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Goals of this Course

Goals of this Course. Numerical Financial Engineering Accurate numerical approximations to financial modelling problems Construct robust schemes that can be implemented in a programming language Develop insights into modelling lifecycle. Core Processes in Course.

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Goals of this Course

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  1. Goals of this Course • Numerical Financial Engineering • Accurate numerical approximations to financial modelling problems • Construct robust schemes that can be implemented in a programming language • Develop insights into modelling lifecycle

  2. Core Processes in Course • We must decide how to realise our goals • We construct a lifecycle model • Focus is on Partial Differential Equations (PDE) • Focus is on Finite Difference Methods and schemes (FDM) • Some attention to be paid to algorithms and coding issues

  3. Main Activities in Numerical Financial Engineering

  4. Creating PDE (1/2) • Map financial model to a PDE model • PDE is (usually) of parabolic type • Take initial and boundary conditions into account • Applicable to European exercise

  5. Creating PDE (2/2) • One-factor models • Models for plain options • Two-factor and many-factor models • Exotic options • Create an unambiguous PDE model

  6. American-style Options • PDE solution no longer applicable • Problems have free boundaries • Must use Parabolic Variational Inequalities (PVI) • Can extend finite differences to support PVI

  7. Finite Differences • Well-established theory (200 years old!) • We use various kinds of FDM • The most appropriate FDM for the problem at hand • Robust analysis of suitability of FDM for option modelling

  8. Algorithms and Closing to Code • Describe finite difference schemes by discrete algorithms • Document unambiguously! • Rules and tips for mapping to C++, VB.Net, Java and C# • Interfacing to Excel (some tips)

  9. Advantages of this Approach • Well-defined process from A to Z • Use proven techniques and results • Mathematically sound • High relevance to current problems in financial engineering

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