The current price of a stock is $55. Calculate the value of an American put option on the stock using a two-step binomial tree given the following information. The strike price of the option, K = $57, each time step is one year, the risk-free interest rate,
r = 5%, u =1.25, d = 0.8, and p = 0.6282

$5.95

Explanation:

Risk neutral probability,

                                           =

The value of stock lattice is shown below :

 85.9375

68.7555

554435.2

t=0t=1t=2

Value of the American put option when the stock price is $85.9375 at t=2

= max(57-85.9375,0) = 0

The value of the American put option when the stock price is $55 at t=2

= max(57-55,0) = 2

The value of American put option when the stock price is $85.9375 at t=2

= max(57-35.2,0) = 21.8

The value of a American put option when the stock price is $68.75 at t=1

= max        =  $0.84656

The value of the American put option when stock price is $44 at t=1

= max    = $13

The value of American put option today when the stock price is $55 at t=0

=  max     = $ 5.95

Thus, the value of American put option today is $5.95

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