Stochastic Processes and Finance (MA30089)

Semester II, 2024-25

This site to be used in conjunction with the course Moodle page.

Content:

Discrete time: trading portfolio, Binomial model, arbitrage, derivative pricing using arbitrage. Radon-Nikodym derivative, change of measure, Fundamental Theorem of Asset pricing. Brownian motion: definition, basic properties, reflection principle. Using related martingales, and computing quantitative properties of Brownian motion. Sketch introduction to Stochastic Integration and stochastic differential equations. Ito's Lemma, Girsanov's Theorem. Black-Scholes model: Geometric Brownian motion as a model for asset prices, risk-neutral measure, European call price formula, Fundamental Theorem of Asset pricing.

News

Lectures normally on: Tuesdays 11:15 (8W 3.14) and Thursdays 16.15 (3E 2.2).
Problems classes: These will be IN PERSON, Friday 18.15 (5W2.01) from Week 6 onward (i.e. starting March 14).
Office Hour: Fridays 2.15-3.10 in 4W4.11 (or by appointment).

Consolidated lecture notes

Consolidated lecture notes for Chapters 1-5, including all corrections spotted up to March 21. pdf file.

Lecture notes

virtual whiteboards from Lecture 1 (unfortunately I forgot to video-record the lecture) zip file.
Pages 1 to 5: pdf file.
Pages 6 to 9: pdf file.
Pages 10 to 17 (preliminary version): pdf file.
Pages 10 to 18 (updated version 10 Feb): pdf file.
Pages 10 to 18 (further updated version 13 Feb): pdf file.
On Page 12, in the last display (11 lines from the bottom, formula for EX), it should say 0 <= Y <= X rather than just Y <=X.
Pages 19 to 20: pdf file.
Pages 21 to 22 (preliminary version): pdf file.
Pages 21 to 27 (Posted Feb 17, including updated version of p21-22 ): pdf file.
There is a typo on Page 26: in the 2nd line to the solution of Example 3.9, the 3600 should be 2700.
Also on Page 27, on the third line both times it says C_2 that should be C_3.
Pages 28 to 33: pdf file.
Pages 34 to 41 (first version, posted 3 March): pdf file.
Pages 34 to 41 (updated version posted 5 March with several corrections): pdf file.
Pages 34 to 41 (further updated version posted 21 March: includes remarks on L2 spaces from lectures and updated proof of quadratic variation): pdf file.
Pages 42 to 44 (posted March 10) pdf file.
Pages 42 to 48 (posted March 13, including minor corrections to the previously posted version of Pages 42-44) pdf file.
Pages 42 to 48 (further updated version posted March 28, to better reflect the lectures: unfortunately I posted the wrong link on March 24 so that was the same as the March 13 version) pdf file.
Pages 49 to 52 (posted March 17) pdf file.
Pages 49 to 52 (updated version, posted March 24) pdf file.
Pages 53 to 56 (posted March 24) pdf file.
Pages 57 to 63 (posted March 31) pdf file.

Problem sheets

Sheet 1 pdf file. (In Q1 the (S_1,S_2,S_3) should be (S_0,S_1,S_2).)
Sheet 2 pdf file.
Sheet 3 pdf file.
Sheet 4 pdf file.
Sheet 5 pdf file.
Sheet 6 pdf file.
Sheet 7 pdf file.
Sheet 8 pdf file.

Solutions to problem sheets

Problem Sheet 1 pdf file.
Problem Sheet 2 pdf file.
Problem Sheet 3 pdf file.
Problem Sheet 4 pdf file.
Problem Sheet 5 pdf file.
Problem Sheet 6 pdf file.
Problem Sheet 7 pdf file.

Tutorial (problems class) questions

Week 3 tutorial pdf file.
Week 4 tutorial pdf file.
Week 5 tutorial pdf file.
Week 6 tutorial pdf file (borrowed from a previous year so the numbering and the name of the lecturer are different from on the others)
Week 7 tutorial pdf file
Week 8 tutorial pdf file

Solutions to tutorial questions

Week 3 tutorial pdf file.
Week 4 tutorial pdf file.
Week 5 tutorial zip file. (unfortunately I forgot to record this online class)
Week 6 tutorial pdf file.
Week 7 tutorial pdf file.