Syllabus

First Semester of Academic Year 2015-2016
MA 372 Stochastic Calculus for Finance
Syllabus

Pre-requisites: MA 224 (Real Analysis) & MA 271 (Financial Engineering I)

General probability spaces, filtrations, conditional expectations, martingales and stopping times, Markov processes; Brownian motion and its properties; Itô's integral and its extension to wider classes of integrands, isometry and martingale properties of Itô's integral, Itô processes, Itô-Doeblin formula; derivation of the Black-Scholes-Merton differential equation, Black-Scholes-Merton formula, the Greeks, put-call parity, multi-variable stochastic calculus; Risk-neutral valuation: risk-neutral measure, Girsanov's theorem for change of measure, martingale representation theorems, representation of Brownian martingales, the fundamental theorems of asset pricing; Stochastic differential equations, existence and uniqueness of solutions, Feynman-Kac formula and its applications.

Texts:

S. Shreve, Stochastic Calculus for Finance, Vol.2, Springer India, 2004.

M. Baxter and A. Rennie, Financial Calculus, Cambridge University Press, 1996.

References:

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

A. Etheridge, A Course in Financial Calculus, Cambridge University Press, 2003.

J. M. Steele, Stochastic Calculus and Financial Applications, Springer, 2001.

T. Bjork, Arbitrage theory in Continuous Time, 3rd edition, Oxford University Press, 2003.

R. J. Elliott and P. E. Kopp, Mathematics of Financial Markets, Springer, 1999.

D. Lamberton and B. Lapeyre, Introduction to Stochastic Calculus Applied to Finance, Chapmans & Hall/CRC, 2000.

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