Black-Scholes-Merton model:

Spot Price = 56

Strike Price (k) = 58

Risk Free rate = 6% per annum with continuous compounding

Volatility = 18%

T = 2/3

Using the information given above regarding the spot price (56) and strike price (58), risk-free rate of return (6% per annum with continous compounding) and the fact that the volatility of the share price is 18%, answer following questions:

1. What is the price of an eight-month American call? [1 mark]
2. What is the price of an eight-month European put? [1 mark]
3. How would your result from k. change if a dividend of $1 is expected in three months? How would your result from k. change if a dividend of $1 is expected in ten months? [2 marks]

Note for calculations with the BSM model: Keep four decimal points for d1 and d2. Use the Table for N(x) with interpolation in calculating N(d1) and N(d2).

Finally,

4. Compare the results you obtained for the prices of European puts and calls using binomial trees and Black-Scholes-Merton model. How large are the differences when expressed as a percentage of the spot price of the share? Provide a possible explanation for these differences. [2 marks]