MA51118: Financial Mathematics

MA51118
Course name	Financial Mathematics
Offered by	Mathematics
Credits	4
L-T-P	3-1-0
Previous Year Grade Distribution
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Semester	Spring

Syllabus

Syllabus mentioned in ERP

Prerequisite: voidIntroduction to Mathematical Finance: Stocks, bonds and financial markets, Options and forward contracts, Pricing by no-arbitrage considerations, One-period binomial model, The Fundamental Theorems of Asset Pricing. The Binomial Asset Pricing Model: Pricing by replication in a multiperiod model, Basic probability, Martingales and European derivative securities, The risk-neutral probability measure, Derivative securities with random payment times, Computational issues. The Black-Scholes Formula: Scaling time and model parameters, Using the Central Limit Theorem to obtain a limit, The role of volatility. Brownian motion: Limit of scaled random walks, Definition of Brownian motion, Quadratic variation of Brownian motion, The problem of integration with respect to Brownian motion. Stochastic calculus: Ito s integral, Ito s formula, Geometric Brownian motion. he Black-Scholes Formula Revisited: Evolution of a call option price, Evolution of a replicating portfolio, Matching evolutions to price the call. Optimal Consumption and Investment in the Binomial Model: Risk aversion, some decision theory and utility functions, Dynamic programming. Optimal Consumption and Investment in the Brownian Motion Model: The Merton problem, The optimal-control formulation and the Hamilton-Jacobi-Bellman (HJB) equation, Constant relative risk aversion (CRRA) utilities and proportional investment strategies, Further Topics in Optimal Consumption and Investment. The martingale method, Complete and incomplete markets.