COMP0048 Financial Engineering

This database contains the 2018-19 versions of syllabuses. These are still being finalised and changes may occur before the start of the session.

Syllabuses from the 2017-18 session are available here.

Academic session

2018-19

Module

Financial Engineering

Code

COMP0048

Module delivery

1819/A7P/T1/COMP0048 Postgraduate

Related deliveries

None

Prior deliveries

COMPG012

Level

Postgraduate

FHEQ Level

L7

FHEQ credits

15

Term/s

Term 1

Module leader

Ahmad, Riaz

Contributors

Ahmad, Riaz

Module administrator

Nolan, Martin

Aims

This module introduces the applied mathematical and computational aspects of Quantitative Finance.

Learning outcomes

On successful completion of the module, a student will be able to successfully apply the necessary probability and differential equation based approach to the pricing of financial derivatives; using both quantitative and numerical techniques.

Availability and prerequisites

This module delivery is available for selection on the below-listed programmes. The relevant programme structure will specify whether the module is core, optional, or elective.

In order to be eligible to select this module as optional or elective, where available, students must meet all prerequisite conditions to the satisfaction of the module leader. Places for students taking the module as optional or elective are limited and will be allocated according to the department’s module selection policy.

Programmes on which available:

  • MSc Computational Finance
  • MSc Computational Statistics and Machine Learning
  • MSc Financial Risk Management
  • MSc Engineering with Finance

Prerequisites:

In order to be eligible to select this module, student must have a good understanding of basic probability and differential equations.

Content

Financial Products and Markets

Time value of money and applications. Equities, indices, foreign exchange and commodities. Futures, Forwards and Options. Payoff and P&L diagrams. Put-Call parity.

Stochastic Calculus

Brownian motion and properties, Itô’s lemma and Itô integral. Stochastic Differential Equations – drift and diffusion; Geometric Brownian Motion and Vasicek model. Forward and Backward Kolmogorov equations for the transition density.

Black-Scholes Model

Assumptions, PDE and pricing formulae for European calls and puts. Extending to dividends, FX and commodities. The Greeks and risk management - theta, delta, gamma, vega & rho and their role in hedging. Two factor models and multi-asset options.

Mathematics of early exercise

Perpetual American calls and puts; optimal exercise strategy and the smooth pasting condition.

Computational Finance

Solving the pricing PDEs numerically using Explicit Finite Difference Scheme. Random number generation in Excel – RAND(), NORMSINV(), simulating random walks, correlations. Examining statistical properties of stock returns.

Stochastic interest rate models

Fixed income world – zero coupon bonds and coupon bearing bonds; yield curves, duration and convexity. Bond Pricing Equation (BPE). Popular models for the spot rate - Vasicek, CIR, Ho & Lee and Hull & White. Solutions of the BPE.

Introduction to Exotics

Basic features and classification of exotic options. Simple exotics – Binaries, one-touch, power options, compound and exchange options. Weak and strong path dependency - barriers, Asians and Lookbacks. Sampling - continuous and discrete. Pricing using the PDE framework.

An indicative reading list is available via http://readinglists.ucl.ac.uk/departments/comps_eng.html.

Delivery

The module is delivered through a combination of lectures and computing sessions.

Assessment

This module delivery is assessed as below:

#

Title

Weight (%)

Notes

1

Written exam (2hrs 30mins)

70

 

2

Coursework 1

5

 

3

Coursework 2

5

 

4

Coursework 3

5

 

5

In-class test

15

 

In order to pass this module delivery, students must achieve an overall weighted module mark of 50%.

Resources

Recommended Books

  • Paul Wilmott, Paul Wilmott Introduces Quantitative Finance, John Wiley & Sons