Stochastic Calculus for Finance

Code: MA372 | L-T-P-C: 3-0-0-6

Prerequisites: MA224 or equivalent and MA271 or equivalent

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:

1. S. Shreve, Stochastic Calculus for Finance, Vol. II, Springer, 2004.

References:

1. F. C. Klebaner, Introduction to Stochastic Calculus with Applications, 3rd Ed., Imperial College Press, 2012.
2. S. Shreve, Stochastic Calculus for Finance, Vol. I, Springer, 2004.
3. M. Baxter and A. Rennie, Financial Calculus, Cambridge University Press, 1996.
4. A. Etheridge, A Course in Financial Calculus, Cambridge University Press, 2003.
5. R. J. Elliott and P. E. Kopp, Mathematics of Financial Markets, Springer, 1999.