A stock price is currently $60. Over each of the next two three-month periods it is expected to go up by 6% or down by 5%. The risk-free interest rate is 8% per annum with continuous compounding. What is the value of a six-month European call option with a strike price of $61?

Strike price = $61

Stock price = $60

Max price after one move = $60 x 106% = $63.6

Min price after one move = $60 x 95% = $57

Max price after 2 moves = $67.42 [60 x 1.06 x 1.06]; profit = $6.42

u = Max/Spot = 1.06

d = Min/Spot = 0.95

Probability = (e0.08x3/12 - 0.95) / (1.06 - 0.95) = (1.0202 - 0.95) / 0.11 = 63.82%

At the end of 3 months: Value will be ($6.42 x 0.6382) / 1.0202 = $4.02

Now, the value will be ($4.02 x 0.6382) / 1.0202 = $2.51

For the situation considered in previous problem, what is the value of a six-month European put option with a strike price of $61? Verify that the European call and European put prices satisfy putcall parity. If the put option were American, would it ever be optimal to exercise it early at any of the nodes on the tree?

Please answer the question in bold text and show all calculations.