Monte Carlo Methods in Finance

Code: MA3461H | L-T-P-C: 3-0-2-4

Principles of Monte-Carlo simulation; Generation of uniform (LCG and its variations), general (inverse transform method, acceptance-rejection method) and normal (Box-Muller method) random variables; Generation of multivariate normal random vectors, Cholesky factorization; Generation of sample paths, Brownian motion, geometric Brownian motion, jump-diffusion process; Monte-Carlo for valuation of European, American and exotic options and Greeks; Gaussian short rate models, forward rate models, LIBOR market model, volatility structure and calibration; Variance reduction techniques, control variates, antithetic variates, stratified sampling, importance sampling; Applications in risk management, Value-at-Risk (VaR), credit risk.

Texts:

• P. Glasserman, Monte Carlo Methods in Financial Engineering, Springer, 2004.
• R. U. Seydel, Tools for Computational Finance, Sixth Edition, Springer, 2017.

 

References:

• R. Korn, E. Korn and G. Kroisandt, Monte Carlo Methods and Models in Finance and Insurance, CRC Press, 2023.
• Desmond J. Higham, An Introduction to Financial Option Valuation: Mathematics, Stochastics and Computation, Cambridge University Press, 2004.