Consider an American Put option with time to expiry of 5 months and a strike price of 82. The current price of the underlying stock is 80. Divide the time to expiry into five 1-month intervals. In each interval, the stock price can either rise by 6, or fall by 6, with unknown probability. The risk-free rate is 4.2% per annum, continuously compounded. Use Binomial Model.

(a) What is the evolution of the prices of the underlying asset in time? Show it on a binomial tree.

Find the fair value of an European call option and an Americanput option using the incoherent and coherent binomial option treeif the underlying asset pays dividend of 4 PLN in one and halfmonth. The initial stock price is 60 PLN, the strike price of 58PLN is expiring at the end of the third month, the continuouslycompounded risk-free interest rate is 10% per annum, and the stockvolatility is 20%.

Find the current price of a one-year, $110-strike American put option on a non-dividend-paying stock whose current price is S(0)=$100. Assume that the continuously compounded interest rate equals r=0.08. Use a two-period binomial tree with u=1.2 and d=0.8 to calculate the price of the put option.

Assume that the current stock price is $25 per share, the exercise price is $26 per share, the risk-free rate is 2.00%, time to expiration is 9 months and the standard deviation of the underlying stock price is 20%. The current call option price should be closest to: