MTH 9821 Numerical Methods for Finance I 2010-12-03T16:28:21+00:00

Fall 2009

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Instructor: Dan Stefanica

Topics:

  • 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;
Textbooks:
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