Consider a put option on the ASX200 index. Assume the index currently stands at 5,768. It is expected to increase or decrease by 15% over each of the next two time periods of two months. The risk-free rate is 5.75% and the dividend yield on the index is 2.5%.

a) What is the value of the option if it is European with four-months to maturity and has an exercise price of 5,700. Show your calculations.

b) What is the value of the option if it is American with four-months to maturity and has an exercise price of 5,700. Show your calculations.