The goal of the course is to refresh and expand your knowledge of
several important topics of the Master Program, such as object-oriented programming with C++, calibration of financial models,
pricing of derivative securities, numerical analysis, and stochastic
calculus. The course is organized around a project of the design and
implementation of a powerful C++ library for pricing of derivative
securities.
several important topics of the Master Program, such as object-oriented programming with C++, calibration of financial models,
pricing of derivative securities, numerical analysis, and stochastic
calculus. The course is organized around a project of the design and
implementation of a powerful C++ library for pricing of derivative
securities.
- Lecturer: Dmitry Kramkov
Course Term: Hilary
Course Lecture Information: 16 lectures
Course Overview:
The goal of this course is to refresh and expand knowledge of several important topics of the MSc, such as Object Oriented Programming with C++, theory of pricing and hedging of derivative securities, numerical analysis and stochastic calculus. The course is organized around a project for the design and implementation of a powerful C++ library for pricing of derivative securities. The students will learn important principles of implementation of financial models and master algorithms of evaluation of different types of derivative securities: European, American, standard, barrier and path dependent options on stocks and interest rates. The course will be organised in 8 three-hour sessions. All course materials will be supplied.
Learning Outcomes:
You will master algorithms of evaluation of different types of
derivative securities: European and American, standard and barrier
options on stocks and interest rates. A special attention will be
given to the topic of calibration of financial models with emphasis on
interpolation and least-squares fitting. The course prepares you for a
quantitative position in structured financial products and risk
management.
derivative securities: European and American, standard and barrier
options on stocks and interest rates. A special attention will be
given to the topic of calibration of financial models with emphasis on
interpolation and least-squares fitting. The course prepares you for a
quantitative position in structured financial products and risk
management.
Course Synopsis:
1. Elements of C++: namespaces, STL, inheritance and templates,
exceptions and assertions, smart pointers, RAII and PIMPL design
principles.
2. Construction of analytic data curves.
3. Root finding with polishing and bracketing algorithms and
implied parameters.
4. Calibration through interpolation. Basic interpolation methods:
linear interpolation, cubic spline, Akima, and Steffen splines.
5. Calibration through least-squares fitting. Multi-dimensional
linear least-squares fitting.
6. Design of a financial model for the pricing of derivatives: rollback
operator and state processes.
7. Evaluation of standard European and American options on a stock.
8. Evaluation of standard European and American options on interest
rates.
1. Elements of C++: namespaces, STL, inheritance and templates,
exceptions and assertions, smart pointers, RAII and PIMPL design
principles.
2. Construction of analytic data curves.
3. Root finding with polishing and bracketing algorithms and
implied parameters.
4. Calibration through interpolation. Basic interpolation methods:
linear interpolation, cubic spline, Akima, and Steffen splines.
5. Calibration through least-squares fitting. Multi-dimensional
linear least-squares fitting.
6. Design of a financial model for the pricing of derivatives: rollback
operator and state processes.
7. Evaluation of standard European and American options on a stock.
8. Evaluation of standard European and American options on interest
rates.