Syllabus

Review of financial models for option pricing and interest rate modeling, Black -Scholes PDE; Finite difference methods, Crank-Nicolson method, American option as free boundary problems, computation of American options, pricing of exotic options, upwind scheme and other methods, Lax-Wendroff method. Monte-Carlo simulation, generating sample paths, discretization of SDE, Monte-Carlo for option valuation and Greeks, Monte-Carlo for American and exotic options; Term-structure modeling, short rate models, bond prices, multifactor models; Forward rate models, implementation of Heath-Jarrow-Morton model; LIBOR market model, Volatility structure and Calibration.

Texts

1. P. Glasserman, Monte Carlo Methods in Financial Engineering, Springer, 2004.

2. R. U. Seydel, Tools for Computational Finance, 4th Ed., Springer, 2009.

References

1. Y.-l. Zhu, X. Wu, I-L. Chern and Z.-z. Sun, Derivative Securities and Difference Methods, 2nd Ed., Springer, 2013.

2. D. Higham, Introduction to Financial Option Valuation: Mathematics, Stochastics and Computation, Cambridge University Press, 2004

3. P. Wilmott, S. Howison and J. Dewynne, The Mathematics of Financial Derivatives, Cambridge University Press, 1997.

4. Y. Lyuu, Financial Engineering and Computation, Cambridge University Press, 2002.