FMSN25 / MASM24/MASM34, 7,5 credits, A (Second Cycle)

General Information

Elective for: F5, F5-fm, I5-fir, Pi5-fm, R5, Master Mathematical Statistics
Language of instruction: The course will be given in English

Contents

The course consists of two related parts. In the first part we will look at option theory in discrete time. The purpose is to quickly introduce fundamental concepts of financial markets such as free of arbitrage and completeness as well as martingales and martingale measures. We will use tree structures to model time dynamics of stock prices and information flows.

In the second part we will study models formulated in continuous time. The models we focus on are formulated as stochastic differential equations (SDE:s). The theories behind Brownian motion, stochastic integrals, Ito-'s formula, measures changes and numeraires are presented and applied to option theory both for the stock and the interest rate markets. We derive e.g. the Black-Scholes formula and how to create a replicating portfolio for a derivative contract.

Examination details

LTH:

Grading scale: TH - (U,3,4,5) - (Fail, Three, Four, Five)
Assessment: Written exam, compulsory computer exercises, and written home assignments.

The examiner, in consultation with Disability Support Services, may deviate from the regular form of examination in order to provide a permanently disabled student with a form of examination equivalent to that of a student without a disability.

Parts:
Code: 0115. Name: Written Examination.
Credits: 6. Grading scale: TH. Assessment: Written examination.
Code: 0215. Name: Laboratory Part 1.
Credits: 0,5. Grading scale: UG. Assessment: The first computer exercise
Code: 0315. Name: Laboratory Part 2.
Credits: 1. Grading scale: UG. Assessment: The rest of the computer exercises, including a written assignment

NF:

Parts:

0703 Laboratory Work part 1, 0,5 hp
Grading scale: Fail, Pass
0704 Laboratory Work part 2, 1,0 hp
Grading scale: Fail, Pass
0705 Exam, 6,0 hp
Grading scale: Fail, Pass, Pass with distinction

Admission

Admission requirements LTH:

FMSF10 Stationary Stochastic Processes or FMSF15 Markov Processes

Assumed prior knowledge: Probability theory corresponding to FMSF05 or equivalent helps.
The number of participants is limited to: No
The course overlaps following course/s: MASM24, FMS170, MASM19

Entry requirements Science faculty:

For admission to the course knowledge equivalent to the courses MASA01,
Mathematical Statistics: Basic Course, 15 credits and MASC03, Markov processes, 7.5
credits are required together with English B

Reading list

Björk, T.: Arbitrage Theory in Continuous Time, 4th ed. Oxford University Press, 2020, ISBN: 978-0-19-885161-5
Åberg, S.: Derivative Pricing. 2019, KFS.

Contact and other information

Director of studies: studierektor@matstat.lu.se
The number of participants is not limited.
The course overlaps following course/s: MASM24, FMS170, MASM19

Official Course Description