Lecturers(s): Dr Vicky Henderson
Important: This module is Core for MSc Financial Mathematics students. It is not available to undergraduates. Other students interested in taking the module should consult the lecturer.
1 x 2 hour lecture plus 1 hour tutorial per week. This module runs in Term 1.
To provide an introduction to derivative securities and their pricing. The module aims to introduce various types of instruments traded in financial markets, along with the concepts of no-arbitrage pricing and hedging.
Upon completing this module students will be able to:
- Characterise different classes of derivatives in different markets
- Explain the use of derivatives for hedging and risk management
- Apply the theory of stochastic processes and martingales to calculate the prices of options.
Introduction to derivatives: forwards, futures, European and American options, Real Options. Rationale for using options. Case study.
Arbitrage, no-arbitrage and hedging. Put-call parity, no-arbitrage restrictions, option strategies eg. calendar and butterfly spreads.
Interest rates and interest rate derivatives: zero coupon bonds, spot and forward rates, LIBOR. FRAs. Interest rate swaps.
The Black-Scholes formula and assumptions. Model calibration. Implied volatility. Delta hedging. Greeks. Exotic options. Black-scholes pde.
Introduction to credit and credit derivatives. Defaultable ZCBs and CDS.
One-period Binomial model for option pricing. Replication. Risk-neutral probabilities.
Multi-period models. Pricing via martingales. Binomial martingale representation theorem. Discrete time changes of measure.
Trinomial models. Complete markets. Convergence of the binomial to the Black-Scholes model. American options in binomial model.
Application of Ito's formula, the Brownian martingale representation theorem and Girsanov's theorem to derive the Black-Scholes formula.
Black Scholes extensions - Black Scholes with default, Options on forwards and futures, FX and quantos. Commodities and Energy derivatives.
Options, Futures and Other Derivatives (Hull)
Stochastic Calculus for Finance I and II (Shreve)
Financial Calculus (Baxter and Rennie)
A Course in Derivative Securities (Back)
Examination (80%) Coursework (20%)
Coursework will be comprised of 4 class tests (best 3 of 4 marks will be used). Class tests will be held during class in weeks 3, 5, 7 and 9.
Feedback will be returned after 2 weeks.