Quantitative Finance: Mathematics in Investment Banking

About

Quantitative Finance remains one of the fastest growing areas in modern finance, often referred to as Financial Engineering, Mathematical Finance or Financial Mathematics.

This application-based module focuses on the mathematical and computational aspects of derivative pricing, sitting at the intersection of mathematics, computing, finance and economics. Both theory and numerical techniques will be presented, with computer simulations performed using Microsoft Excel.

If you are interested in technical finance and have wondered what Brownian motion is, or how Monte Carlo methods are used to price options, this module is precisely what you are looking for. It covers Itô Calculus, the Black-Scholes world and Monte Carlo simulations.

This is not a theorem-proof-based module, but all results will be derived.

Week one
Maths refresher: differential equations and probability theory
Introduction to the global financial markets and products that are traded in them – asset classes, futures/forwards and options. Fixed income world and bonds
Modelling stock price returns – Excel based exercise

Week two
Binomial Model – no arbitrage and delta hedging; risk-neutrality and risk-neutral probabilities
Applied Stochastic Calculus – Brownian motion (construction and properties), Itô’s lemma and applications. Models for stocks, interest rates, volatility

Week three
Black-Scholes model – assumptions, equation and famous Nobel prize winning formula.
Plain vanillas and simple exotics
Monte Carlo Method – connection between option prices and simulations

Course leader

Dr Riaz Ahmad

Course aim

This module aims to:

- Develop your competence and confidence in understanding essential mathematical and numerical techniques, and their practical use in investment banking to price options.
- Introduce you to mathematical methods and computational finance schemes, such as Monte Carlo simulation.
- Provide you with the opportunity to study a popular yet specialised branch of finance in an accessible way, building on UCL’s strong foundation in mathematics.
- Stimulate further interest in technical finance and demonstrate that quantitative finance does not need to appear inaccessible or overly complex.

Fee info