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||Second Semester|
|Domestic Tuition Fees (NZD)||$1,079.88|
|International Tuition Fees (NZD)||$4,786.79|
- 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
- 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
- Upon successful completion of this paper, you should be able to:
- 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