Options, Futures and Other Financial Derivatives

This course delivers the concepts and models underlying the modern analysis and pricing of financial derivatives. The underlying philosophy of the course is to first provide the firm foundations for understanding derivatives in general.

The required technical tools will be explained carefully, allowing students to learn the language and to be able to converse with derivatives professionals. Once the tools are in place, those same tools can then be applied to any derivative. Special emphasis will be put on those derivatives that shape the modern world.

The first half of the course involves the review of the required tools, the setup of the pricing framework, the intuition of the methodology and the application to plain vanilla derivatives.

The second half of the course applies those techniques to more advanced topics: exotic derivatives, volatility modelling (including stochastic volatility, local volatility and volatility derivatives such as variance swaps) and interest-rate derivatives.

Programme structure:

- Arbitrage and Risk-Neutral Pricing
- Basic Properties of Forwards and Options
- The Binomial model of Cox, Ross and Rubinstein
- A primer on Stochastic Calculus and continuous-time modelling
- The Model of Black and Scholes
- Greeks and Hedging Schemes
- Forwards and Futures
- American Options
- Exotic and Path-Dependent Options, Structured Products
- Historical Volatility, Implied Volatility and Heston’s Stochastic Volatility model
- Local Volatility
- Variance and Correlation Swaps
- Introduction to Fixed-Income and Interest Rate derivatives
- Interest Rate Options

Course leader

Dr Jean-Pierre Zigrand and Dr Rohit Rahi

Target group

Undergraduate and Graduate students.

Prerequisites:
Calculus and statistics at the intermediate undergraduate level. Students must have a good grounding in differential calculus, including Taylor series, and some grounding in integration (including computing expectations of random variables).

Course aim

Programme structure:

- Arbitrage and Risk-Neutral Pricing
- Basic Properties of Forwards and Options
- The Binomial model of Cox, Ross and Rubinstein
- A primer on Stochastic Calculus and continuous-time modelling
- The Model of Black and Scholes
- Greeks and Hedging Schemes
- Forwards and Futures
- American Options
- Exotic and Path-Dependent Options, Structured Products
- Historical Volatility, Implied Volatility and Heston’s Stochastic Volatility model
- Local Volatility
- Variance and Correlation Swaps
- Introduction to Fixed-Income and Interest Rate derivatives
- Interest Rate Options

Credits info

4 EC
Typical credit: 3-4 credits (US) 7.5 ECTS points (EU). You will need to check with your home institution. Assessment is optional.

Fee info

GBP 2500: Discounts apply when booking multiple courses. LSE Summer School runs three sessions during the summer, and students can book one course per session. Save 32% on your second course and 68% on your third course when booking.