# Course syllabus - Analytical Finance I 7.5 credits

### Analytisk finans I

 Course code: MMA707 Valid from: Autumn semester13 Level of education: Second cycle Subject: Mathematics Main Field(s) of Study: Mathematics/Applied Mathematics, In-Depth Level: A1N (Second cycle, has only first-cycle course/s as entry requirements), School: UKK Ratification date: 2013-02-01

## 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.

## Teaching methods

Lectures and a seminar project where the students will implement and model financial contracts using numerical methods.

## Specific entry requirements

At least 120 credits totally from these areas: technical, natural sciences, business administration or economics where Probability 7,5 credits or equivalent is included. 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 MDH 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 (2016/0601). 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.

## Enviromental aspects

The course does not contain any specific environmental considerations.

Course literature is preliminary until 3 weeks before the course starts. Literature may be valid over several terms.

Valid from: Autumn semester14

Decision date: 2014-08-08

Last update: 2014-08-28

AFI

AFII

## Compendiums

Analytical Finance 1& 2

## Reference Literature

Options, futures, and other derivatives

ISBN: 978-0-273-75907-2 (pbk) LIBRIS-ID: 12308484

xxi, 847 s.

Valid from: Spring semester17

Decision date: 2017-02-22

Last update: 2017-02-22

## Books

AFII

Analytical Finance: Volume I. The Mathematics of Equity Derivatives, Markets, Risk and Valuation

## Compendiums

Analytical Finance 1& 2

## Reference Literature

Options, futures, and other derivatives

ISBN: 978-0-273-75907-2 (pbk) LIBRIS-ID: 12308484

xxi, 847 s.