Course syllabus - Analytical Finance II 7.5 credits

Analytisk finans II

Course code: MMA708
Valid from: Autumn semester13
Level of education: Second cycle
Subject: Mathematics
Main Field(s) of Study: Mathematics/Applied Mathematics,
In-Depth Level: A1F (Second cycle, has second-cycle course/s as entry requirements),
School: UKK
Ratification date: 2013-02-01

Objectives

In Analytical Finance II the students will broaden their knowledge of models and methods used in the financial industry. The major part of the course will focus on mathematical and numerical methods for fixed income instruments such as bills, notes and bonds, caps, floors and swaps and many others. By the end of this course the students should have broad knowledge in solving financial problems.

Learning outcomes

At the end of the course the student is expected to be able to
- transform between different interest rates (simple, discounting, continuous, spot, forward etc.).
- explain the concepts of day count conventions, quote types, future and present values, accrued interest rate and hazard rates.
- explain different kinds of fix-income instruments and calculate different kinds of risk measures.
- use bootstrapping on bonds and swaps to calculate yield curves using linear methods, Nelson-Siegel and Cox-Ingersoll-Ross and calculate Zero-Coupon bond prices with different short rate models.
- derive and solve the term-structure partial differential equation for the short rate models above and derive and use the Heath-Jarrow-Morton framework.
- use the Girsanov theorem, Radon-Nikodym derivative and martingale representation theorems to calculate values of financial contracts by changing probability measures.
- use the Black-Derman-Toy Model to calculate interest rate derivatives and calibrate the tree to market interest rate and volatility.
- manage an advanced project where the above mentioned abilities are used and make a well written report on the project.

Course content

Bonds and interest rates: yield, YTM, bootstrapping, discounting, present and future value, spot rates, and forward rates. Par rates, par yield, and repo rates. Inter bank rates (LIBOR, STIBOR, etc). Macaulay's, Fisher-Weil and modified duration and convexity. Risk measures in fixed-income. The cash flow of bonds and accrued interest rates. Interest rate derivatives. Numerical methods in finance: Binomial trees for interest rates. Bonds with embedded options: Callable and putable bonds and Option Adjusted Spread. Interest rate models: Hull-White, Ho-Lee and Heath-Jarrow-Morton. Portfolio Immunization and hedging with duration and convexity. Market price of interest rate risk. Forward measures. Convexity Adjustments. Convertible Bonds. The Libor Market Model.

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 Analytical Finance I 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.

Rules and regulations for examinations

Marks

Three-grade scale

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

Books

Röman, Jan;

AFI

Röman, Jan;

AFII

Compendiums

Analytical Finance 1& 2

Reference Literature

Hull, John;

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

Röman, Jan;

AFI

Röman, Jan R. M.;

Analytical Finance: Volume II. The Mathematics of Interest Rate Derivatives, Markets and Valuation

ISBN: 9783319525839

Compendiums

Analytical Finance 1& 2

Röman, Jan R.M.;

Problems and solutions to Analytical Finance

Reference Literature

Hull, John;

Options, futures, and other derivatives

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

xxi, 847 s.

Valid from: Autumn semester19

Decision date: 2019-08-21

Last update: 2019-09-04

Books

Röman, Jan;

AFI

Röman, Jan R. M.;

Analytical Finance: Volume II : The Mathematics of Interest Rate Derivatives, Markets, Risk and Valuation

ISBN: 9783319525846 LIBRIS-ID: 22250725

XXXI, 728 p. 141 illus.

Compendiums

Analytical Finance 1 & 2

Röman, Jan R.M.;

Problems and solutions to Analytical Finance

Reference Literature

Hull, John;

Options, futures, and other derivatives

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

xxi, 847 s.