Question

IBM stock currently sells for 100 dollars per share. The implied volatility equals 20.0. The risk-free rate of interest is 4.0 percent continuously compounded. What is the value of a call option with strike price 95 and maturity 6 months? Answer should be to the nearest cent (2 decimal places).

Answer 1

INPUTS		Outputs	Value
Standard deviation (Annual) σ	20.00%	d1	0.5748
Expiration (in Years) T	0.50	d2	0.4334
Risk free rates (annual) r	4.00%	N(d1)	0.7173
Current stock price (S0)	$100.00	N(d2)	0.6676
Strike price (X)	$95.00	B/S call Price	9.5597
Dividend yield (annual)	0	B/S Put Price	2.6786

Value of call option is $9.5597 or $9.56

Formulas used in excel:

Outputs di 1 INPUTS 2 Standard deviation (Annual) 3 Expiration (in Years) T 4 Risk free rates (annual) 5 Current stock price (SO) 6 Strike price (X) 7 Dividend yield (annual) =6/12 0.04 d2 Nd1) N(02) B/S call Price B/S Put Price D Value I=(LN(B5/B6)+(B4-B7+0.5*B2^2) * B3)/(B2SQRT(B3) =D2-B2*SQRT(B3) =NORMSDIST(D2) =NORMSDIST(D3) =B5*EXP(-B7*B3) *D4-B6*EXP(-B4*B3) *D5 =B6*EXP(-B4*B3)*(1-05)-B5*EXP(-B7*B3)*(1-04)