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    The necessary mathematical techniques used in continuous-time finance, including stochastic calculus, partial differential equations and applied probability.

    After completing this paper, one should be able to fully understand no-arbitrage theory, the Black-Scholes equation, risk-neutral probability and martingale. The purpose of this paper is to lay down a solid mathematical foundation for students to learn more advanced topics in financial engineering, such as exotic options, interest rate derivatives and credit risk models.

    About this paper

    Paper title Mathematical Finance
    Subject Finance
    EFTS 0.1667
    Points 20 points
    Teaching period Semester 2 (On campus)
    Domestic Tuition Fees ( NZD ) $1,196.41
    International Tuition Fees Tuition Fees for international students are elsewhere on this website.
    Normally available only to postgraduate students.
    Knowledge on derivatives securities and advanced calculus is required.
    Teaching staff
    Professor Jin Zhang
    Teaching Arrangements

    This paper is taught via lectures with in-class exercises.


    Textbooks are not required for this paper, but students will find the following reference books useful:

    1. Cerny, Ales, 2009, Mathematical Techniques in Finance: Tools for Incomplete Markets, Princeton University Press.
    2. McDonald, Robert L.,2013, Derivatives Markets, 3rd edition, Pearson.
    Course outline
    View the course outline for FINC 405
    Graduate Attributes Emphasised
    Communication, Critical thinking, Information literacy, Research, Self-motivation.
    View more information about Otago's graduate attributes.
    Learning Outcomes

    Students who successfully complete this paper should:

    1. Understand the concept of Brownian motion, expectations and martingale
    2. Learn how to model stock and option prices and to derive a PDE for option price by using the no-arbitrage principle
    3. Learn how to solve the Black-Scholes equation


    Semester 2

    Teaching method
    This paper is taught On Campus
    Learning management system


    Stream Days Times Weeks
    L1 Tuesday 12:00-13:50 29-35, 37-42
    Thursday 12:00-13:50 29-35, 37-42
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