# ST957: Financial Derivatives

###### 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.**

**Commitment:**

1 x 2 hour lecture plus 1 hour tutorial per week. This module runs in Term 1.

**Summary:
**

**Aims:**

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.

**Learning Outcomes:**

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.

**Content:**

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.

**Books:**

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)

**Assessment: **

Examination (80%) Coursework (20%)

**Deadline:**

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:**** **

Feedback will be returned after 2 weeks.