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Quantitative & Computational Finance

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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

    Taught By: Riaz Ahmad (100%)

    ‘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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