Introductory Mathematical Finance

FOR10 Introductory Mathematical Finance

  • Topics

    Topics

    The objective of the course is to introduce the theory of mathematical finance and the mathematical tools on which this is based. The focus chosen is on the pricing of financial assets via arbitrage theory. We will concentrate on discrete time models, e.g. Cox-Ross-Rubinstein and multinomial models, and classical assets as European call and put options.

    In the above market models we will also study optimal portfolio problems, that is we study how to obtain a strategy maximizing the expected utility of the final wealth. For this we will concentrate on complete markets.

    The mathematical tools presented in the course belong to the theory of probability and stochastic processes. They include the concepts of probability measures, conditional expectations, and martingales. The concepts, methods, and models discussed have a value by themselves and can be applied beyond the focus of this course. They also constitute the base for follow-up courses at master level.

    Topics

    • Elements of probability theory and stochastic processes: probability measures, conditional expectations, convergences, filtrations, martingales, change of measure
    • Financial assets: derivatives of European type
    • Discrete time models: Cox-Ross-Rubinstein and multinomial models as preparation to the classical Black-Scholes model
    • Pricing methods: concept on arbitrage, risk-neutral evaluation, Snell envelope
    • Optimal portfolio problems via martingale methods

  • Learning outcome

    Learning outcome

     Introductory Mathematical Finance is a semi-intensive course that equips the students with the foundation of financial modeling in a single and multi-period trading framework. The focus is on the rigorous understanding of the principle of finance merged into the model aimed at the pricing of financial derivatives. The students will be learning about pricing and hedging financial derivatives and will learn the basis of utility optimization and optimal portfolios.

     

    At the end of the course the students will:

    1. Have a good understanding of the foundation of financial modeling in a single and a multi-period trading model

    2. Be able to define arbitrage and understand the concept of fair pricing

    3. Be able to distinguish between complete and incomplete markets and what makes the difference

    4. Be able to find no-arbitrage prices of any feasible financial derivative using the no-arbitrage principle

    5. Be able to find hedging strategies of feasible financial derivatives

    6. Be able to solve optimal portfolio problems in single and multiperiod markets

     

    Besides, the students will be equipped with some universal mathematical tools:

    1. Stochastic processes and the information flow

    2. Probability measures, probability distributions, and changes of probabilities: risk-neutral measures

    3. Expectations and conditional expectations

    4. Martingales

    5. Stochastic optimal control problems

  • Teaching

    Teaching

    The course will be delivered through a combination of lectures and exercise classes in which some selection of the exercises suggested during lectures are going to be corrected. There will be 32 lectures grouped in in 7-8 days of semi-intensive work according to schedule. Exercises will be posted on the webpage along with their solutions. There will be 2 compulsory assignments during the course.

  • Required prerequisites

    Required prerequisites

    There are no formal requirements for this course, however any background knowledge or insight in the mathematical directions can facilitate the participation.

    Very useful background knowledge is to be able to solve a to solve a linear system of equations. Good knowledge of the concept of random variable, probability distribution, stochastic process, expectation and variance is also helpful.

    For example useful background courses could be: MAT10 Analyse og lineær algebra; MAT11/MAT011 Differense og differensiallikninger; MAT12/MAT013 Matematisk statistikk; MAT13/MAT016 Optimering

  • Credit reduction due to overlap

    Credit reduction due to overlap

    Overlap with VOA038

  • Requirements for course approval

    Requirements for course approval

    2 approved assignments given during the course.

  • Assessment

    Assessment

    Three hour written exam.

    If nothing else is determined by the course start, the examination can only be written in English.

  • Grading Scale

    Grading Scale

    Grading scale A - F

  • Semester

    Semester

    Spring (biannual).Offered next time spring 2018.

  • Literature

    Literature

    The recommended text for this course is

    "Derivative Pricing in Discrete Time", by Nigel Cutland and Alet Roux, Springer 2012.

    Lecture notes on selected topics will be made available.

    Useful alternative text can be e.g.:

    "Risk-Neutral Valuation. Pricing and Hedging of financial Derivatives", by N.H. Bingham and Rüdiger Kiesel, Springer 2000.

Overview

ECTS Credits
7.5
Teaching language
English
Semester
Spring

Course responsible

 Giulia di Nunno, Department of Business and Management Science