Mathematics

ECMM739 - Numerical Finance (2015)

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MODULE TITLENumerical Finance CREDIT VALUE30
MODULE CODEECMM739 MODULE CONVENERDr Dominic McCarthy (Coordinator)
DURATION: TERM 1 2 3
DURATION: WEEKS 0 11 11
Number of Students Taking Module (anticipated)
DESCRIPTION - summary of the module content

Numerical and computational methods are used widely in the field of quantitative finance. In this module you will study some of the most important of these methods, with an emphasis on Monte Carlo and lattice methods for option pricing. We further extend these methods to price exotic options and calculate risk metrics such as Value-at Risk. Additionally you will study methods to price credit derivatives and counter-party risk. This module is computational in nature and you are expected to implement these methods in C++ and additionally MATLAB.

AIMS - intentions of the module

The aim of this module is to provide a solid grounding in modern numerical and computational methods for option pricing and portfolio risk management. There will be some emphasis on potential interview questions where appropriate.
 

INTENDED LEARNING OUTCOMES (ILOs) (see assessment section below for how ILOs will be assessed)

On successful completion of this module you should be able to:

Module Specific Skills and Knowledge

1 Implement Monte Carlo methods.
2 Demonstrate knowledge of numerical option pricing techniques.
3 Show why credit derivatives are used and how they can be priced.

Discipline Specific Skills and Knowledge

4 Analyse and evaluate appropriate mathematical and computational methods required to tackle option pricing problems.
5 Assess the impact of different numerical option pricing methods.
6 Identify appropriate risk management strategies for a portfolio.

 
Personal and Key Transferable / Employment Skills and Knowledge
 
7 Present and communicate your methods and ideas in a professional manner.
8 Prepare for an interview for a quantitative position in finance.
 

 

SYLLABUS PLAN - summary of the structure and academic content of the module

Introduction to Options

Options and Payoff Functions, Stochastic Processes and Risk Neutral Valuation, The Black-Scholes equation, Binomial Methods and Algorithms.

Monte Carlo Methods

Computation of Random Numbers, Uniform Random Numbers, Linear Congruential and Fibonacci Generators, Random Vectors,
Normally Distributed Random Numbers, Correlated Normal Random Numbers Correlation Matrices, Cholesky Decomposition, Eigenvalue Methods, Low Discrepancy Sequences and Measures, Monte Carlo Simulation, Monte Carlo Integral, Monte Carlo Error,
Variance Reduction Methods, Antithetic Methods, Control Variate Methods, Monte Carlo for American Options, Quasi Monte Carlo Methods.

Finite Difference Methods

Finite Difference Methods, Approximation Methods, Explicit and Implicit Methods, Crank-Nicolson Method


Risk Measurement
Credit Derivatives and Risk Management, Hazard Rates, Credit Spreads, Credit Default Swaps, Collateralised Debt Obligations, Value at Risk, Credit Value at Risk, Historic Value at Risk Methods, Monte-Carlo Value at Risk Methods, Expected Shortfall, Credit Value Adjustment

 

LEARNING AND TEACHING
LEARNING ACTIVITIES AND TEACHING METHODS (given in hours of study time)
Scheduled Learning & Teaching Activities 66.00 Guided Independent Study 234.00 Placement / Study Abroad 0.00
DETAILS OF LEARNING ACTIVITIES AND TEACHING METHODS
Category Hours of study time Description
Scheduled learning and teaching activities 44 Lectures
Scheduled learning and teaching activities 22 Laboratory Sessions
Guided independent study 50 Formative and summative coursework
Guided independent study 184 Lecture and assessment preparation; private study

 

ASSESSMENT
FORMATIVE ASSESSMENT - for feedback and development purposes; does not count towards module grade
Form of Assessment Size of Assessment (e.g. duration/length) ILOs Assessed Feedback Method
Write Computer Code to solve numerical problem. 10 All Lecture
       
       
       
       

 

SUMMATIVE ASSESSMENT (% of credit)
Coursework 20 Written Exams 80 Practical Exams 0
DETAILS OF SUMMATIVE ASSESSMENT
Form of Assessment % of Credit Size of Assessment (e.g. duration/length) ILOs Assessed Feedback Method
Written exam 1– closed book 40 2 hours All Available on request
Written exam 2– closed book. 40 2 hours All Available on request
Assignment 1 10 20 hours 1, 2, 3, 4, 5 Lecture and individual feedback
Assignment 2 10 20 hours 1, 2, 3, 4, 5 Lecture and individual feedback
         

 

DETAILS OF RE-ASSESSMENT (where required by referral or deferral)
Original Form of Assessment Form of Re-assessment ILOs Re-assessed Time Scale for Re-assessment
All Examination 100% All August Ref/Def Period
       
       

 

RE-ASSESSMENT NOTES

If a module is normally assessed entirely by coursework, all referred/deferred assessments will normally be by assignment.

If a module is normally assessed by examination or examination plus coursework, referred and deferred assessment will normally be by examination. For referrals, only the examination will count, a mark of 40% being awarded if the examination is passed. For deferrals, candidates will be awarded the higher of the deferred examination mark or the deferred examination mark combined with the original coursework mark.

RESOURCES
INDICATIVE LEARNING RESOURCES - The following list is offered as an indication of the type & level of
information that you are expected to consult. Further guidance will be provided by the Module Convener

Basic reading:

 

ELE: http://vle.exeter.ac.uk/

 

Web based and Electronic Resources:

 

Other Resources:

 

Reading list for this module:

Type Author Title Edition Publisher Year ISBN Search
Set John C. Hull Options, Futures, and Other Derivatives 8th 2012 [Library]
Set Seydel RĂ¼diger U Tools for Computational Finance 5th 2012 [Library]
CREDIT VALUE 30 ECTS VALUE 15
PRE-REQUISITE MODULES None
CO-REQUISITE MODULES None
NQF LEVEL (FHEQ) 7 AVAILABLE AS DISTANCE LEARNING No
ORIGIN DATE Friday 09 January 2015 LAST REVISION DATE Tuesday 26 January 2016
KEY WORDS SEARCH Monte Carlo methods, Option Pricing, Credit Derivatives, Computational methods