In: Finance
post all the steps
Let S = $50, r = 4% (continuously compounded), d = 3%, s = 30%, T = 1.5. In this situation, the appropriate values of u and d are 1.30644 and 0.77701, respectively. Using a 2-step binomial tree, calculate the value of a $45-strike American call option.
a. |
$10.477 |
|
b. |
$9.867 |
|
c. |
$10.168 |
|
d. |
$9.919 |
|
e. |
$10.367 |
here , S0 = current stock price
Su = stock price after 1 year if stock price increases
Sd = stock price after 1 year if stock price decreases
Suu = stock price after 2 years if stock price increases
Sdd = stock price after 2 years if stock price decreases
Sud = stock price after 2 years if stock price after 1 year increases and in the 2nd year it decreases
fu = value of option after 1 year if stock price increases
fd = value of option after 1 year if stock price decreases
fuu = value of option after 2 years if stock price increases
fdd = value of option after 2 years if stock price decreases in both years
fud = value of option after 2 years if stock price increases after 1st year and decreases after 2nd year
f = value of option today
for american options , the value of option after one year fu calculated as per the equation and the one calculated in the table ( value of fu on early exercise) are compared, and the one with the higher value if used in the equation to calculate current option value (f), and similarly fd is taken by comparing the values
hence correct option is d) $9.919