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In: Accounting

You own 250 call options on Exxon that expire in 6 months. The current stock price...

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.

Solutions

Expert Solution

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

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