B.Tech Mathematics

 

MA 372                Stochastic Calculus for Finance                     3-0-0-6

 

 

Syllabus: 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. Shreve, Stochastic Calculus for Finance, Volume II, Springer, 2004.

 

References:

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