See: http://www.golden.net/~pjponzo/black-scholes-3.htm Have fun!
Enter the data in red squares like so: gummy
(1) Strike Prices & Option Premiums for Example: Note: Enter Expiry Month as mmm (like sep
Strike = $90.00 $100.00 $105.00 etc.
Premium = $18.4127 $13.9410 #NUM! etc.
90% 100% 105% These just give Strike Prices as percentages of Stock P
(2) The Current Price of the stock for Example: (You can change them.)
Current Price = $100.0000 Initial Cost
(3) The Return, Standard Deviation & Risk-free Rate for the stock (if you know these*) #NUM!
Mean Return = 10%
Std Devn = 25% This just
Risk-free Rate 4% gives the
(4) The start and increment for the plot (if you want to change these) percentages
PLOT from $80.00 increments of $1.00 where you
(5) PLAY with the number of contracts which you write or buy MAKE or
# contracts = 0 0 1 etc. LOSE money within the
NOW: gaze in awe and admiration at the plot of total gain and probabilities RANGE OF THE PLOT, currently
… and, of course, repeat (5) till you see something you like! This gives your initial outlay of money.
P.S. You can, of course, just INVENT a stock … with invented strike prices and If it's negative, you RECEIVE a (net) amount.
Current Stock Price. BUT … what about the option premium? (because of calls you WRITE).
Just type in the Black-Scholes price; it's pretty accurate. For Covered Calls, it includes the cost of shares.
* If you don't know the Standard Deviation invent one so that the Black-Scholes You can choose to write Covered or Uncovered Call
price is close to the actual Option Premium. (This is an "implied volatility".) COVERED Calls (y/n) ?
Assuming a Log-normal Distribution of Returns,
this gives the probability that, at expiry, you'll LOSE!
Expiry Month = sep
Enter Expiry Month as mmm (like sep
give Strike Prices as percentages of Stock Price.
In the range
$80 to $107
#NUM!
#NUM!
the Max Gain is
#NUM!
the Min Gain is
#NUM!
LOSE money within the
RANGE OF THE PLOT, currently($80 to $107)
s your initial outlay of money.
ative, you RECEIVE a (net) amount.
of calls you WRITE).
d Calls, it includes the cost of shares.
oose to write Covered or Uncovered Calls
COVERED Calls (y/n) ? n
Prob. of Loss
#NUM!
Stock Name You're writing 1 (Uncovered) calls and buying 1 COVERED Calls (y/n) ?
XYZ 90% 100% 105% 90% 100% 105%
WRITE a call Uncovered BUY a call
# contracts = 0 0 1 1 0 0
Strike = $90.00 $100.00 $105.00 $90.00 $100.00 $105.00
Premium = $18.41 $13.94 #NUM! $18.41 $13.94 #NUM!
Black-Scholes = 18.41 13.94 #NUM! 18.41 13.94 #NUM!
Gain/Loss Cumulative Distribution 100% to scale
not
$1 #NUM! 100% #NUM!
90%
#NUM! #NUM!
$1 90%
80% Cumulative Distribution
'Expected' Gain = $36
$1 80% 70% Gain/Loss
$1 70% 60%
$1 60% 50%
$1 50% 40%
30%
$0 40%
20%
$0 30%
10%
$0 20%
0%
$80
$85
$90
$95
$100
$105
$110
$115
$120
$0 10%
292 days to expiration:
BreakEven
$0 0% Expected Price = $108.00
#NUM!
$
$
$
$
$
$
$
$
$
PLOT from $80.00 increments of $1.00 'Expected' Gain = $36
Your PLOT is from 80% to 107% of the 'Current Price' 292 days to expiration: Return =10% SD =25%
n 1
Current Price = $100.0000 0.7260983 0.254911749 0.036715502 Black 0.7260983
Expiry Month = sep 0.847756218
0.502491502
0.640763242
0.031304952
0.5207052
-0.186891296
Scholes
stuff 0.847756218
0.502491502
Today is 0.761343317 0.51765616 #NUM! stuff 0.761343317
4-Dec-11 99.55 #NUM! $9.55
zero loss #NUM!
CALL expires 21-sep12 #NUM! #NUM! 1 0 0
292 days to expiry WIN #NUM! #NUM! $90.000 $100.000 $105.000
Assumptions: (annual data) or Stock Price $18.413 $13.941 #NUM!
Mean Return = 10% LOSE? at expiration Combination BUY call options
Std Devn = 25% #NUM! $80.00 #NUM! -$1,841.27 $0.00 #NUM!
Risk-free Rate = 4% #NUM! $81.00 #NUM! -$1,841.27 $0.00 #NUM!
Initial Cost In the range #NUM! $82.00 #NUM! -$1,841.27 $0.00 #NUM!
#NUM! $80 to $107 #NUM! $83.00 #NUM! -$1,841.27 $0.00 #NUM!
Covered Calls #NUM! #NUM! $84.00 #NUM! -$1,841.27 $0.00 #NUM!
Cost of buying #NUM! #NUM! $85.00 #NUM! -$1,841.27 $0.00 #NUM!
100 the Max Gain is #NUM! $86.00 #NUM! -$1,841.27 $0.00 #NUM!
shares at #NUM! #NUM! $87.00 #NUM! -$1,841.27 $0.00 #NUM!
$100.0000 the Min Gain is #NUM! $88.00 #NUM! -$1,841.27 $0.00 #NUM!
$10,000.00 #NUM! #NUM! $89.00 #NUM! -$1,841.27 $0.00 #NUM!
Prob. of Loss #NUM! $90.00 #NUM! -$1,841.27 $0.00 #NUM!
#NUM! #NUM! $91.00 #NUM! -$1,741.27 $0.00 #NUM!
#NUM! $92.00 #NUM! -$1,641.27 $0.00 #NUM!
Change ONLY #NUM! $93.00 #NUM! -$1,541.27 $0.00 #NUM!
numbers in #NUM! $94.00 #NUM! -$1,441.27 $0.00 #NUM!
a red square #NUM! $95.00 #NUM! -$1,341.27 $0.00 #NUM!
#NUM! $96.00 #NUM! -$1,241.27 $0.00 #NUM!
#NUM! $97.00 #NUM! -$1,141.27 $0.00 #NUM!
#NUM! $98.00 #NUM! -$1,041.27 $0.00 #NUM!
#NUM! $99.00 #NUM! -$941.27 $0.00 #NUM!
#NUM! $100.00 #NUM! -$841.27 $0.00 #NUM!
#NUM! $101.00 #NUM! -$741.27 $0.00 #NUM!
#NUM! $102.00 #NUM! -$641.27 $0.00 #NUM!
#NUM! $103.00 #NUM! -$541.27 $0.00 #NUM!
#NUM! $104.00 #NUM! -$441.27 $0.00 #NUM!
#NUM! $105.00 #NUM! -$341.27 $0.00 #NUM!
#NUM! $106.00 #NUM! -$241.27 $0.00 #NUM!
#NUM! $107.00 #NUM! -$141.27 $0.00 #NUM!
#NUM! $108.00 #NUM! -$41.27 $0.00 #NUM!
#NUM! $109.00 #NUM! $58.73 $0.00 #NUM!
#NUM! $110.00 #NUM! $158.73 $0.00 #NUM!
#NUM! $111.00 #NUM! $258.73 $0.00 #NUM!
#NUM! $112.00 #NUM! $358.73 $0.00 #NUM!
#NUM! $113.00 #NUM! $458.73 $0.00 #NUM!
#NUM! $114.00 #NUM! $558.73 $0.00 #NUM!
#NUM! $115.00 #NUM! $658.73 $0.00 #NUM!
#NUM! $116.00 #NUM! $758.73 $0.00 #NUM!
#NUM! $117.00 #NUM! $858.73 $0.00 #NUM!
#NUM! $118.00 #NUM! $958.73 $0.00 #NUM!
#NUM! $119.00 #NUM! $1,058.73 $0.00 #NUM!
#NUM! $120.00 #NUM! $1,158.73 $0.00 #NUM!
#NUM! $121.00 #NUM! $1,258.73 $0.00 #NUM!
#NUM! $122.00 #NUM! $1,358.73 $0.00 #NUM!
0.254911749 0.036715502 Annualized Gain
100%
0.640763242 0.5207052
0.031304952 -0.186891296 90%
0.51765616 #NUM! 80%
70%
Calculation of60% Dec 4/11 100 11
0 0 1 Writing Expiry stuff 50% sep 1-sep
$90.000 $100.000 $105.000 Uncovered 40%
$18.413 $13.941 #NUM! Calls 30% Dates expires 21-sep12
TOTAL WRITE call options TOTAL zero 20%
Index sep12 Fridays Expiry
#NUM! $0.00 $0.00 #NUM! #NUM! 0
10%
1 1-sep12
#NUM! $0.00 $0.00 #NUM! #NUM! 0 2
0% 2-sep12
$
$
$
$
$
$
$
$
#NUM! $0.00 $0.00 #NUM! #NUM! 0 3 3-sep12
#NUM! $0.00 $0.00 #NUM! #NUM! 0 4 4-sep12
#NUM! $0.00 $0.00 #NUM! #NUM! 0 5 5-sep12
#NUM! $0.00 $0.00 #NUM! #NUM! 0 6 6-sep12
#NUM! $0.00 $0.00 #NUM! #NUM! 0 7 7-sep12 1
#NUM! $0.00 $0.00 #NUM! #NUM! 0 8 8-sep12
#NUM! $0.00 $0.00 #NUM! #NUM! 0 9 9-sep12
#NUM! $0.00 $0.00 #NUM! #NUM! 0 10 10-sep12
#NUM! $0.00 $0.00 #NUM! #NUM! 0 11 11-sep12
#NUM! $0.00 $0.00 #NUM! #NUM! 0 12 12-sep12
#NUM! $0.00 $0.00 #NUM! #NUM! 0 13 13-sep12
#NUM! $0.00 $0.00 #NUM! #NUM! 0 14 14-sep12 1
#NUM! $0.00 $0.00 #NUM! #NUM! 0 15 15-sep12
#NUM! $0.00 $0.00 #NUM! #NUM! 0 16 16-sep12
#NUM! $0.00 $0.00 #NUM! #NUM! 0 17 17-sep12
#NUM! $0.00 $0.00 #NUM! #NUM! 0 18 18-sep12
#NUM! $0.00 $0.00 #NUM! #NUM! 0 19 19-sep12
#NUM! $0.00 $0.00 #NUM! #NUM! 0 20 20-sep12
#NUM! $0.00 $0.00 #NUM! #NUM! 0 21 21-sep12 1
#NUM! $0.00 $0.00 #NUM! #NUM! 22 0 22 22-sep12 22-sep12
#NUM! $0.00 $0.00 #NUM! #NUM! 0 23 23-sep12 23-sep12
#NUM! $0.00 $0.00 #NUM! #NUM! 0 24 24-sep12 24-sep12
#NUM! $0.00 $0.00 #NUM! #NUM! 0 25 25-sep12 25-sep12
#NUM! $0.00 $0.00 #NUM! #NUM! 0 26 26-sep12 26-sep12
#NUM! $0.00 $0.00 #NUM! #NUM! 0 27 27-sep12 27-sep12
#NUM! $0.00 $0.00 #NUM! #NUM! 0 28 28-sep12 1 28-sep12
#NUM! $0.00 $0.00 #NUM! #NUM! 0 29
#NUM! $0.00 $0.00 #NUM! #NUM! 0 30
#NUM! $0.00 $0.00 #NUM! #NUM! 0 31
#NUM! $0.00 $0.00 #NUM! #NUM! 0 32
#NUM! $0.00 $0.00 #NUM! #NUM! 0 33
#NUM! $0.00 $0.00 #NUM! #NUM! 0 34
#NUM! $0.00 $0.00 #NUM! #NUM! 0 35
#NUM! $0.00 $0.00 #NUM! #NUM! 0 36
#NUM! $0.00 $0.00 #NUM! #NUM! 0 37
#NUM! $0.00 $0.00 #NUM! #NUM! 0 38
#NUM! $0.00 $0.00 #NUM! #NUM! 0 39
#NUM! $0.00 $0.00 #NUM! #NUM! 0 40
#NUM! $0.00 $0.00 #NUM! #NUM! 0 41
#NUM! $0.00 $0.00 #NUM! #NUM! 0 42
#NUM! $0.00 $0.00 #NUM! #NUM! 0 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
lognormal Mean = 7.01% 5.61%
lognormal SD = 22.44% 20.07% $1.00
#NUM! Distribution of Prices at Expiry $0.90
Mean Return = 10.00% Expected Gain = $35.69 $0.80
Standard Deviation = 25.00% #NUM! $0.70
Annualized Return = 7.12% Break Even Price = #NUM! $0.60
### Price at Expiry (est.) = $105.66 Break Even Price = #N/A 1.81% $0.50
### Std Dev at Expiry (est.) = $23.63 Prob of Loss = #NUM! Expected Price = $108.00 $0.40
### increment = $4.00 check 62.7% $108.00 Prob of Loss =
$0.30
Stocks only Annualized Gain price Break Even Cum Dist Price Density Dist Density Dist Expected Price Price
$0.20
-$2,000.00 #NUM! ### #NUM! 4.79% $80.00 32.66% 0.59% -1 75.72%
$0.10
-$1,900.00 #NUM! ### #NUM! 5.44% $81.00 35.79% 0.65% -1 76.66%
$0.00
$
$
$4
-$1,800.00 #NUM! ### #NUM! 6.15% $82.00 39.02% 0.71% -1 77.61%
-$1,700.00 #NUM! ### #NUM! 6.92% $83.00 42.33% 0.77% -1 78.56%
-$1,600.00 #NUM! ### #NUM! 7.75% $84.00 45.72% 0.83% -1 79.50%
-$1,500.00 #NUM! ### #NUM! 8.64% $85.00 49.15% 0.89% -1 80.45%
-$1,400.00 #NUM! ### #NUM! 9.59% $86.00 52.62% 0.95% -1 81.39%
-$1,300.00 #NUM! ### #NUM! 10.61% $87.00 56.09% 1.02% -1 82.34%
-$1,200.00 #NUM! ### #NUM! 11.69% $88.00 59.55% 1.08% -1 83.29%
-$1,100.00 #NUM! ### #NUM! 12.83% $89.00 62.99% 1.14% -1 84.23%
-$1,000.00 #NUM! ### #NUM! 14.04% $90.00 66.37% 1.20% -1 85.18%
-$900.00 #NUM! ### #NUM! 15.30% $91.00 69.67% 1.26% -1 86.13%
-$800.00 #NUM! ### #NUM! 16.63% $92.00 72.88% 1.32% -1 87.07%
-$700.00 #NUM! ### #NUM! 18.00% $93.00 75.98% 1.38% -1 88.02%
-$600.00 #NUM! ### #NUM! 19.44% $94.00 78.94% 1.43% -1 88.97%
-$500.00 #NUM! ### #NUM! 20.92% $95.00 81.76% 1.48% -1 89.91%
-$400.00 #NUM! ### #NUM! 22.45% $96.00 84.41% 1.53% -1 90.86%
-$300.00 #NUM! ### #NUM! 24.03% $97.00 86.88% 1.58% -1 91.81%
-$200.00 #NUM! ### #NUM! 25.65% $98.00 89.16% 1.62% -1 92.75%
-$100.00 #NUM! ### #NUM! 27.30% $99.00 91.24% 1.66% -1 93.70%
$0.00 #NUM! ### #NUM! 28.99% $100.00 93.11% 1.69% -1 94.65%
$100.00 #NUM! ### #NUM! 30.71% $101.00 94.76% 1.72% -1 95.59%
$200.00 #NUM! ### #NUM! 32.45% $102.00 96.19% 1.75% -1 96.54%
$300.00 #NUM! ### #NUM! 34.22% $103.00 97.39% 1.77% -1 97.48%
$400.00 #NUM! ### #NUM! 36.01% $104.00 98.37% 1.78% -1 98.43%
$500.00 #NUM! ### #NUM! 37.80% $105.00 99.11% 1.80% -1 99.38%
$600.00 #NUM! ### #NUM! 39.61% $106.00 99.63% 1.81% -1 100.32%
$700.00 #NUM! ### #NUM! 41.43% $107.00 99.93% 1.81% -1 101.27%
$800.00 #NUM! ### #NUM! 43.24% $108.00 100.00% 1.81% 0 102.22%
$900.00 #NUM! ### #NUM! 45.05% $109.00 99.86% 1.81% -1 103.16%
$1,000.00 #NUM! ### #NUM! 46.86% $110.00 99.51% 1.81% -1 104.11%
$1,100.00 #NUM! ### #NUM! 48.65% $111.00 98.97% 1.80% -1 105.06%
$1,200.00 #NUM! ### #NUM! 50.44% $112.00 98.23% 1.78% -1 106.00%
$1,300.00 #NUM! ### #NUM! 52.20% $113.00 97.31% 1.77% -1 106.95%
$1,400.00 #NUM! ### #NUM! 53.95% $114.00 96.22% 1.75% -1 107.90%
$1,500.00 #NUM! ### #NUM! 55.67% $115.00 94.96% 1.72% -1 108.84%
$1,600.00 #NUM! ### #NUM! 57.37% $116.00 93.56% 1.70% -1 109.79%
$1,700.00 #NUM! ### #NUM! 59.04% $117.00 92.02% 1.67% -1 110.73%
$1,800.00 #NUM! ### #NUM! 60.68% $118.00 90.36% 1.64% -1 111.68%
$1,900.00 #NUM! ### #NUM! 62.28% $119.00 88.58% 1.61% -1 112.63%
$2,000.00 #NUM! ### #NUM! 63.86% $120.00 86.69% 1.57% -1 113.57%
$2,100.00 #NUM! ### #NUM! 65.39% $121.00 84.72% 1.54% -1 114.52%
$2,200.00 #NUM! ### #NUM! 66.89% $122.00 82.66% 1.50% -1 115.47%
'Expected' Gains
100.00% 'Expected' Gains
#NUM! Cum Density
Price Distn Distn #NUM!
#NUM! $4.00 0.00% 0.00% #NUM! #NUM! #NUM!
#NUM! $8.00 0.00% 0.00% #NUM! #NUM! #NUM!
$…
$…
$…
$…
$…
$…
$…
$…
$…
$…
$…
$…
#NUM! $12.00 0.00% $…
0.00% #NUM! #NUM! #NUM!
#NUM! $16.00 0.00% 0.00% #NUM! #NUM! #NUM!
#NUM! $20.00 0.00% 0.00% #NUM! #NUM! #NUM!
#NUM! $24.00 0.00% 0.00% #NUM! #NUM! #NUM!
#NUM! $28.00 0.00% 0.00% #NUM! #NUM! #NUM!
#NUM! $32.00 0.00% 0.00% #NUM! #NUM! #NUM!
#NUM! $36.00 0.00% 0.00% #NUM! #NUM! #NUM!
#NUM! $40.00 0.00% 0.00% #NUM! #NUM! #NUM!
#NUM! $44.00 0.00% 0.00% #NUM! #NUM! #NUM!
#NUM! $48.00 0.00% 0.00% #NUM! #NUM! #NUM!
#NUM! $52.00 0.01% 0.01% #NUM! #NUM! #NUM!
#NUM! $56.00 0.03% 0.02% #NUM! #NUM! #NUM!
#NUM! $60.00 0.10% 0.07% #NUM! #NUM! #NUM!
#NUM! $64.00 0.27% 0.18% #NUM! #NUM! #NUM!
#NUM! $68.00 0.67% 0.39% #NUM! #NUM! #NUM!
#NUM! $72.00 1.43% 0.76% #NUM! #NUM! #NUM!
#NUM! $76.00 2.74% 1.31% #NUM! #NUM! #NUM!
#NUM! $80.00 4.79% 2.05% #NUM! #NUM! #NUM!
#NUM! $84.00 7.75% 2.96% #NUM! #NUM! #NUM!
#NUM! $88.00 11.69% 3.94% #NUM! #NUM! #NUM!
#NUM! $92.00 16.63% 4.93% #NUM! #NUM! #NUM!
#NUM! $96.00 22.45% 5.83% #NUM! #NUM! #NUM!
#NUM! $100.00 28.99% 6.54% #NUM! #NUM! #NUM!
#NUM! $104.00 36.01% 7.02% #NUM! #NUM! #NUM!
#NUM! $108.00 43.24% 7.23% #NUM! #NUM! #NUM!
#NUM! $112.00 50.44% 7.20% #NUM! #NUM! #NUM!
#NUM! $116.00 57.37% 6.93% #NUM! #NUM! #NUM!
#NUM! $120.00 63.86% 6.49% #NUM! #NUM! #NUM!
#NUM! $124.00 69.78% 5.92% #NUM! #NUM! #NUM!
#NUM! $128.00 75.05% 5.28% #NUM! #NUM! #NUM!
#NUM! $132.00 79.66% 4.60% #NUM! #NUM! #NUM!
#NUM! $136.00 83.60% 3.94% #NUM! #NUM! #NUM!
#NUM! $140.00 86.92% 3.32% #NUM! #NUM! #NUM!
#NUM! $144.00 89.67% 2.75% #NUM! #NUM! #NUM!
#NUM! $148.00 91.92% 2.25% #NUM! #NUM! #NUM!
#NUM! $152.00 93.73% 1.81% #NUM! #NUM! #NUM!
#NUM! $156.00 95.17% 1.44% #NUM! #NUM! #NUM!
#NUM! $160.00 96.31% 1.14% #NUM! #NUM! #NUM!
#NUM! $164.00 97.20% 0.89% #NUM! #NUM! #NUM!
#NUM! $168.00 97.89% 0.69% #NUM! #NUM! #NUM!
#NUM! $172.00 98.41% 0.53% #NUM! #NUM! #NUM!
$176.00 98.82% 0.40% #NUM! #NUM! #NUM!
$180.00 99.12% 0.30% #NUM! #NUM! #NUM!
$184.00 99.35% 0.23% #NUM! #NUM! #NUM!
$188.00 99.52% 0.17% #NUM! #NUM! #NUM!
$192.00 99.65% 0.13% #NUM! #NUM! #NUM!
$196.00 99.74% 0.09% #NUM! #NUM! #NUM!
$200.00 99.81% 0.07% #NUM! #NUM! #NUM!
$204.00 99.86% 0.05% #NUM! #NUM! #NUM!
$208.00 99.90% 0.04% #NUM! #NUM! #NUM!
$212.00 99.93% 0.03% #NUM! #NUM! #NUM!
$216.00 99.95% 0.02% #NUM! #NUM! #NUM!
$220.00 99.96% 0.01% #NUM! #NUM! #NUM!
$224.00 99.97% 0.01% #NUM! #NUM! #NUM!
$228.00 99.98% 0.01% #NUM! #NUM! #NUM!
$232.00 99.99% 0.01% #NUM! #NUM! #NUM!
$236.00 99.99% 0.00% #NUM! #NUM! #NUM!
$240.00 99.99% 0.00% #NUM! #NUM! #NUM!
$244.00 99.99% 0.00% #NUM! #NUM! #NUM!
$248.00 100.00% 0.00% #NUM! #NUM! #NUM!
$252.00 100.00% 0.00% #NUM! #NUM! #NUM!
$256.00 100.00% 0.00% #NUM! #NUM! #NUM!
$260.00 100.00% 0.00% #NUM! #NUM! #NUM!
$264.00 100.00% 0.00% #NUM! #NUM! #NUM!
$268.00 100.00% 0.00% #NUM! #NUM! #NUM!
$272.00 100.00% 0.00% #NUM! #NUM! #NUM!
$276.00 100.00% 0.00% #NUM! #NUM! #NUM!
$280.00 100.00% 0.00% #NUM! #NUM! #NUM!