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
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Lectures normally on: Tuesdays 11:15 (8W 3.14) and Thursdays 16.15 (3E 2.2).
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Problems classes:
These will be IN PERSON,
Friday 18.15 (5W2.01) from Week 6 onward (i.e. starting March 14).
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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.
- Consolidated lecture notes for Chapters 6-7,
including all corrections spotted up to April 7.
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.
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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.
- In the above version,
there are still some typos in some of the subscripts in
the proof of Theorem 6.4 (p45). Fixed in the consolidated notes.
- 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.
- Pages 64 to 68 (posted April 7)
pdf file.
- Page 68 (posted April 11) added some hints for the exam at the end.
pdf file.
Problem sheets
Solutions to problem sheets
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
- Week 9 tutorial. No extra questions were considered besides
those in Problem Sheet 8.
Solutions to tutorial questions