A stock index level is currently 2,000. Its volatility is 25%. The risk-free rate is 4% per annum (continuously compounded) for all maturities and the dividend yield on the index is 2%. Using the Black-Scholes model:

1. a) Derive the value a 6-month European put option with a strike price of 2020.

2. b) Derive the position in the index that is needed today to hedge a long position in the put option. Assume

   that the option is written on 250 times the index.

3. c) What is todays probability (implied by the Black-Scholes model) that the index price will be greater

   than 2020 in 6 months?