Question

Use an options calculator for the first 2 problems 1a prices of a one month put and call options with a strike price of $50 For a stock trading at $50 with 15% volatility and 2% risk free interest rate, find the Determine the effect on both the put and call of increasing the strike price to $55 b. Determine the effect of doubling the time to maturity C.

Answer 1

a. We can use excel in following manner to calculate the value of call option and put option:

INPUTS		Outputs	Value
Standard deviation (Annual) σ	15.00%	d1	0.0601
Expiration (in Years) T	0.08	d2	0.0168
Risk free rates (annual) r	2.00%	N(d1)	0.5240
Current stock price (S)	$50.00	N(d2)	0.5067
Strike price (K)	$50.00	B/S call Price	0.9052
Dividend yield (annual)	0	B/S Put Price	0.8220

Call Price = $0.9052

Put Price = $0.8220

b. Strike price is increased from $50 to $55

INPUTS		Outputs	Value
Standard deviation (Annual) σ	15.00%	d1	-2.1410
Expiration (in Years) T	0.08	d2	-2.1843
Risk free rates (annual) r	2.00%	N(d1)	0.0161
Current stock price (S)	$50.00	N(d2)	0.0145
Strike price (K)	$55.00	B/S call Price	0.0123
Dividend yield (annual)	0	B/S Put Price	4.9207

Call Price = $0.0123

Put Price = $4.9207

c. Doubling the time of maturity form one month (1/12 =0.08 years) to two months (=2/12 =0.17 years). Strike price is assumed at original level ($50)

INPUTS		Outputs	Value
Standard deviation (Annual) σ	15.00%	d1	0.0851
Expiration (in Years) T	0.17	d2	0.0238
Risk free rates (annual) r	2.00%	N(d1)	0.5339
Current stock price (S)	$50.00	N(d2)	0.5095
Strike price (K)	$50.00	B/S call Price	1.3043
Dividend yield (annual)	0	B/S Put Price	1.1379

Call Price = $1.3043

Put Price = $1.1379

Formulas used in excel calculation:

Outputs d1 0.15 =1/12 0.02 N(1) N(2) B/S call Price B/S Put Price Value =(LN(B5/B6)+(B4-B7+0.5*B2^2) *B3)/(B2*SQRT(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) Outputs 0.15 1-1/12 А 1 INPUTS 2 Standard deviation (Annual) o 3 Expiration in Years) T 4 Risk free rates (annual) 5 Current stock price (S) 6 Strike price (K) 7 Dividend yield (annual) 8 9 INPUTS 10 Standard deviation (Annual) o 11 Expiration (in Years) T 12 Risk free rates (annual) 13 Current stock price (S) 14 Strike price (K) 15 Dividend yield (annual) 16 17 INPUTS 18 Standard deviation (Annual) o 19 Expiration (in Years) T 20 Risk free rates (annual) 21 Current stock price (s) 22 Strike price (K) 23 Dividend yield (annual) 0.02 N(1) Value =(LN(B13/B14)+(B12-B15+0.5*B10^2) *B11)/(810*SQRT(B11)) 1=D10-B10*SQRT(B11) =NORMSDIST(D10) =NORMSDIST(D11) =B13*EXP(-B15*B11) *D12-B14*EXP(-812*811) *D13 =B14*EXP(-B12*B11)*(1-D13)-B13*EXP(-B15*B11)*(1-D12) 50 B/S call Price B/S Put Price 0.15 =2/12 0.02 Outputs di d2 N(1) N(2) B/S call Price B/S Put Price Value = (LN(B21/B22)+(B20-B23+0.5*B18^2) *B19)/(B18*SQRT(B19)) =D18-B18*SQRT(B19) =NORMSDIST(D18) =NORMSDIST(D19) =B21*EXP(-B23*B19) *D20-B22*EXP(-B20*B19) *D21 =B22*EXP(-B20*B19)*(1-D21)-B21*EXP(-B23*B19) *(1-D20)