Syllabus

First Semester of Academic Year 2010-2011
MA 471 Financial Engineering II
Syllabus

Pre-requisite: MA 372 Stochastic Calculus for Finance

Continuous time financial market models, Black-Scholes model, Black-Scholes PDE and formulas, risk-neutral valuation, change of numeraire, pricing and hedging of contingent claims, Greeks, implied volatility; Options on futures, European, American and Exotic options. Incomplete markets, market models with stochastic volatility, pricing and hedging in incomplete markets. Bond markets, term-structures of interest rates, bond pricing; Short rate models, martingale models for short rate (Vasicek, Ho-Lee, Cox-Ingersoll-Ross and Hull-White models), multifactor models; Forward rate models, Heath-Jarrow-Morton framework, pricing and hedging under short rate and forward rate models, swaps and caps; LIBOR and Swap market models, caps, swaps, swaptions, calibration and simulation. Introduction to credit risk modeling, credit derivatives, CDS and CDO.

Texts:

T. Bjork, Arbitrage Theory in Continuous Time, 2nd edition, Oxford University Press, 2003.

J.C. Hull, Options, Futures and Other Derivatives, 7th Edition, Prentice Hall of India / Pearson Education, 2008.

References:

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

D. Brigo and F. Mercurio, Interest rate models:Theory and Practice, Springer, 2006.

N. H. Bingham and R. Kiesel, Risk Neutral Valuation, 2nd Edition, Springer, 2004.

J.Cvitanic and F. Zapatero, Introduction to the Economics and Mathematics of Financial Markets, Prentice-Hall of India, 2007.

M. Musiela and M. Rutkwoski, Martingale Method in Financial Modelling, 2nd edition, Springer, 2005.

P. Wilmott, Derivatives: The Theory and Practice of Financial Engineering, Wiley, 1998.

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