Most realistic quantitative finance models are too complex to allow explicit analytic solutions and are solved by numerical computational methods. The first part of the course covers the application of finite difference methods to the partial differential equations arising in option pricing and model calibration. Topics included are explicit, implicit and Crank-Nicholson finite difference schemes for fixed and free boundary value problems, their convergence and stability. The second part of the course focuses on modern advancements in financial computational methods, including Monte Carlo simulation techniques and machine learning applications. Topics include random number generation, variance reduction techniques, importance sampling, and reinforcement learning.
A solid background in calculus-based probability, multivariable calculus, and linear algebra is recommended.