1. Mathematics in Finance Binomial model of options pricing.

2. 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,...

3. 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)

4. strike underlyingmaturity volatility Interest rate Option value dividends

5. Derivatives - Options

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

7. Replicating portfolio

8. Binomial one period method

11. Binomial n-period method

14. Algorithm for binomial method

15. Example 150 120 96 187.5 120 76.8 234.38 96 150 61.44 0 164.38 80 26 120.09 52.92 13.59 85.37 33.46 58.91

16. Numerical implementation

17. Some versions of binomial model

18. Extensions of binomial model

19. Black-Scholes formula

21. Conclusions