Computational and Quantitative Finance with C++
1st Semester, Course Code: ΜΕΧΤΕ104
Credits: 7,5
Learning Outcomes
The intent of this course is to describe the technical and algorithmic aspects of a wide spectrum of computer applications currently used in the financial industry, and to prepare students for the development of new applications. It addresses to those who wish to learn modern and state-of-the art C++ language features, de-facto standard C++ libraries, and use them to create financial applications. The course uses object-oriented, modular and generic programming techniques, design patterns, and the interoperability with Excel to create efficient applications for a range of derivatives, such as equity and options.
Upon successful completion of the course, the students will be able to
- develop numerical algorithms in C++ for pricing financial derivatives and computing their Greek letters with the simulation method of Monte Carlo.
- employ variance reduction techniques for the numerical improvement of simulation methods of random numbers.
- develop numerical lattice algorithms in C++ for pricing financial derivatives with the method of Binomial Tree.
- solve numerically partial differential equations in C++ for pricing financial derivatives with the method of Finite Differences.
- construct in C++ numerical paths of Geometric Brownian Motion for simulating dynamic risk hedging and pricing path-dependent financial derivatives with the simulation method of Monte Carlo
General Competences
- Search for, analysis and synthesis of data and information, with the use of the necessary technology.
- Adapting to new situations.
- Decision-making.
- Working independently.
- Team work.
- Working in an interdisciplinary environment.
- Introduction of innovative research.
- Critical thinking.
- Development of free, creative and inductive thinking.
Course Content
The following sections will be presented:
- Monte Carlo Simulation: Generating Random Numbers, Expected Value Estimation, Pricing of European Options, Number of Replications.
- Variance Reduction Techniques: Antithetic Sampling, Control Variates, Common Random Numbers – Estimation of the Greeks.
- Binomial Model Simulation: Construction of Binomial Tree, Pricing of European and American Options.
- Finite Difference Method: Difference Quotients, Construction of Grid, Boundary Conditions, Explicit and Implicit Methods in Pricing European Options, Connection with Trinomial Tree.
- Simulation of Geometric Brownian Motion: Sources of Errors, Asset Path Generation, Stop-Loss and Delta Hedging Strategies, Pricing of Exotic Options – Asian, Barrier and Lookback Options.
Student Performance Evaluation
- Project (40%) that includes the development and execution of computational algorithms for pricing and/or hedging financial derivatives.
- Presentation (30%) of the above project.
- Coursework (30%) that includes the development and execution of computational algorithms for the numerical solution of problems, subject to the material taught in class.
Bibliography
Suggested Bibliography
- Erik Schlogl, Quantitative Finance: An Object-Oriented Approach in C++, 1st Edition, Kindle Edition, Chapman and Hall/CRC Financial Mathematics, 2018.
- John C. Hall, Options, Futures, And Other Derivatives, 8th Edition, Prentice Hall, New Jersey, 2011.
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