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Introduction

This course provides a 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 other hedging techniques, exotic derivatives, real 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's lemma, Black-Scholes-Merton and beyond
• The Greeks

3. Numerical Methods and Applications

• Empirical performance of option pricing models, volatility smiles
• Numerical techniques, exotic options
• Real options, credit Risk
• International derivatives markets