Question

XYZ Corp. will pay a $2 per share dividend in two months. Its stock price currently is $64 per share. A call option on XYZ has an exercise price of $58 and 3-month time to expiration. The risk-free interest rate is 0.7% per month, and the stock’s volatility (standard deviation) = 8% per month. Find the Black-Scholes value of the American call option. (Hint: Try defining one “period” as a month, rather than as a year, and think about the net-of-dividend value of each share.) (Round your answer to 2 decimal places.) Ps: The answers to this question already on chegg are incorrect.

Answer 1

Expected dividend in two months = $2 per share

Current stock price = $64 per share

Risk free rate r = 0.7% per month

Present value of expected dividend = $2/ (1 +0.7%) ^ (2) = $1.9723

Net-of-dividend Or Dividend-adjusted stock price S = $64 – $1.9723 = $62.0277

Now call option price calculation:

INPUTS		Outputs	Value
Standard deviation (monthly) σ	8.00%	d1	0.7054
Expiration (in months) T	3.00	d2	0.5668
Risk free rates (monthly) r	0.70%	N(d1)	0.7597
Current stock price (S)	$62.0277	N(d2)	0.7146
Exercise price (X)	$58.00	B/S call Price	$6.54
Dividend yield	0	B/S Put Price	$1.31

formulas used in excel: