Module Title:
Financial Mathematics
Module Code:
DSA6231

Module Content

The simplex model of financial markets: One- period finite state model, Stochastic models for stock prices, Binomial option pricing model, Risk-neutral valuation, replication and pricing of contingent claims, Black-Scholes analysis, Interest rate models, Securities and their par-offs, Securities as vectors, Operations on securities, The matrix as a collection of securities, Matrix multiplication and portfolios, System of equations and Hedging, Linear independent and redundant securities

• The structure of the marketed subspace
• The identity matrix and arrow –debreu securities
• Matrix inverse and replicating portfolios
• Complete market hedging formula
• Arbitrage and pricing in the one-period Model
• Pricing in dynamically complete markets
• Towards continuous time
• Brownian motion and Ito formulae