Financial Mathematics

Module Title:
Financial Mathematics
Module Code:

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