Course Introduction
This module is aimed at final year undergraduate students, master students and PhD students who want to continue with higher studies in Stochastic Analysis or Mathematical Finance or who want to work in the financial industry.
It will introduce you some basic but important concepts, notations and theories of Stochastic Analysis and Mathematical Finance (e.g. Brownian Motion, Quadratic Variation, Stochastic Differential Equations, Ito’s Formula, Black-Scholes-Merton Formula, Financial Derivatives). This module will be helpful (if not necessary) for the pursuing of advanced Quantitative Finance modules.
Schedule
- Introduction; Conditional Expectation
- Brownian Motion
- Quadratic Variation
- Itô’s Integral
- Itô’s Formula
- SDE; Change of Probabilities
- Girsanov Theorem; First Passage Time
- A Model for Stocks; PDE
- Risk-Neutral Pricing
- Change of Numeraire
- PDE and FK formula
- Extensions and Hedging (Greeks)
- American Options
Books
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Stochastic Calculus for Finance II : Continuous-Time Models, Steven Shreve
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Brownian Motion and Stochastic Calculus, Ioannis Karatzas, Steven Shreve.
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Methods of Mathematical Finance, Ioannis Karatzas, Steven Shreve.
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Martingale Methods in Financial Modelling, Marek Musiela, Marek Rutkowski.
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Paul Wilmott on Quantitative Finance, , Second Edition, Paul Wilmott.