## General

This page gives some General Information on the course, and each week I will indicate here which material has been treated.

Literature used

We use the two books Stochastic Calculus for Finance, volume I (The binomial asset pricing model) and volume II (Continuous-Time models) by S.E. Shreve.

## Homework assignments

Three times a set of Homework exercises will be given (and posted on this page, in the section `Material treated' below). For each set, the students have about 9 days to make the exercises. Working on homework in pairs is encouraged. The average homework grade contributes twenty percent to the final grade (see below). The first set of exercises has been posted September 19. The second set has been posted October 31. The third set has been posted Monday November 25.

The homework will be graded by Dr. Christoph Temmel. Here are his (updated) HOMEWORK RULES and LaTex Template. For questions concerning these rules, or the template, please ask Christoph; e-mail: C.Temmel@vu.nl.

There was a written exam on Friday, December 20. (See info about the nature of this exam at the end of this page). The final grade is based on the grade for the written exam (eighty percent) and the average grade for the homework assignments (twenty percent).

Here are the ANSWERS TO THE EXAM PROBLEMS (without, or with only brief, explanation).

The re-examination will take place on February 12, at 18:30 in room Q112 in the WN-building.

## Material treated

Here I will mark each week which material I have treated.

week 36: Shreve, vol.I, Section 1.1.

week 37: Shreve vol. I, Sections 1.2, 2.1, 2.2 and 2.3.

week 38: Shreve vol. I, Section 2.4 up to (and including) Theorem 2.4.7. HOMEWORK I.

week 39: no class.

week 40: Shreve, vol. II: Sections 3.1, 3.2.1, 3.2.2, 3.2.5, 3.2.6 (where I considered the Central Limit Theorem as known, so skipped almost all of the proof of Theorem 3.2.1), 3.3.1, 3.4.2 (up to, and including, the proof of Theorem 3.4.3).

week 41: Shreve, vol II: Sections 3.3.3 (informally; also treated, informally, the analog for Brownian motion of Theorem 2.3.2 in volume I), 3.3.4, 3.7, 4.1, 4.2 until (not including) Theorem 4.2.3.

week 42: Shreve, volume II: Theorem 4.2.3 and its proof, Section 4.3, the (informal) beginning of Section 4.4.1 (until, but not including, Theorem 4.4.1).

week 43: no class.

week 44: Shreve, Vol.II: Sections 4.4.1 and 4.4.2, and part of Example 4.4.8 in Section 4.4.3. HOMEWORK II.

week 45: Shreve, Vol. II: Sections 4.5.1, 4.5.2, 4.5.3 and 4.5.4.

week 46: Shreve, Vol. II: Made some additional remarks concerning Section 4.5.4. Further: Section 5.2.4 and 5.2.5 for constant sigma and r (and explained in a way which is somewhat different from the book but leads to the same computations (5.2.33)-(5.2.36)), and Section 6.4 until (but not including) Example 6.4.4.

week 47. Discussion of previous homework, and Shreve Vol. II Section 4.5.6 (by Christoph Temmel). HOMEWORK III.

week 48. Shreve, Vol. II: First half of Section 4.5.5 (in particular derived equation (4.5.23)); Section 4.6.2; treated an example of pricing some special derivative security (with essentially the arguments in Section 5.2.4 and the first half of 5.2.5, but explained in a somewhat different way).

week 49. Shreve Vol. II: Mentioned Theorem 7.2.1 and Corollary 7.2.2. Gave a brief summary of Section 7.3.1, 7.3.2 and 7.3.3. Treated Section 7.5.1 and 7.5.2 in detail. After the break, homework solutions were presented and discussed by Christoph.

week 50. Recalled last part of Section 7.5.2 and derived explicit solution for the case K=0 (which corresponds with Exercise 7.7 (i) and (ii)). Did some extra exercises and gave a brief review.
SOME REMARKS CONCERNING THE EXAM: The exam will consist of about six exercises (of which one concerns the discrete model), of various level of difficulty, comparable with the homework exercises. Use of textbooks, personal notes and calculator is not allowed. The students evidently have to know by heart the risk neutral pricing formula (for the discrete as well as the continuous model), the basic properties of Brownian motion (including the distribution of the maximum of a Brownian motion over the time interval [0,t]) and stochastic integrals (in particular Theorem 4.3.1), the rules of stochastic calculus (Ito formulas, in particular Theorem 4.4.1, Remark 4.4.2, Theorem 4.4.6 and Remark 4.4.7), the notion of martingales, and the definition of the standard Black-Scholes dynamics. But ALSO the explicit formula (as a geometric Brownian motion) for the stock price in the standard Black-Scholes model, and the Feynman-Kac theorem.