## Computational Finance

### Module aims

After this course, the students will:
- understand the basic concepts of quantitative finance and financial engineering;
- be aware of the major decision, hedging, and pricing problems in finance, know how to formulate these problems as mathematical models, and understand the computational techniques to solve the arising models.

### Learning outcomes

Knowledge and Understanding, i.e. what they we end up knowing. Useful verbs: recall, explain, state, describe…

Explain the basic theory of interest and term structure

Describe the basic principles of risk management

Explain derivative pricing

Describe the role of derivative pricing in risk management

Explain the Capital Asset Pricing Model

Intellectual Skills, i.e. what problems they can solve, e.g. 'on paper'. Useful verbs: design, derive, compute, specify, analyse, evaluate, prove…

Analyse the term structure of interest rates

Compute optimal weights for a portfolio of stocks

Design strategies to hedge risk

Specify diversification strategies to reduce risk

Practical skills, i.e. what problems they can solve in a lab environment. Useful verbs: use, deploy, program, configure, apply…

Program binomial pricing models

Apply quadratic programming solvers in finance

Program Monte Carlo simulations

### Module syllabus

This course introduces the theory and application of modern quantitative finance from an engineering perspective.

This course will enable the students to:
- compare and appraise the basic theories that underlie current thinking in finance and investment;
- describe how these theories are applied in practical situations;
- describe the properties of the principle asset classes and securities;
- apply the basic analytical methods and computational tools used in finance;
- solve portfolio selection problems with off-the-shelf optimization software;
- solve option pricing problems based on binomial lattices;
- be able to read the technical literature in computational finance and undertake independent self-study (or research) in the future.

Course Outline:

1. Introduction to Computational Finance
1.1 Course Organization
1.2 Cash Flow Streams
1.3 Investments and the Market
1.4 Toy Example for Financial Option Pricing
2. Mathematical Preliminaries
2.1 Functions
2.2 Differential Calculus
2.3 Optimization
2.4 Probability Theory
3. The Basic Theory of Interest
3.1 The Time Value of Money
3.2 Net Present Value
3.3 The Term Structure of Interest Rates
4. Fixed-Income Securities
4.1 Terminology and Examples
4.2 Pricing of Fixed-Income Securities
4.3 Risk-Management of Fixed-Income Securities
5. Mean-Variance Portfolio Theory
5.1 Asset Returns
5.2 Variance as a Risk Measure
5.3 Markowitz Problem
5.4 Parameter Estimation
6. The Capital Asset Pricing Model (CAPM)
6.1 The One- and Two-Fund Theorems
6.2 The Capital Market Line
6.3 Systematic and Unsystematic Risk
6.4 CAPM as a Pricing Formula
7. General Principles
7.1 Utility Theory and Risk Aversion
7.2 Portfolio Choice and Linear Pricing
7.3 Risk-Neutral Pricing
8. Asset Price Dynamics
8.1 Binomial Lattices
8.2 Ito Processes
9. Basic Options Theory
9.1 Definitions, Terminology, and Payoff Diagrams
9.2 Single-Period Binomial Options Theory
9.3 Multi-Period Binomial Options Theory
9.4 Real Options

### Pre-requisites

Required: C233 - Computational Techniques (for computing students). All students are assumed to be familiar with basic analysis and linear algebra. The lecture notes for C233 are available from http://www.doc.ic.ac.uk/%7Eim/LectureNotes/comtec17e.pdf.

Recommended: C343 - Operations Research. Students who have not taken this course are assumed to be familiar with linear programming duality. The lecture notes for C343 are available from http://www.doc.ic.ac.uk/~dkuhn/Teaching.html.

### Teaching methods

Lectures and tutorials.

Two assessed courseworks will be given throughout the course.

### Assessments

*This is a level 7/M course

### Core

• #### Investment science

Luenberger, David G.

2nd., Oxford University Press

### Supplementary

Hull, John

9th, Pearson

• #### Optimization methods in finance

Cornuejols, Gerard

Cambridge University Press

• #### Dynamic asset pricing theory

Duffie, Darrell

3rd, Princeton University Press

• #### Introduction to financial option valuation mathematics, stochastics, and computation

Higham, D. J

Cambridge University Press

• #### An Introduction to Financial Option Valuation : [electronic resource] Mathematics, Stochastics and Computation / Desmond Higham.

Higham, Desmond,

Cambridge University Press,