Mathematics in Finance Binomial model of options pricing.

Derivatives - Options Give the holder the right to buy or sell the underlying at a certain date for a certain price. (European options) Right to buy  call option Right to sell  put option Payoff function Cash settlement Exchanges: AMEX, CBOT, Eurex, LIFFE, EOE,...

IV Derivatives - Options Example 1: Long Call on stock S with strike K=32, maturity T, price P=10. Payoff function: f(S) = max(0,S(T) – K)

strike underlyingmaturity volatility Interest rate Option value dividends

Derivatives - Options

Problem: How can options be priced? –Modelling –Black-Scholes –Solving partial differential equations –Monte-Carlo simulation –...

Replicating portfolio

Binomial one period method

Binomial n-period method

Algorithm for binomial method

Example

Numerical implementation

Some versions of binomial model

Extensions of binomial model

Black-Scholes formula

Conclusions