Respuesta :
Answer:
$5.95
Explanation:
Risk neutral probability, [tex]$ q = \frac{(1+u)^t - d}{u-d} $[/tex]
= [tex]$ \frac {1.05-0.8}{1.25-0.8} = 0.5556 $[/tex]
The value of stock lattice is shown below :
85.9375
68.75 55
55 44 35.2
t=0 t=1 t=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 $68.75 at t=1
= max [tex]$ \frac{0.5556 \times 0 + 0.4444 \times 2}{1.05,57 - 68.75,0} $[/tex] = $0.84656
The value of the American put option when stock price is $44 at t=1
= max [tex]$ \frac{0.5556 \times 2 + 0.4444 \times 21.8}{1.05,57 - 44,0} $[/tex] = $13
The value of American put option today when the stock price is $55 at t=0
= max [tex]$ \frac{0.5556 \times 0.84656 + 0.4444 \times 13}{1.05,57 - 55,0} $[/tex] = $ 5.95
Thus, the value of American put option today is $5.95
