Derivatives and risk management systematically addresses three basic questions: how do these products work, i.e. what are their payoffs? How can they be used, for hedging purposes or as part of trading strategies? And above all: how are they priced?
The course emphasises a small number of powerful ideas: absence of arbitrage, replication, and risk-neutral pricing. These are typically introduced in the context of discrete-time models, but the course also covers some well-known continuous-time models, starting with a comprehensive treatment of the Black-Scholes model. The course also covers important topics in risk management, in particular financial risk analysis and financial risk forecasting. The course provides students with a thorough understanding of market risk from both a practical and technical point of view.
Main topics of the module include:
- empirical properties of market prices (fat tails, volatility clusters)
- forecasting univariate and multivariate volatility models (ARCH, GARCH)
- concepts of financial risk (volatility, Value-at-Risk and Expected shortfall)
If you complete the course successfully, you should be able to:
- Apply risk-neutral valuation methods in continues time mathematics.
- Derive the Black-Scholes option valuation model, including its sensitivity measures (Greeks) and apply them to hedging techniques.
- Summarise empirical evidence on volatility smiles and its link to volatility models.
- Apply continuous time valuation techniques to price exotic option, forwards and futures and interest rate option.
- Identify the time series properties of financial asset prices and returns.
- Define and compare different risk measures: volatility, value at risk and expected shortfall.
- Master the analytical derivation of the above risk measures including alternative conditional volatility models.
Unseen written exam (3 hrs).
- Options, Futures, and Other Derivatives by John Hull, Pearson.
- Financial Risk Forecasting: The Theory and Practice of Forecasting by Jon Danielsson, Wiley.
Course information sheets
Download the course information sheets from the LSE website.