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 normally on: Monday 12.15 *online*.

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.
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.

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.

Solutions to problem sheets

Problem Sheet 1 pdf file.

Tutorial (problems class) questions

Week 3 tutorial pdf file.
Week 4 tutorial pdf file.

Solutions to tutorial questions

Week 3 tutorial pdf file.