Vertex Pharmaceuticals (VRTX) is trading at a price of $200.00 per share. The standard deviation of the yearly return on the stock is 32 percent (.32). Vertex is not expected to pay a dividend during the next year. A call option on VRTX with a strike price of $210 and three months to expiration (0.25 years) has a hedge ratio equal to 0.42076, based on a value for d1 of 0.19994. The continuously compounded risk-free interest rate is 1.60 percent (.016), so that present value of a risk-free $1 to be received in three months is $0.996008. Assuming that the risk-adjusted probability that a European put option on Vertex having a strike price of 210 and three months to expiration will finish in the money is 0.64055, determine:

a. the risk-adjusted probability that an American call option on Vertex having a strike price of 210 and three months to expiration finishes in the money

b. the price of an American call option on Vertex having a strike price of 210 and three months to expiration.

c. the price of a European put option on Vertex having a strike price of 210 and three months to expiration.