Syllabus

Second Semester of Academic Year 2022-2023
MA 373 Financial Engineering II
Syllabus

Pre-requisite: MA 372 (Stochastic Calculus for Finance) or equivalent

Continuous time financial market models, Black-Scholes-Merton model, Black-Scholes-Merton equation and formula, dividend paying assets, forwards and futures, risk-neutral valuation of European, American and Exotic derivative securities, change of numeraire, hedging of contingent claims, Greeks, implied volatility, volatility smile; Options on futures; Incomplete markets, stochastic volatility models, pricing and hedging in incomplete markets; Fixed income markets, bonds and interest rates, pricing of fixed income securities, term structure equation; Short rate models, martingale models for short rate (Vasicek, Cox-Ingersoll-Ross, Dothan, Ho-Lee and Hull-White models), multifactor models; Forward rate models, Heath-Jarrow-Morton framework, pricing and hedging under short rate and forward rate models, swaps, caps and floors; LIBOR and swap market models.

Texts:

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

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

References:

J.C. Hull, Options, Futures and Other Derivatives, 10th Edition, Pearson India, 2018.

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.

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