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# Quantitative & Computational Finance

By Loretta Murphy,2014-08-08 08:08
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Quantitative & Computational Finance

Quantitative and Computational Finance

Code: GM21 (previously Applied Mathematical Finance)

Year: MSc

Prerequisites: A degree in mathematics, physics or engineering

Term: 2

‘Quantitative Finance’ as a branch of modern finance

is one of the fastest growing areas within the

corporate world. Together with the sophistication

and complexity of modern financial products, this

exciting discipline continues to act as the motivating

factor for new mathematical models and the

subsequent development of associated

computational schemes. Alternative names for this

subject area are Mathematical Finance, Financial

Mathematics or Financial Engineering. This is a

course in the applied aspects of mathematical Aims: finance, in particular derivative pricing. The

necessary understanding of products and markets

required will be covered during the course. The

overall theme of the course is to develop the Partial

Differential Equation (PDE) approach to the pricing

of options. As well as a two hour examination during

the summer term, students will undertake a short

computing project where they will use numerical and

computational techniques to perform derivative

pricing.

Students upon completion will obtain a flavour of the

mathematical models and computational schemes

used in investment banks and hedge funds, by

quantitative analysts working in derivative pricing Learning roles. In addition to understanding the mathematics

Outcomes: of stochastic differential equations (SDEs), students

will be able to simulate these for underlying assets

and derive the PDEs for pricing options on various

asset classes. During the computational project

students will demonstrate their understanding of the

numerical and computational methods, by

formulating and solving a real life derivative pricing

problem. The course will also be useful as a starting

point and/or for generating interest for possible PhD

research.

Content:

Brief introduction to Stochastic Differential Simulation Equations (SDEs) drift, diffusion, Itô’s Lemma. Methods in The statistics of random number generation in Finance Excel. Simulating asset price SDEs in Excel.

Introduction to the financial markets and the Financial products which are traded in them: Equities, Products and indices, foreign exchange, fixed income world and Markets commodities. Options contracts and strategies for

speculation and hedging.

Similarity reduction and fundamental solution for

the heat equation. Black-Scholes PDE: simple

European calls and puts; put-call parity. The PDE Black-Scholes for pricing commodity and currency options. framework Discontinuous payoffs Binary and Digital options.

The greeks: theta, delta, gamma, vega & rho and

their role in hedging.

Solving the pricing PDEs numerically using Explicit, Computational Implicit and Crank-Nicholson Finite Difference

Finance Schemes. Stability criteria. Monte Carlo Technique

for derivative pricing.

Introduction to the properties and features of fixed

income products; yield, duration & convexity.

Stochastic interest rate models: stochastic Fixed-Income differential equation for the spot interest rate; bond Products pricing PDE; popular models for the spot rate

(Vasicek, CIR and Hull & White); solutions of the

bond pricing equation;

Method of Instruction:

Mainly formal lectures. A few computing classes (where appropriate)

where students will be able to perform computer simulations and

pricing.

Assessment:

The course has the following assessment components:

; Two hour written examination in the summer (90%)

; Individual Project (10%)

To pass this course, students must:

; Obtain an overall combined mark of at least 50%

Note:

Due to the heavy mathematical nature of this module - a background in calculus, probability and differential equations obtained in an undergraduate degree is a compulsory requirement for this course. Resources:

Paul Wilmott Introduces Quantitative Finance Paul Wilmott. J. Wiley & Sons. 2nd Edition, 2007

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