Advanced Financial Models

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.

Revision class

NEW: My notes from the revision class pdf
NEW: My video from the revision class mp4
sample online exam questions pdf . (no arbitrage assumption now made explicit in 2(b) )
Example sheet 2.6(c) video.
Example sheet 2.6(g)(6) pdf.
2019 exam 1(d) pdf.
Lecture notes page 78 (d) pdf.
Sample 1(b) and (c) pdf.
An infinite horizon example where there is a numeraire and a martingale deflator, but no equivalent martingale measure. pdf.
Sample 4 pdf.
On the definition of numeraire strategy pdf.
Sample 5 pdf.
On the self-financing condition pdf.
Sample 2(b) pdf.
On martingales and change of measure pdf.

Example sheets

Example sheet 1 and solutions.
Example sheet 2 and solutions. (problem 1 and solution to problem 7 edited)
Example sheet 3 and solutions.
Example sheet 4 and solutions.

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 take-home 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.

Last updated 18 May 2020.