Stochastic Calculus for Finance

Code: MA3161 | L-T-P-C: 3-0-0-6

General probability spaces, filtrations, conditional expectations, martingales and stopping times, Markov processes; Random walks, Brownian motion and its properties; Itô integral and its properties, Itô processes, Itô-Doeblin formula; Derivation of the Black-Scholes-Merton equation, Black-Scholes-Merton formula, multi-variable stochastic calculus; Risk-neutral valuation, risk-neutral measure, Girsanov's theorem for change of measure, martingale representation theorem, fundamental theorems of asset pricing; Stochastic differential equations and their solutions, Feynman-Kac theorem and its applications.

Texts:

• S. Shreve, Stochastic Calculus for Finance, Volume II, Springer, 2004.

 

References:

• F. C. Klebaner, Introduction to Stochastic Calculus with Applications, Third Edition, Imperial College Press, 2012.
• S. Shreve, Stochastic Calculus for Finance, Volume I, Springer, 2004.
• M. Baxter and A. Rennie, Financial Calculus, Cambridge University Press, 1996.
• A. Etheridge, A Course in Financial Calculus, Cambridge University Press, 2003.
• R. J. Elliott and P. E. Kopp, Mathematics of Financial Markets, Springer, 1999.