Question

1. You own 250 call options on Exxon that expire in 6 months. The current stock price of EXXON is 240. The interest rate is 2 percent, the standard deviation of EXXON stock is 28 percent, and the strike price is 250. Using the Black-Sholes formula, graph the value of your options as the standard deviation goes from 20 to 50 percent.

Please make an Excel Graph with 50 data points and show the formulas used
I will thumbs up your answer!

Answer 1

Computation of value of call using Black Scholes model:
C0	= S0*N(d1) - (X/e^rt)*N(d2)
where,
S0	= Stock Price = 240
X	= Strick Price = 250
r	= Interest Rate = 2% p.a
t	= 0.5 year
SD	= Standard Deviation
d1	= (log(S0/X)+(r+SD^2/2)t)/(SD*√t))
d2	= (log(S0/X)+(r - (SD^2/2))t)/(SD*√t))
Basic Calculations:
log(S0/X)	= Log(240/250)
	= log (0.96)
	= - 0.01773
e^rt	= e^(0.02*0.5)
	= e^0.01
	= 1.0101
X/e^rt	= 250/1.0101
	= 247.50
At SD	d1	d2	N(d1)	N(d2)	C0
0.20	0.02	-0.13	0.0080	0.4483	-109.034
0.25	0.04	-0.13	0.0160	0.4483	-107.114
0.28	0.06	-0.14	0.0239	0.4443	-104.228
0.30	0.07	-0.14	0.0279	0.4443	-103.268
0.35	0.09	-0.15	0.0359	0.4404	-100.383
0.40	0.11	-0.17	0.0439	0.4325	-96.5078
0.45	0.13	-0.18	0.0517	0.4286	-93.6705
0.50	0.15	-0.20	0.0596	0.4207	-89.8193