Prerequisites: 16:642:621, 16:642:573, and 16:332:503, or equivalent courses. Students learn how to implement financial option-pricing and risk-management models using C++, building on previous and concurrent courses on object-oriented programming with C++, numerical analysis, and mathematical finance. MATLAB, Python, and Excel-VBA may also be used, though primarily as tools for benchmarking and C++ code interfacing. Numerical methods discussed include Monte Carlo simulation, finite difference, finite element, and spectral element solution of partial differential equations, binomial and trinomial trees, the fast Fourier transform (FFT). Asset classes discussed include equities, fixed income and interest rates, foreign exchange, and commodities, though the majority ofapplications will be for equity derivatives for simplicity and access to market data.