1. Use the Black-Scholes formula to price both a put and a call option with strike K = 45 expiring in six months on an underlying asset with spot price 50 and volatility 20% paying dividends continuously at 2%, if interest rates are constant at 6%.
2. Consider 3 month options with strike prices of K = 45. The variance of the underlying asset is 2 = 0.20. The risk free interest rate is r = 6%. The spot price of the underlying asset is S = 30. Also, q=0.
(a) Determine the Black Scholes prices for call and put options.
(b) Check that your calculations satisfy put call parity.