post all the steps Let S = $50, r = 4% (continuously compounded), d = 3%,...

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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

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Expert Solution

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

jeff jeffy answered 1 year ago

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