You are here:

Derivatives and risk management FN3206

The course focuses on derivatives, with a particular emphasis on equity derivatives (standard call and put options, exotic options), futures and forward contracts, and interest rate derivatives (swaps, caps and floors, swaptions).

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.

Topics covered

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)

Learning outcomes

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).

Essential reading

  • 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.