| TAMS29 |
Stochastic Processes Applied to Financial Models, 6 ECTS credits.
/Stokastiska processer för finansmarknadsmodeller/
For:
I
Ii
MMAT
Y
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Prel. scheduled
hours: 48
Rec. self-study hours: 112
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Area of Education: Science
Main field of studies: Mathematics, Applied Mathematics
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Advancement level
(G1, G2, A): A
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Aim:
The course gives an introduction to the theory of stochastic processes and the Black-Scholes model. After a completed course the student is expected to be able to:
- handle advanced items and theorems within the theory of stochastic processes, such as the
Kolmogorov extension theorem, ergodicity of time discrete Markov chains, the Kolmogorov
differential equations for time continuous Markov chains, Wiener process, Ornstein-Uhlenbeck
process, stochastic Itô-integral, Itô-formula, Martingales in discrete and continuous time
Doleans measure and stopping
- construct solutions to stochastic differential equations
- understand the two different approaches to the Black-Scholes formula, on the one hand by means
of the geometric Brownian motion and related partial differential equations, on the other hand
by means of the fundamental theorem of pricing
- calculate the fair price of certain financial assets
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Prerequisites: (valid for students admitted to programmes within which the course is offered)
Linear Algebra, Analysis. Introduction to Probability Theory. A second course in mathematical analysis is useful.
Note: Admission requirements for non-programme students usually also include admission requirements for the programme and threshhold requirements for progression within the programme, or corresponding.
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Organisation:
Lectures and tutorials.
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Course contents:
Martingales, Markov processes, stochastic integrals, stochastic differential equations, Brownian motion, Itô's formula, Girsanov's theorem,
diffusion processes, random walk, Ising model,
Black-Scholes formula, risk-neutal valuation, volatility,
geometric Brownian motion and statistical analysis of stock prices,
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Course literature:
Wolfgang Paul, Jörg Baschnagel: Stochastic Processes: From Physics to Finance
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Examination: |
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Written examination
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6 ECTS
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Course language is English.
Department offering the course: MAI.
Director of Studies: Ingegerd Skoglund
Examiner: Jörg-Uwe Löbus
Link to the course homepage at the department
Course Syllabus in Swedish
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