This work contains all of the homework assignments I did in Quantitative Methods for Computational Finance and Risk Management.
This MS-CFRM pre-program course reviews the mathematical methods fundamental for the study of quantitative and computational finance. The areas of focus include calculus and multivariable calculus, constrained and unconstrained optimization, and linear algebra.
Topics covered include the following:
- Functions and inverse functions
- Limits, derivatives, partial derivatives, and chain rule
- Integrals and multiple integrals, changing the order of differentiation and integration
- Taylor series approximations
- Newton’s method
- Lagrange multiplier method
- Vector and matrix arithmetic, determinants, eigenvalue-eigenvector decomposition, singular value decomposition
- Numerical methods for optimization
Upon completion of the course students I know the fundamental mathematical concepts needed to effectively study quantitative finance areas such as fixed income, options and derivatives, portfolio optimization, and quantitative risk management.