# FINANCIAL DERIVATIVES - 2019/0

Module code: PHY3048

## Module Overview

This module covers various different descriptions of diffusion, and the application of statistical physics to model share prices. This mathematics is then applied to calculating prices for some vanilla financial derivatives, followed by some exotic derivatives.

### Module provider

Physics

SWEENEY Stephen (Physics)

### Module cap (Maximum number of students): N/A

Independent Learning Hours: 117

Lecture Hours: 33

Semester 2

None.

## Module content

Indicative content includes:

Financial products and markets: Cash, interest rates, Stocks, dividends, Bonds, Credit Default

Swaps, Commodities, Derivatives, Markets, participants, Bid-Offer spread, Kelly Criterion, Arbitrage.

Stochastic Processes: Random Variables, Probabilities, Variance, Correlation, Central limit theorem, Normal distribution, Fat tails, Brownian motion, Langevin equation, Diffusion, Stochastic

Processes, Wiener process, Ito Calculus, Fokker-Planck equation.

Option Pricing: Binomial trees, Share price models, drift and volatility, Forward contracts, European and American options, Calls and Puts, Binomial pricing model.

Option Pricing: Continuous time, Black-Scholes model, Greeks, Discrete delta hedging, Implied volatility, volatility smiles.

Barrier options: Diffusion with absorbing barrier, knock-out and knock-in options, hedging in practice.

Portfolio optimisation theory.

## Assessment pattern

Assessment type Unit of assessment Weighting
Coursework COURSEWORK 30
Examination EXAMINATION - 1.5 HOURS 70

## Alternative Assessment

Alternative assessment: None

## Assessment Strategy

The assessment strategy is designed to provide students with the opportunity to demonstrate:

• Understanding of the concepts of derivative pricing, and underlying mathematics.

Thus, the summative assessment for this module consists of:

• coursework assignment involving data analysis and computational modelling of financial instruments, and a final examination of 1.5h duration in which 2 questions from 3 must be answered.

Formative assessment

Many problem sets are issued during the course, and feedback will be given during tutorial sessions.

## Module aims

• The aims are to expose the students to the fundamentals of financial derivatives, to explore their underlying science by analogy to physical systems, and to show, by various methods, how the fair price of financial options may be determined.

## Learning outcomes

 Attributes Developed 001 Understand the mathematics and models that underpin the analysis of financial data, including the properties of random variables, probability distributions (including the Levy distribution) and share price models and be able to assess their validity and remit; KCT 003 Know about a range of common financial derivatives, be able to explain financial terminology and produce pay-off and profit diagrams for forward contracts, put and call options; KC 004 Understand and be able to derive and use the Black-Scholes-Merton equation and be able to determine the prices of European options through its solution or through binomial models; KC 005 Examine and explain the role of quantities known as the “greeks” in financial analysis. KC 002 Understand Brownian motion process, Ito’s lemma, and the corresponding Fokker-Planck equations. Solve the diffusion equation using Fourier transforms. KC 006 Understand and be able to derive the price of barrier call and put options using the method of images. K 007 Understand basic portfolio optimisation theory KC

Attributes Developed

C - Cognitive/analytical

K - Subject knowledge

T - Transferable skills

P - Professional/Practical skills

## Methods of Teaching / Learning

The learning and teaching strategy is designed to:

Help students develop an understanding of how the ideas of Brownian processes can be applied to financial derivatives.

The learning and teaching methods include:

33 hours of lecture classes/tutorials and computer-based problem-solving

Indicated Lecture Hours (which may also include seminars, tutorials, workshops and other contact time) are approximate and may include in-class tests where one or more of these are an assessment on the module. In-class tests are scheduled/organised separately to taught content and will be published on to student personal timetables, where they apply to taken modules, as soon as they are finalised by central administration. This will usually be after the initial publication of the teaching timetable for the relevant semester.

Upon accessing the reading list, please search for the module using the module code: PHY3048

## Programmes this module appears in

Programme Semester Classification Qualifying conditions
Physics BSc (Hons) 2 Optional A weighted aggregate mark of 40% is required to pass the module
Physics with Nuclear Astrophysics BSc (Hons) 2 Optional A weighted aggregate mark of 40% is required to pass the module
Physics with Astronomy BSc (Hons) 2 Optional A weighted aggregate mark of 40% is required to pass the module
Mathematics and Physics BSc (Hons) 2 Optional A weighted aggregate mark of 40% is required to pass the module
Mathematics and Physics MPhys 2 Optional A weighted aggregate mark of 40% is required to pass the module
Mathematics and Physics MMath 2 Optional A weighted aggregate mark of 40% is required to pass the module
Financial Mathematics BSc (Hons) 2 Optional A weighted aggregate mark of 40% is required to pass the module

Please note that the information detailed within this record is accurate at the time of publishing and may be subject to change. This record contains information for the most up to date version of the programme / module for the 2019/0 academic year.