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FINC405 Mathematical Finance

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.

Paper title Mathematical Finance
Paper code FINC405
Subject Finance
EFTS 0.1667
Points 20 points
Teaching period Second Semester
Domestic Tuition Fees (NZD) $1,058.71
International Tuition Fees (NZD) $4,692.94

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Normally available only to postgraduate students.
Knowledge on derivatives securities and advanced calculus is required.
Teaching staff
Professor Jin Zhang
Teaching Arrangements
Lectures with in-class exercises.
Text books 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
Upon successful completion of this paper, you should be able to:
  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

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Second Semester

Teaching method
This paper is taught On Campus
Learning management system


Stream Days Times Weeks
L1 Tuesday 12:00-13:50 28-34, 36-41
Thursday 12:00-13:50 28-34, 36-41