# FINANCIAL DERIVATIVES - 2024/5

Module code: PHY3048

## Module Overview

This module covers various the application of statistical physics to model share prices. This mathematics is then applied to calculating prices for some examples of financial derivatives.

### Module provider

Mathematics & Physics

NOEL Noelia (Maths & Phys)

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

Independent Learning Hours: 107

Lecture Hours: 22

Tutorial Hours: 11

Guided Learning: 10

Semester 2

None.

## Module content

Indicative content includes:

Financial products and markets:

Cash, interest rates, Stocks, dividends, Bonds, Swaps, Commodities, Derivatives, Markets, participants, arbitrage.

Stochastic Processes:

Random Variables, Probabilities, Variance, Normal and Lognormal distributions, Brownian motion, Wiener process, Ito Calculus.

Option Pricing:

Binomial trees, Share price models, drift and volatility, Forward contracts, European and American options, Calls and Puts, Binomial pricing model, Black-Scholes model and hedging.

Portfolio optimisation theory and types of trade.

## Assessment pattern

Assessment type Unit of assessment Weighting
Coursework COURSEWORK 100

## 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.

The summative assessment for this module consists of:

• Coursework assignment involving data analysis and modeling of financial instruments.

Formative assessment

Problem sheets 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 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. KCP 004 Understand and be able to derive and use Binomial Tree models and the Black-Scholes-Merton model. KCP 005 Examine and explain the role of quantities such as the “greeks” in financial analysis. KC 002 Understand Brownian motion process and Ito’s lemma. KC 006 Understand and be able to derive the price of call and put options. KCPT 007 Understand basic portfolio optimisation theory and types of trading and traders. KCP

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 stochastic 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.