Please email me questions  from the lectures, example sheets, past exams, etc.  to discuss.
Example sheets
Supplemental reading
Here is a (very incomplete) list of textbooks on financial mathematics. Nearly every topic in
Advanced Financial Models is also discussed in at least one of these books.

M. Baxter and A. Rennie. Financial Calculus: An Introduction to Derivative Pricing. Cambridge University Press. 1996

T. Bjork. Arbitrage Theory in Continuous Time. Oxford Unversity Press. 2004.

M. Capinski and T. Zastawniak. Mathematics for Finance: An Introduction to Financial Engineering. Springer. 2003

R.J. Elliott and P.E. Kopp. Mathematics of Financial Markets. Springer. 2001
 D.P. Kennedy. Stochastic Financial Models. CRC Press. 2010

D. Lamberton and B. Lapeyre. Introduction to Stochastic Calculus Applied to Finance. CRC Press. 1996

M. Musiela and M. Rutkowski. Martingale Methods in Financial Modelling. Springer. 2006

S.E. Shreve. Stochastic Calculus for Finance: Vol. 1 and 2. Springer. 2004

R.J. Williams. Introduction to the Mathematics of Finance. American Mathematical Society. 2006
Several of the books above (and the AFM lecture notes)
contain introductions to
stochastic calculus applied to finance. Those interested in learning more
stochastic calculus and its applications to science,
engineering, and other branches of mathematics are encouraged to attend
the Stochastic Calculus Part III course in Lent term. Here are some classic
books:

I. Karatzas and S. Shreve. Brownian Motion and Stochastic Calculus. Springer. 1998
 D. Revuz and M. Yor. Continuous Martingales and Brownian Motion.
Springer. 2001.

L.C.G. Rogers and D. Williams. Diffusions, Markov Processes, and Martingales:
Vol. 1 and 2. Cambridge University Press. 2002.
Here are some books on probability theory at the level encountered in this
course.

G. Grimmett and D. Stirzaker. Probability and Random Processes. Oxford University Press. 2001

D. Williams. Probability with Martingales. Cambridge University Press. 1991
Finally, here is a famous
interview
with Michel Rocard on the 2008 financial crisis.
The takehome quote: Des professeurs de maths enseignent à leurs étudiants comment
faire des coups boursiers. Ce qu'ils font relève, sans qu'ils le sachent, du crime contre l'humanité.
Maths lecturers teach their students how to beat the markets. What they do is, without knowing it, a crime against humanity.
Interesting links
The probability seminar.
The finance workshop.
Advice for PhD applicants in financial mathematics in Cambridge.
Employment contacts
For those interested in employment in a bank or hedge fund,
here is a
list
of people to contact.
Exam rubric
The Faculty Board requires Part III lecturers to announce the
wording of the rubric
for the exam. Here it is:
Attempt no more than FOUR questions.
There are SIX questions in total.
The questions carry equal weight.
Last updated 5 Feb 2020.