Question

Assume we have the following information for the call option written on CCC stock. Current price of CCC stock is $160. Continuously compounded risk-free rate is 4%. Exercise price of the call option is $165, time to maturity is six months and the volatility of the BBB stock is 25%. Assume also that the continuously compounded dividend yield is 2.1%. i. Find the (theoretical) value of the call option using BSM valuation model. ii. Note that the only difference between company BBB and CCC is the dividend payment of CCC. Compare the call options prices of both and what is your conclusion about the effect of dividend on call option price?

Answer 1

Black and Scholes model of option valuation without dividend

Black and Scholes model of option valuation with dividend

Input Data		CCC	BBB
Stock Price now (S)-		160	160
Exercise Price of Option (K)		165	165
Compounded Dividend yield Rate (q)		2.10%	0
Number of periods to Exercise in years (t)		0.50	0.50
Compounded Risk-Free Interest Rate (rf)		4.00%	4.00%
Standard Deviation (annualized s)		25.00%	25.00%

Output Data		CCC	BBB
Present Value of Exercise Price (PV(K))		163.4399	161.733
s*t^.5		0.1768	0.177
d1		-0.0319	0.027
d2		-0.2087	-0.149
Delta N(d1) Normal Cumulative Density Function		0.4873	0.511
N(d2)*PV(K)		68.2090	71.268
Value of Call		8.9381	10.485

Dividend yield has inverse relation with call price , i.e Call Price reduces with increase of dividend yield of shares