Pre-requisite: MA 225 Probability Theory and Random Processes

Financial markets; Cash flow, time value of money, net present value, net future value; Fixed income securities: Bonds and bonds pricing, yield curves, duration and convexity. Term structure of interest rates, spot and forward rates; Equities, risk-reward analysis, asset pricing models, mean variance portfolio optimization, Markowitz model and efficient frontier, CAPM and APT; Discrete time market models: Assumptions, portfolios and trading strategies, replicating portfolios, risk neutral probability measures, valuation of contingent claims, fundamental theorem of asset pricing; The Cox-Ross-Rubinstein (CRR) model, pricing in CRR model, Black-Scholes formula derived as a limit of the CRR pricing formula; Derivative securities: futures and forward contracts, hedging strategies using futures, pricing of futures and forward contracts, interest rate futures; Properties of options, contingent claims, trading strategies and binomial trees, pricing of stock options, options on stock indices, currencies and futures, European and American options; Greeks, delta hedging and risk management, volatility smiles; Interest rate derivatives (basic term structure model, swaps and swaptions, caps and floors).

Texts:

• S.R. Pliska, Introduction to Mathematical Finance: Discrete Time Models, Blackwell, 1997.
• M. Capinski and T. Zastawniak, Mathematics for Finance: An Introduction to Financial Engineering, Springer, 2005.
• S. Roman, Introduction to the Mathematics of Finance: From Risk Management to Options Pricing, Springer, 2004.
• J.C. Hull, Options, Futures and Other Derivatives, 6th Edition, Prentice Hall of India / Pearson Education, 2006. [7th international edition is available now.]