A stock is worth $50 on december, 1st 2021. This price increases by 4% and decreases by 4% every 2 months. The flat continuous rate of interest is 5% and the continuous rate of dividend is 2%.

a) What is the premium of an American call on this stock with a maturity of 6 months and a strike price of $48?

b) What is the premium a European puts on the stock? Maturity and strike price remain unchanged.

c) In option pricing theory, what does risk neutral probability mean? What is the probability the European put gets exercised?

Note:

No excel