Option Pricing Model Answers
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3 4 5 6 7 8 9 10 11 12 13 14
AB
C
D
E
Inputs Option Type (graph): Current Stock Price (S) Exercise or Strike Price (X) Risk Free Rate Annual (krf)
H
35.00
50 43.00 3.25%
Time to Expiration Yrs (T) Standard Deviation Annual (sigma)
0.7
18
N(d1)
0.7282
19 20 21 22 23 24 25
N(d2)
0.5585
Call Price Put Price
$ $
30.00 25.00 20.00 15.00 10.00 5.00 0.00
55.00%
0.1471
0
5
10
15
20
30
35
Call Price
40
45
50
55
60
Intrinsic Value
Hedge Ratios Short Calls Long Puts Delta
1.37 To hedge, short calls or long delta shares of stock 3.68 To hedge, long puts or long (delta-1) shares of stock 0.7282 Rate of change of option price with respect to the stock price
12.934 4.967
call price = C = S [N(d1)] - ( X / ert ) [N(d2)] d1 = [ln (S/ X ) + (krf + .5 var ) t] / [ stdev x t 1/2 ]
29
d2 = d1 - stdev x t1/2
31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75
25
Stock Price - S ($)
27
30
J
Black-Scholes Price vs Intrinsic Value
0.6073
28
I
40.00
Call
d1
26
G
Black-Scholes Option-Pricing Model
d2
15 16 17
F
Option Value
1 2
put price = P = x / ert - S + C Stock Price 1 5 10 12 14 16 18 20 22 24 25 26 28 30 32 34 36 38 40 42 44 46 48 50 52 54 56 58 60 62 64 66 68 70 72 74 76 78 80
Call Price 12.93 0.00 0.00 0.00 0.01 0.03 0.08 0.16 0.29 0.50 0.78 0.95 1.15 1.61 2.17 2.84 3.61 4.47 5.44 6.49 7.63 8.85 10.14 11.51 12.93 14.42 15.95 17.54 19.17 20.83 22.53 24.27 26.03 27.81 29.62 31.45 33.30 35.16 37.04 38.93
Intrinsic Value 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37
65
70
75
80
AB
C
D
E
Inputs Option Type (graph): Current Stock Price (S) Exercise or Strike Price (X) Risk Free Rate Annual (krf)
H
35.00
50 43.00 3.25%
Time to Expiration Yrs (T) Standard Deviation Annual (sigma)
0.7
18
N(d1)
0.7282
19 20 21 22 23 24 25
N(d2)
0.5585
Call Price Put Price
$ $
30.00 25.00 20.00 15.00 10.00 5.00 0.00
55.00%
0.1471
0
5
10
15
20
30
35
Call Price
40
45
50
55
60
Intrinsic Value
Hedge Ratios Short Calls Long Puts Delta
1.37 To hedge, short calls or long delta shares of stock 3.68 To hedge, long puts or long (delta-1) shares of stock 0.7282 Rate of change of option price with respect to the stock price
12.934 4.967
call price = C = S [N(d1)] - ( X / ert ) [N(d2)] d1 = [ln (S/ X ) + (krf + .5 var ) t] / [ stdev x t 1/2 ]
29
d2 = d1 - stdev x t1/2
31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75
25
Stock Price - S ($)
27
30
J
Black-Scholes Price vs Intrinsic Value
0.6073
28
I
40.00
Call
d1
26
G
Black-Scholes Option-Pricing Model
d2
15 16 17
F
Option Value
1 2
put price = P = x / ert - S + C Stock Price 1 5 10 12 14 16 18 20 22 24 25 26 28 30 32 34 36 38 40 42 44 46 48 50 52 54 56 58 60 62 64 66 68 70 72 74 76 78 80
Call Price 12.93 0.00 0.00 0.00 0.01 0.03 0.08 0.16 0.29 0.50 0.78 0.95 1.15 1.61 2.17 2.84 3.61 4.47 5.44 6.49 7.63 8.85 10.14 11.51 12.93 14.42 15.95 17.54 19.17 20.83 22.53 24.27 26.03 27.81 29.62 31.45 33.30 35.16 37.04 38.93
Intrinsic Value 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37
65
70
75
80
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