Question: Please do step by step and show the calculation it will help me understand better. A stock price is currently $55 . Over each of

Please do step by step and show the calculation it will help me understand better.

A stock price is currently $55 . Over each of the next two 1-month periods it is expected to go up or down . The risk free interest rate is 10 % per annum with continuous compounding . The volatility is 40% per annum. If a dividend of $3 is expected in 1.5 months and another dividend of $2.75 is expected in 2.5 months .

1- Calculate the price of a 2-month American put option on the above dividend paying stock with a strike price of $50.

2- Calculate the price of a 2 -month American call option on the above dividend paying stock with a strike price of $ 50.

3- Assume there are no dividends , determine the price of a 2-month European call option on the above stock with a strike price of $ 50.

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