Course description



This course provides thorough understanding of the workings and pricing of derivative securities.

We cover model-free no-arbitrage bounds for derivatives prices, the binomial model and its continuous time limit, the mathematics of continuous time, the Black-Scholes model and its derivation, adjusting the Black-Scholes and binomial models to price futures and currency options, delta hedging and more fancy hedging, exotic derivatives, real options, executive options, credit risk, etc. A significant part of the course focuses on the numerical valuation of options.

Course content

1. Introduction

  • Options markets
  • Model-free no-arbitrage bounds
  • Trading strategies with options

2. Pricing

  • Binomial Trees
  • Wiener Processes, Ito¬ís Lemma, Black-Scholes-Merton and beyond
  • The Greeks

3. Numerical Methods and Applications

  • Empirical Performance of Option Pricing Models
  • Numerical Techniques
  • Exotic Options, Volatility Smiles, Risk Management
  • Real Options and Credit Risk

Learning outcome knowledge

By the end of the course the students are expected to know:

  • model-free no-arbitrage bounds for derivatives prices
  • the binomial option pricing model
  • the Black-Scholes model
  • arbitraging mispriced options
  • delta hedging of options
  • hedging options with the Greeks
  • extensions of plain vanilla options
  • option valuation with stochastic volatility
  • empirical performance of option pricing models
  • valuation of executive options
  • valuation real options
  • credit risk valuation using option pricing

Exam organisation

  • Class participation: 20%
  • Home exam: 20%
  • Written exam: 60%