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|
|Teaching period||Semester 2 (On campus)|
|Domestic Tuition Fees (NZD)||$1,163.90|
|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:
- Cerny, Ales, 2009, Mathematical Techniques in Finance: Tools for Incomplete Markets, Princeton University Press.
- 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:
- Understand the concept of Brownian motion, expectations and martingale
- Learn how to model stock and option prices and to derive a PDE for option price by using the no-arbitrage principle
- Learn how to solve the Black-Scholes equation