Print Course syllabus
Course syllabus - Analytical Finance I
Scope
7.5 credits
Course code
MMA707
Valid from
Autumn semester 2013
Education level
Second cycle
Progressive Specialisation
A1N (Second cycle, has only first-cycle course/s as entry requirements).
Main area(s)
Mathematics/Applied Mathematics
School
School of Education, Culture and Communication
Ratified
2013-02-01
Literature lists
Course literature is preliminary up to 8 weeks before course start. Course literature can be valid over several semesters.
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Books
Analytical Finance: Volume I. The Mathematics of Equity Derivatives, Markets, Risk and Valuation
Compendiums
Analytical Finance 1& 2
Akademin för utbildning, kultur och kommunikation,
Reference Literature
Options, futures, and other derivatives
8. ed., Global ed. : Boston : Pearson, cop. 2012 (dvs. 2011) - xxi, 847 s.
ISBN: 978-0-273-75907-2 (pbk) LIBRIS-ID: 12308484
-
Books
Analytical Finance: Volume I. The Mathematics of Equity Derivatives, Markets, Risk and Valuation
Compendiums
Analytical Finance 1& 2
Akademin för utbildning, kultur och kommunikation,
Reference Literature
Options, futures, and other derivatives
8. ed., Global ed. : Boston : Pearson, cop. 2012 (dvs. 2011) - xxi, 847 s.
ISBN: 978-0-273-75907-2 (pbk) LIBRIS-ID: 12308484
-
Books
Compendiums
Analytical Finance 1& 2
Akademin för utbildning, kultur och kommunikation,
Reference Literature
Options, futures, and other derivatives
8. ed., Global ed. : Boston : Pearson, cop. 2012 (dvs. 2011) - xxi, 847 s.
ISBN: 978-0-273-75907-2 (pbk) LIBRIS-ID: 12308484
Objectives
On exchanges and on the OTC (Over The Counter) markets, wide ranges of financial instruments are traded. These instruments are valued by mathematical models or by simulations. In financial engineering, valuation models are developed, studied and used to create new types of instruments by combinations of other instruments. The course in Analytical Finance I provide the students with a knowledge of models and methods used in the financial industry. A major part of the course discusses mathematical and numerical models for various instruments. By the end of this course the students should have sufficient knowledge of quantitative finance to understand most of the derivative contracts traded in the equity markets and to value them.
Learning outcomes
At the end of the course the student is expected to be able to
- calculate the fair value, the hedge parameters and replicating portfolios of American and European options using the binomial model.
- derive and solve the Black-Scholes partial differential equation.
- solve parabolic partial differential equations using the Feynman-Kac representation.
- calculate simple stochastic integrals using the Itô lemma.
- use the Girsanov theorem, Radon-Nikodym derivative and martingale representation theorems to calculate values of financial contracts by changing probability measures.
- implement financial models in Excel/VBA, Java or Matlab.
- calculate delta and delta-gamma hedge of a portfolio.
- determine the arbitrage free prices of financial contracts in the Black-Scholes world.
Course content
Products and markets. Derivative contracts: American-, Bermudan- and European options, forwards and futures. Strategies with options. Random behaviour of assets. Elementary stochastic processes. Introduction to partial differential equations. Pricing via Arbitrage. Martingales. Binomial models. Replicated portfolios. Finite difference methods. The Black-Scholes model and the hedge parameters. Introduction to exotic and path-dependent options. Numerical methods in finance: Binomial trees, finite difference and Monte Carlo simulations Radon-Nikodym derivative. Itô lemma. Feynman-Kac representation. Analytical pricing formulas for American options. Girsanov transformations. Market price of risk. Stopping times and American-type securities. Volatility models. Pricing using deflators.
Tuition
Lectures and a seminar project where the students will implement and model financial contracts using numerical methods.
Specific requirements
At least totally 120 credits in the engineering, natural sciences, business administration or economics areas including Probability 7.5 credits or equivalent. In addition Swedish course B/Swedish course 3 and English course A/English course 6 are required. For courses given entirely in English exemption is made from the requirement in Swedish course B/Swedish course 3.
Examination
Seminar (SEM1), 1.5 credits, marks Pass (G) or Pass with distinction (VG)
Written examination (TEN1), 6 credits, marks Pass (G) or Pass with distinction (VG)
A student who has a certificate from MDU regarding a disability has the opportunity to submit a request for supportive measures during written examinations or other forms of examination, in accordance with the Rules and Regulations for Examinations at First-cycle and Second-cycle Level at Mälardalen University (2020/1655). It is the examiner who takes decisions on any supportive measures, based on what kind of certificate is issued, and in that case which measures are to be applied.
Suspicions of attempting to deceive in examinations (cheating) are reported to the Vice-Chancellor, in accordance with the Higher Education Ordinance, and are examined by the University’s Disciplinary Board. If the Disciplinary Board considers the student to be guilty of a disciplinary offence, the Board will take a decision on disciplinary action, which will be a warning or suspension.
Grade
Pass with distinction, Pass, Fail