VALUATION OF DERIVATIVE ASSETS, FMSN25/MASM24

COURSE PROGRAMME HT-17

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 8^{00}-11^{00}, 13^{00}-16^{00}, 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**-

- T. Björk (2009)
*Arbitrage Theory in Continuous Time.*3rd. ed. Oxford University Press.

(2nd ed. of Björk from 2004 will also work. It is available as e-book for students with stil identities:

`http://www.oxfordscholarship.com.ludwig.lub.lu.se/oso/public/content/economicsfinance/9780199271269/toc.html`.

See`http://www.maths.lth.se/matstat/kurser/fmsn25masm24/ht17/chtrans.html`for translation between the chapter numbers in 3rd and 2nd ed of Björk) - S. Åberg (2017)
*Derivative Pricing.*KF-Sigma, Lund. Chapter 3 is replaced by a hand out of a correct version of chapter 3 (see home page).

*Derivative Pricing*contains material for some lectures, exercises and answers to the exercises. It is sold at KF-sigma. - T. Björk (2009)
**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- Correctly completed the home assignment.
- Participated on both the compulsory computer exercises.
- Obtained a passing grade on the written exam. A passing grade is 3, 4 for 5 LTH students and G or VG for faculty of science students. Allowed aid: pocket calculator, pencil and eraser.

**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 .

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 should be**),**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),**P**1.5.1. **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^{*}),**P**1.1.2. **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 .