Instructor: Dan Stefanica
- LU decomposition with pivoting;
- Cholesky decomposition;
- Jacobi, Gauss-Siedel, SOR; Projected SOR;
- Least Squares;
- Eigenvalue methods;
- Black-Scholes formula;
- Greeks; Hedging;
- Black-Scholes PDE;
- Finite difference discretizations and solutions of parabolic PDEs;
- Forward Euler, Backward Euler, Crank-Nicolson;
- Valuation and Greeks estimations for plain vanilla European and American options, barrier options, Bermudan options;
- Implied volatility computations using finite difference methods;
- Barone-Adesi–Whaley approximate formula for American plain vanilla options; implied volatility;
- Numerical Linear Algebra, by Lloyd Trefethen and David Bau. Publisher: Society for Industrial and Applied Mathematics, 1997.
- The Mathematics of Financial Derivatives: A Student Introduction, by Paul Wilmott, Sam Howison, and Jeff Dewynne. Publisher: Cambridge University Press, 1995.
- Applied Numerical Linear Algebra, by James Demmel. Publisher: Cambridge University Press, 1997.
- Implementing Derivative Models, by Les Clewlow and Chris Strickland. Publisher: Wiley, Series in Financial Engineering, 1998.
- Introduction to Linear Algebra, by Gilbert Strang. Publisher: Wellesley-Cambridge Press, 4th Edition, 2009.