number of credit points: 6
This course gives an introduction into
financial mathematics. The emphasis is on analysis, although
the first few weeks a more stochastic approach is sketched.
For the latter part we use the book: Financial Calculus, An
introduction to derivative pricing, by Martin Baxter and
Andrew Rennie (Cambridge University Press, Cambridge, 1996),
out of which we treat the first two chapters.
The rest of the course is based on the book The Mathematics of
Financial Derivatives, A student introduction, by
P. Wilmott, S. Howison, and J. Dewynne (Cambridge Unversity
Press, 1995). Out of this book we treat at least chapters 1,
2, 3, 4, 5, 7, 8, 9. The student should also read chapter 10.
The following topics are treated:
Course schedule and grading
Lectures will be on Monday (11.00-13.45 in F647) and
Wednesday (11.00-13.45 in C121).
There will be homework to be
handed in, this counts towards the grade. There will be a
final oral examination.
literature
Prerequisites:
Calculus, Probability Theory and Analysis.
Intended audience: 3W, 3 Ectr, Master BMI, Master Mathematics, Master SFM.
First homework. Read Chapter 1 of the book by Wilmott et al.
Produce and hand in a plot containing the payoff diagram (as a
function of exercise price, and for a fixed share price) of an
option (either call or put), combined with option prices.
(Compare the graph in the book, or the graphs produced in class.)
You have to be explicit about the source of your data, and about
what the graph actually shows.
The deadline for this is Friday,
September 11.
Second set of homework is available as a pdf file by clicking
here .
The deadline for this is Friday September 18.
Third homework is to complete an argument we started in class.
See here .
The deadline is Friday September 25.
Fourth set of exercises: Chapter 2, exercises 1, 3, 5.
The deadline is Friday October 2.
Fifth set of exercises: Chapter 3, Excercises 2 a, e (only the
pay-off diagrams), 3, 7 a, 7b.
Deadline is Friday October 9.
On October 7 and October 8 we covered most of chapter 4, plus some extra material.
The slides for the extra material are available here .
Enjoy them.
Sixth set of homework: Exercises 4.1 and 4.3.
Up to the autumn break we covered basically Chapters 1-5 of the book.
The exercises assigned the last week before the break were:
Seventh set of homework: 5.2 and 5.8.
In the two weeks after the autumn break we finished chapter 5, covered chapter 7 of the book, and did a small introduction to chapter 8. In chapter 7 the obstacle problem is duscussed, there was a small extra explanation with some examples. The slides are available .
Eigth homework: 5.16 (this one has no hint at the back of the book), 7.2 (this one does have a hint). Hint for 7.2: follow the hint!!! Hint for 5.16: first think about it, and read on page 82 what it sais there about a cash-or-nothing call. Then think about the relation between an ordinary call, the cash-or-nothing and the asset-or-nothing call. Then if you still don't see it, come and talk to me.
In the week of November 11 we discussed the explicit finite difference method. Our discussion of the stability of the algorithm deviates from what the book suggests in exercise 8.5 (see pages 143, 161 and 301). We use linear algebra techniques instead, these will be helpful later on anyway. The presentation can be found here.
Slides of November 18 are available.
Final set of homework: 8.2, 8.16 and 9.2.