TIES678 COM4: Numerical Methods for Finance (3 cr)
In financial markets, many different kinds of assets are available.
For investment purposes the most important ones are stocks and interest bearing instruments. The basic models for these are described. For example, a geometrical Brownian motion is a common model for stocks. The Monte Carlo method based on simulating paths for these and portfolios combining these is considered. Also simple portfolio analyses and optimizations based on these simulations are considered.
Vanilla options giving the right to sell (put) or buy (call) a given underlying asset like stock at its expiry. The Monte Carlo method is also considered for pricing options. Another approach is to formulate a partial differential equation (PDE) for the option price. A famous example is the Black-Scholes PDE. A basic finite difference method is described for solving resulting PDEs.