LUNDS INSTITUTE OF TECHNOLOGYCENTRE FOR MATHEMMATICAL SCIENCES MATHEMATICAL STATISTICS


VALUATION OF DERIVATIVE ASSETS, FMSN25/MASM24
COURSE PROGRAMME HT-17

Home page
 
The course homepage is http://www.maths.lth.se/matstat/kurser/fmsn25masm24/

Course expedition
 
Department Course secretary Maria Lövgren in room 225 A+B in Math-building, southern part.
The expedition is open Mon-Fri 800-1100, 1300-1600, phone: 046-2224577, e-mail: marial@maths.lth.se.
Course responsible
 
Magnus Wiktorsson, room MH 130, phone: 046-2228625, e-mail: magnusw@maths.lth.se
Computer exercise assistants
 
Philip Kennerberg
Carl Åkerlindh

Lectures and Exercises
 
Lecturer:
LP1(First half of semester): Magnus Wiktorsson

Teaching assistant:
LP1: Philip Kennerberg, Carl Åkerlindh

LP Day Time Location
1 Mon 15-17 M:B (E:3308 28/8) (Lecture)
  Tue 10-12 MH:362D (Exercise)
  Thu 10-12 MH:Gårdingsalen (Lecture)
  Fri 13-15 MH:362D (Exercise)

Home assignment
 
The home assignment is handed out in reading reading week 4. It should be handed in on October 6 at 17 at the latest. It is then corrected. The errors should be corrected and the home assignment should be handed in again for correction.
Computer exercises
 
The course has two compulsory computer exercises lasting 2 and 4 hours respectively. The computer exercises are in rooms E:Neptunus and E:Uranus.
Comp Exer 1
(Reading week 2: Tue September 5, at 13-15, 2h.) The computer exercise deals with valuation of options in discrete time using Binomial trees. You will price both European and American type options. You will moreover study the convergence rate for Binomial trees.
Comp Exer 2
(Reading week 6: Tue October 3 at 13-17 4h.) Valuation of derivatives can be done through Monte Carlo simulations. This is the main theme in Computer Exercise 2. You will moreover apply various techniques to improve the simulations.
Note that there is an extra lecture about om simulation related to the computer exercise rw 5.

Literature
 

The compendium Derivative Pricing contains material for some lectures, exercises and answers to the exercises. It is sold at KF-sigma.

Handed out papers
All papers handed out on the lectures will be downloadable from the course homepage.

Examination
 
The exam is in the form of one home assignment and a written exam. To pass the course you need
Exam
 
Ordinary exam: Tuesday October 24, 2017 at 8-13 in VIC:2A.
First Re-exam: Monday January 8, 2018 at 8-13 MA:8.
Second Re-exam: Friday August 31, 2018 at 8-13 MA:10A .

Course content under first half of semester

The chapters are either in T. Björk's bok (B) or S. Åberg (former Rasmus) compendium (Å) and Solved problems handout (P). L is for lectures, E is for teacher assisted exercises. An asterisk (*) after an exercise means that it should be done if you have time. The numbers after Week ``1(35)'' means reading week and calender week respectively.

Week 1(35)

L1: Introduction, definition of different contracts, the economic model and concepts, discrete time models especially the Binomial model in one and multiple periods [Å 1-1.2, Å 2, B 2].
E1: Å 2.(6-8), B 2.(1-3) (Typo in B 2.1b $\Pi(1;X)=X$ should be $\Pi(1;X)\neq X$), Å 3.(1).
L2: Last part of discrete time models [B.2, B.3, Å.3]. Probability theory. [Å 12 (see also B appendix B)]
E2: Å 3.(2-3) Å 12 (1,5,8,9), P1.5.1.
Week 2(36)

Computer exercise 1: Binomial Model (5/9 at 13-15).
L3: The Wiener Process [Å 4.1], The Ito-Integral and Ito's formula.[B 4. (1-5), Å 5.(1-2].
E3: Å 4.(2,3*,9), B 4.(1 (a-d)), Å 4.(10-12).
L4: Filtering, Martingales [Å 4.2, B 4.4]. More Ito's formula and stochastic calculus [Å 5. (3,4), B 4. (5-8)].
E4: Å 4.(14,16,17), Å 5.(2,3(a),4,6,7),B 4.(7*), P1.1.2.
Week 3(37)

L5: SDE:s Geometric Brownian motion, The Ornstein-Uhlenbeck process. The Feynman-Kac's formula. [B 5., Å 5.(3,5)]
E5: Å 5.(9,10,11), P(1.1.1), B 4.(2,4,8), B 5.(5-9).
L6: Portfolio dynamics, Arbitrage-pricing (Classic) [B 6. och B 7.(1-4)].
E6: B 5.(10-12), B 7.(1, 2, 4-7), P (1.3.1).
Week 4(38)

Home assignment is handed out.
L7: B&S-formula [B 7.5]. Completeness [B 8.(1-3)]
and hedging in the B&S model[B 8.(1-3),Å 8 ].
E7: B 8.3, B 9.(2-4, 8-10), P(1.4.1).
L8: Complete, incomplete markets and the modern Arbitrage-pricing [Å 10. B 10.7, 15.]
E8: Å 6.4, Å 10.(2-4,6-8), P(1.5.2).
Week 5(39)

L9: Change of Numerairs and its applications. [Å 10.3, B 26.1-5].
E9: Å 10. (9,10,12,13,15), P.(1.6.1),(1.7.1).
L10: Extra lecture, Tue at 13-15 in MH:309A Beyond the Black-Scholes model. [(Å.7)].
L11: Simulation (a lecture related to computer exercise 2). [Å 11.].
Week 6(40)

Home assignments should be handed in before the end of the week (Fri at. 17)
Computer exercise 2. (Tue) Simulation (3/10 at 13-17).
L12: Introduction to Interest rate theory; Basic products and their arbitrage relations [ B 22., Å 1.4-1.5.3].
E10: B 22.(2, 3, 5, 7), Å 1.(3,6,9), P(1.6.2, 1.8.1).
L13: Market models (LIBOR market models) [B 27].
E11: B23.(1-4).
Week 7(41)

L14: Short rate models [B.23-24].
E12:B 24.(1 (abc), 5, 6) B 25.(1, 2, 5), P 1.8.1.
L15: Martingale models for the short rate and HJM models [ B.24-25].
E13: P 1.9.1,1.9.2 Recapitulation and questions.
Week 8(42)

L16: Extra Lecture: Tue 13-15 (MH:309A) Recapitulation lecture.
Exam
 
Ordinary exam: Tuesday October 24, 2017 at 8-13 in VIC:2A.
First Re-exam: Monday January 8, 2018 at 8-13 MA:8.
Second Re-exam: Friday August 31, 2018 at 8-13 MA:10A .