Introduction to Financial Calculus

Lecturer

Dr Zhou Zhou, The University of Sydney

Synopsis

This course focuses on the mathematics behind modeling of financial markets. You will learn about fundamental problems and solutions in mathematical finance. We will cover pricing financial derivatives, as well as hedging the risk associated with them. We will apply concepts such as arbitrage and martingale measures using tools from stochastic calculus.

Course Overview

  • Week 1: Arbitrage pricing principle, financial instruments, discrete time models, binomial model.
  • Week 2: Introduction to stochastic calculus, Ito’s formula, Feynman-Kac representation.
  • Week 3: Black-Scholes model, fundamental theorems of asset pricing.
  • Week 4: Martingale representation, Girsanov theorem, multiple stock models (topics from week 4 may be omitted or covered partially depending on the time available).

Prerequisites

  • (multivariable) calculus
  • basic probability theory or measure theory
  • no finance knowledge is required

This course covers foundational topics, e.g., stochastic calculus, as well as specialist topics like applications to mathematical finance in continuous time.

Assessment

  • 3x assignments (20% each)
  • Take home exam (40%)

Attendance requirements

TBA

Resources/pre-reading

These references may be useful for preparing for this course:
  • Capiński, M., & Kopp, P. E. (2004). Measure, integral and probability (Vol. 14). New York: Springer.
  • Capinski, M., & Zastawniak, T. J. (2013). Probability through problems. Springer Science & Business Media.

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Take this QUIZ to self-evaluate and get a measure of the key foundational knowledge required.

Dr Zhou Zhou, The University of Sydney

Dr. Zhou Zhou received B.S. in Mathematics from Nankai University in 2010, and Ph.D. in Applied and Interdisciplinary Mathematics from the University of Michigan in 2015. He was a Postdoctoral Fellow at the Institute for Mathematics and its Applications in the University of Minnesota during 2015–2017. He joined the School of Mathematics and Statistics in the University of Sydney in 2018. His research interests include mathematical finance, optimal stopping, stochastic control and games.