# Course syllabus - Differential Equations in Finance 7.5 credits

### Differentialekvationer med finansiella tillämpningar

 Course code: MMA712 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

The aim of the course is to give the students knowledge on how the determination of the prices of financial derivative securities can be reduced to solving boundary value problems for partial differential equations.

## Learning outcomes

At the end of the course the student is expected to be able to
- formulate mathematical models for European, American, exotic options and interest rate derivative securities using boundary value problems for partial differential equations.
- explain the difference between classical boundary problems, linear complementarity problems, and free-boundary problems.
- explain the difference between initial, time-dependent and jump conditions.
- solve those of the above mentioned models that admit closed-form solutions.

## Course content

Partial differential equations in finance:
Derivation of the classical Black-Scholes equation, transformations on the Black-Scholes equation, American option problems as linear complementarity, free-boundary problems, general equations for derivatives, jump conditions, exotic options: barrier, Asian, look back, multi-asset and some other options, interest rate derivative securities: bonds, some explicit solutions of bonds equations, inverse problem on the market price of risk, applications of bond equations, multifactor interest rate models, two-factor convertible bonds.

## Teaching methods

Lectures combined with exercises.

## 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 and/or tests, (SEM1) 1.5 credits, marks Pass (G)
Examination, written and/or oral. May be replaced partially or fully by written assignments. (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 semester13

Decision date: 2013-08-02

Last update: 2013-08-02

## Books

Derivative securities and difference methods

ISBN: 0-387-20842-9 (alk. paper) LIBRIS-ID: 11196669

xviii, 513 s.