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See: http://www.golden.net/~pjponzo/black-scholes-3.htm Have fun! gummy Enter the data in red squares like so: Note: (1) Strike Prices & Option Premiums for Example: Enter Expiry Month as Strike = $90.00 $100.00 $105.00 etc. Premium = Err:502 Err:502 Err:502 etc. These just give Strike Prices as percentages of Stock Pri 90% 100% 105% (You can change them.) (2) The Current Price of the stock for Example: Initial Cost Current Price = $100.0000 Err:502 (3) The Return, Standard Deviation & Risk-free Rate for the stock (if you know these *) 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 MAKE or (5) PLAY with the number of contracts which you write or buy # 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 … 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 Calls 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 Err:502 Err:502 the Max Gain is Err:502 the Min Gain is Err:502 LOSE money within the RANGE OF THE PLOT, currently($0) your initial outlay of money. tive, 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 Err:502
1 $105.00 Err:502 Err:502
1 $90.00 Err:502 Err:502
100%
$1
90%
$1
80%
$1
70%
$1
60%
$0
50%
$0
40%
$0
30%
40%
$0
20%
30%
$0
10%
20%
$0
0%
10%
$80.00 $82.00 $84.00 $86.00 $88.00 $90.00 $92.00 $94.00 $96.00 $98.00 $100.00 $102.00 $104.00 $106.00 $108.00 $110.00 $112.00 $114.00 $116.00 $118.00 $120.00 $122.00
$1
PLOT from
$80.00
90% 80%
Err:502 Err:502 Cumulative Distribution
70% Gain/Loss 60% 50%
Your PLOT is from 80% to 107% of the 'Current Price'
Err:502 Err:502
$122.00
$119.00
$116.00
$113.00
$110.00
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$1.00
$107.00
BreakEven
$104.00
0%
Column AL
increments of
0 $105.00 Err:502 Err:502
100%
$80.00
Column O
0 $100.00 Err:502 Err:502
$98.00
0 $100.00 Err:502 Err:502
$101.00
0 $90.00 Err:502 Err:502
BUY a call
$95.00
# contracts = Strike = Premium = Black-Scholes =
Uncovered
COVERED Calls (y/n) ? 100% 105%
$92.00
WRITE a call
and buying 1 90%
105%
$89.00
100%
$86.00
Err:502 90%
$83.00
Stock Name XYZ
$122.00
$119.00
$116.00
Expiry Month =
$113.00
$110.00
n
Current Price =
1
$100.0000
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sep
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Today is 22-Feb-09
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CALL expires Err:502 Err:502 days to expiry Assumptions: (annual data) Mean Return = 10% Std Devn = 25% Risk-free Rate = 4% Initial Cost In the range Err:502 $80 to $107 Covered Calls Err:502 Cost of buying Err:502 100 the Max Gain is shares at Err:502 the Min Gain is $100.0000 $10,000.00 Err:502 Prob. of Loss Err:502 Change ONLY numbers in a red square
WIN
zero loss Err:502 Err:502
99.55 Err:502 Err:502 Err:502
Err:502 1 $90.000 Err:502
Black Err:502 Scholes Err:502 stuff Err:502 stuff Err:502 $9.55 0 $100.000 Err:502
0 $105.000 Err:502
or
Stock Price
LOSE?
at expiration
Combination
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$80.00
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$81.00
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$82.00
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$83.00
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$84.00
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$85.00
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$86.00
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$87.00
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$88.00
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$89.00
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$90.00
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$91.00
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$92.00
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$93.00
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$94.00
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$95.00
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$96.00
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$97.00
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$98.00
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$99.00
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$100.00
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$101.00
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$102.00
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$103.00
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$104.00
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$105.00
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$106.00
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$107.00
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$108.00
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$109.00
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$110.00
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$111.00
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$112.00
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$113.00
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$114.00
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$115.00
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$116.00
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$117.00
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$118.00
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$119.00
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$120.00
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$121.00
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$122.00
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BUY call options
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100%
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80%
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2
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$122.00
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1
0
$119.00
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0
$116.00
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### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ###
$113.00
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$110.00
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Err:502 Expiry $107.00
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expires Fridays Err:502 Err:502 Err:502 Err:502 Err:502 Err:502 Err:502 Err:502 Err:502 Err:502 Err:502 Err:502 Err:502 Err:502 Err:502 Err:502 Err:502 Err:502 Err:502 Err:502 Err:502 Err:502 Err:502 Err:502 Err:502 Err:502 Err:502 Err:502
$104.00
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Dates Err:502 Err:502 Err:502 Err:502 Err:502 Err:502 Err:502 Err:502 Err:502 Err:502 Err:502 Err:502 Err:502 Err:502 Err:502 Err:502 Err:502 Err:502 Err:502 Err:502 Err:502 Err:502 Err:502 Err:502 Err:502 Err:502 Err:502 Err:502 Err:502
$98.00
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Index
09
$101.00
Err:502
zero
100 1-sep
$95.00
0%
TOTAL
Feb 22/09 sep
$92.00
Calculation of40% Expiry stuff 20%
$89.00
WRITE call options
TOTAL
Writing Uncovered Calls
$86.00
1 $105.000 Err:502
$83.00
0 $100.000 Err:502
$80.00
0 $90.000 Err:502
60%
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 SD =
7.01% 22.44%
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Standard Deviation = 25.00% Annualized Return = 7.12%
Annualized Gain
-$2,000.00
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-$1,900.00
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-$1,800.00
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-$1,700.00
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-$1,600.00
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-$1,500.00
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-$1,400.00
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-$1,300.00
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-$1,200.00
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-$1,100.00
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-$1,000.00
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-$900.00
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-$800.00
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-$700.00
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-$600.00
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-$500.00
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-$400.00
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-$300.00
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-$200.00
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-$100.00
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$0.00
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$100.00
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$200.00
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$300.00
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$400.00
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$500.00
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$600.00
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$700.00
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$800.00
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$900.00
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$1,000.00
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$1,100.00
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$1,200.00
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$1,300.00
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$1,400.00
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$1,500.00
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$1,600.00
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$1,700.00
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$1,800.00
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$1,900.00
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$2,000.00
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$2,100.00
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$2,200.00
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price
### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ###
$1.00
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$0.90
Price at Expiry (est.) = Err:502
$0.70 $0.60
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$0.50
Break Even Price = Err:502
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Break Even Price = #N/A
Std Dev at Expiry (est.) = Err:502
Prob of Loss = Err:502
increment = Err:502
check Err:502
Break Even Cum Dist
$0.80
Expected Gain = Err:502
$0.40 $0.30
Err:502 Err:502
$0.20 Prob of Loss =
Price
Density Dist
Density Dist
Expected Price
$0.10 Price
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$80.00
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$0.00 Err:502
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$81.00
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$112.00
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$122.00
$119.00
$116.00
Stocks only
$113.00
$110.00
$107.00
### #N/A ###
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Distribution of Prices at Expiry
Mean Return = 10.00%
$104.00
$101.00
lognormal Mean =
$1.00 $0.90 $0.80 $0.70 $0.60 $0.50 $0.40 $0.30 $0.20
Err:502 'Expected' Gains Err:502 Price
$0.00
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Density
Distn
Distn
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0.00%
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Expiry Month = sep Enter Expiry Month as mmm (like sep
give Strike Prices as percentages of Stock Price.
In the range $80 to $107 Err:502 Err:502 the Max Gain is Err:502 the Min Gain is Err:502 LOSE money within the RANGE OF THE PLOT, currently($0) your initial outlay of money. tive, 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 Err:502
1 $105.00 Err:502 Err:502
1 $90.00 Err:502 Err:502
100%
$1
90%
$1
80%
$1
70%
$1
60%
$0
50%
$0
40%
$0
30%
40%
$0
20%
30%
$0
10%
20%
$0
0%
10%
$80.00 $82.00 $84.00 $86.00 $88.00 $90.00 $92.00 $94.00 $96.00 $98.00 $100.00 $102.00 $104.00 $106.00 $108.00 $110.00 $112.00 $114.00 $116.00 $118.00 $120.00 $122.00
$1
PLOT from
$80.00
90% 80%
Err:502 Err:502 Cumulative Distribution
70% Gain/Loss 60% 50%
Your PLOT is from 80% to 107% of the 'Current Price'
Err:502 Err:502
$122.00
$119.00
$116.00
$113.00
$110.00
Err:502
$1.00
$107.00
BreakEven
$104.00
0%
Column AL
increments of
0 $105.00 Err:502 Err:502
100%
$80.00
Column O
0 $100.00 Err:502 Err:502
$98.00
0 $100.00 Err:502 Err:502
$101.00
0 $90.00 Err:502 Err:502
BUY a call
$95.00
# contracts = Strike = Premium = Black-Scholes =
Uncovered
COVERED Calls (y/n) ? 100% 105%
$92.00
WRITE a call
and buying 1 90%
105%
$89.00
100%
$86.00
Err:502 90%
$83.00
Stock Name XYZ
$122.00
$119.00
$116.00
Expiry Month =
$113.00
$110.00
n
Current Price =
1
$100.0000
Err:502
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sep
Err:502 Err:502
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Err:502 Err:502
Today is 22-Feb-09
Err:502
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CALL expires Err:502 Err:502 days to expiry Assumptions: (annual data) Mean Return = 10% Std Devn = 25% Risk-free Rate = 4% Initial Cost In the range Err:502 $80 to $107 Covered Calls Err:502 Cost of buying Err:502 100 the Max Gain is shares at Err:502 the Min Gain is $100.0000 $10,000.00 Err:502 Prob. of Loss Err:502 Change ONLY numbers in a red square
WIN
zero loss Err:502 Err:502
99.55 Err:502 Err:502 Err:502
Err:502 1 $90.000 Err:502
Black Err:502 Scholes Err:502 stuff Err:502 stuff Err:502 $9.55 0 $100.000 Err:502
0 $105.000 Err:502
or
Stock Price
LOSE?
at expiration
Combination
Err:502
$80.00
Err:502
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$81.00
Err:502
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$82.00
Err:502
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$83.00
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$84.00
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$85.00
Err:502
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$86.00
Err:502
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$87.00
Err:502
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$88.00
Err:502
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$89.00
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$90.00
Err:502
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$91.00
Err:502
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$92.00
Err:502
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$93.00
Err:502
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$94.00
Err:502
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$95.00
Err:502
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$96.00
Err:502
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$97.00
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$98.00
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$99.00
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$100.00
Err:502
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$101.00
Err:502
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$102.00
Err:502
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$103.00
Err:502
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$104.00
Err:502
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$105.00
Err:502
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$106.00
Err:502
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$107.00
Err:502
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$108.00
Err:502
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$109.00
Err:502
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$110.00
Err:502
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$111.00
Err:502
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$112.00
Err:502
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$113.00
Err:502
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$114.00
Err:502
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Err:502
$115.00
Err:502
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$116.00
Err:502
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$117.00
Err:502
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$118.00
Err:502
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$119.00
Err:502
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$120.00
Err:502
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$121.00
Err:502
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$122.00
Err:502
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BUY call options
Err:502
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100%
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80%
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2
0
3
0
4
0
5
0
6
0
7
0
8
0
9
0
10
0
11
0
12
0
13
0
14
0
15
0
16
0
17
0
18
0
19
0
20
0
21
0
22
0
23
0
24
0
25
0
26
0
27
0
28
0
29
0
30
0
31
0
32
0
33
0
34
0
35
0
36
0
37
0
38
0
39
0
40
0
41
0
42
0
43
Err:502 Err:502 Err:502 Err:502 Err:502 Err:502 Err:502 Err:502 Err:502 Err:502 Err:502 Err:502 Err:502 Err:502 Err:502 Err:502 Err:502 Err:502 Err:502 Err:502 Err:502 Err:502 Err:502 Err:502 Err:502 Err:502 Err:502
$122.00
Err:502
1
0
$119.00
Err:502
0
$116.00
Err:502
### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ###
$113.00
Err:502
$110.00
Err:502
Err:502
Err:502 Expiry $107.00
Err:502
Err:502
expires Fridays Err:502 Err:502 Err:502 Err:502 Err:502 Err:502 Err:502 Err:502 Err:502 Err:502 Err:502 Err:502 Err:502 Err:502 Err:502 Err:502 Err:502 Err:502 Err:502 Err:502 Err:502 Err:502 Err:502 Err:502 Err:502 Err:502 Err:502 Err:502
$104.00
Err:502
Err:502
Dates Err:502 Err:502 Err:502 Err:502 Err:502 Err:502 Err:502 Err:502 Err:502 Err:502 Err:502 Err:502 Err:502 Err:502 Err:502 Err:502 Err:502 Err:502 Err:502 Err:502 Err:502 Err:502 Err:502 Err:502 Err:502 Err:502 Err:502 Err:502 Err:502
$98.00
Err:502
Err:502
Index
09
$101.00
Err:502
zero
100 1-sep
$95.00
0%
TOTAL
Feb 22/09 sep
$92.00
Calculation of40% Expiry stuff 20%
$89.00
WRITE call options
TOTAL
Writing Uncovered Calls
$86.00
1 $105.000 Err:502
$83.00
0 $100.000 Err:502
$80.00
0 $90.000 Err:502
60%
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 SD =
7.01% 22.44%
Err:502
Standard Deviation = 25.00% Annualized Return = 7.12%
Annualized Gain
-$2,000.00
Err:502
-$1,900.00
Err:502
-$1,800.00
Err:502
-$1,700.00
Err:502
-$1,600.00
Err:502
-$1,500.00
Err:502
-$1,400.00
Err:502
-$1,300.00
Err:502
-$1,200.00
Err:502
-$1,100.00
Err:502
-$1,000.00
Err:502
-$900.00
Err:502
-$800.00
Err:502
-$700.00
Err:502
-$600.00
Err:502
-$500.00
Err:502
-$400.00
Err:502
-$300.00
Err:502
-$200.00
Err:502
-$100.00
Err:502
$0.00
Err:502
$100.00
Err:502
$200.00
Err:502
$300.00
Err:502
$400.00
Err:502
$500.00
Err:502
$600.00
Err:502
$700.00
Err:502
$800.00
Err:502
$900.00
Err:502
$1,000.00
Err:502
$1,100.00
Err:502
$1,200.00
Err:502
$1,300.00
Err:502
$1,400.00
Err:502
$1,500.00
Err:502
$1,600.00
Err:502
$1,700.00
Err:502
$1,800.00
Err:502
$1,900.00
Err:502
$2,000.00
Err:502
$2,100.00
Err:502
$2,200.00
Err:502
price
### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ###
$1.00
Err:502
$0.90
Price at Expiry (est.) = Err:502
$0.70 $0.60
Err:502
$0.50
Break Even Price = Err:502
Err:502
Break Even Price = #N/A
Std Dev at Expiry (est.) = Err:502
Prob of Loss = Err:502
increment = Err:502
check Err:502
Break Even Cum Dist
$0.80
Expected Gain = Err:502
$0.40 $0.30
Err:502 Err:502
$0.20 Prob of Loss =
Price
Density Dist
Density Dist
Expected Price
$0.10 Price
Err:502
Err:502
$80.00
Err:502
Err:502
Err:502
$0.00 Err:502
Err:502
Err:502
$81.00
Err:502
Err:502
Err:502
Err:502
Err:502
Err:502
$82.00
Err:502
Err:502
Err:502
Err:502
Err:502
Err:502
$83.00
Err:502
Err:502
Err:502
Err:502
Err:502
Err:502
$84.00
Err:502
Err:502
Err:502
Err:502
Err:502
Err:502
$85.00
Err:502
Err:502
Err:502
Err:502
Err:502
Err:502
$86.00
Err:502
Err:502
Err:502
Err:502
Err:502
Err:502
$87.00
Err:502
Err:502
Err:502
Err:502
Err:502
Err:502
$88.00
Err:502
Err:502
Err:502
Err:502
Err:502
Err:502
$89.00
Err:502
Err:502
Err:502
Err:502
Err:502
Err:502
$90.00
Err:502
Err:502
Err:502
Err:502
Err:502
Err:502
$91.00
Err:502
Err:502
Err:502
Err:502
Err:502
Err:502
$92.00
Err:502
Err:502
Err:502
Err:502
Err:502
Err:502
$93.00
Err:502
Err:502
Err:502
Err:502
Err:502
Err:502
$94.00
Err:502
Err:502
Err:502
Err:502
Err:502
Err:502
$95.00
Err:502
Err:502
Err:502
Err:502
Err:502
Err:502
$96.00
Err:502
Err:502
Err:502
Err:502
Err:502
Err:502
$97.00
Err:502
Err:502
Err:502
Err:502
Err:502
Err:502
$98.00
Err:502
Err:502
Err:502
Err:502
Err:502
Err:502
$99.00
Err:502
Err:502
Err:502
Err:502
Err:502
Err:502
$100.00
Err:502
Err:502
Err:502
Err:502
Err:502
Err:502
$101.00
Err:502
Err:502
Err:502
Err:502
Err:502
Err:502
$102.00
Err:502
Err:502
Err:502
Err:502
Err:502
Err:502
$103.00
Err:502
Err:502
Err:502
Err:502
Err:502
Err:502
$104.00
Err:502
Err:502
Err:502
Err:502
Err:502
Err:502
$105.00
Err:502
Err:502
Err:502
Err:502
Err:502
Err:502
$106.00
Err:502
Err:502
Err:502
Err:502
Err:502
Err:502
$107.00
Err:502
Err:502
Err:502
Err:502
Err:502
Err:502
$108.00
Err:502
Err:502
Err:502
Err:502
Err:502
Err:502
$109.00
Err:502
Err:502
Err:502
Err:502
Err:502
Err:502
$110.00
Err:502
Err:502
Err:502
Err:502
Err:502
Err:502
$111.00
Err:502
Err:502
Err:502
Err:502
Err:502
Err:502
$112.00
Err:502
Err:502
Err:502
Err:502
Err:502
Err:502
$113.00
Err:502
Err:502
Err:502
Err:502
Err:502
Err:502
$114.00
Err:502
Err:502
Err:502
Err:502
Err:502
Err:502
$115.00
Err:502
Err:502
Err:502
Err:502
Err:502
Err:502
$116.00
Err:502
Err:502
Err:502
Err:502
Err:502
Err:502
$117.00
Err:502
Err:502
Err:502
Err:502
Err:502
Err:502
$118.00
Err:502
Err:502
Err:502
Err:502
Err:502
Err:502
$119.00
Err:502
Err:502
Err:502
Err:502
Err:502
Err:502
$120.00
Err:502
Err:502
Err:502
Err:502
Err:502
Err:502
$121.00
Err:502
Err:502
Err:502
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$122.00
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$122.00
$119.00
$116.00
Stocks only
$113.00
$110.00
$107.00
### #N/A ###
Err:502
Distribution of Prices at Expiry
Mean Return = 10.00%
$104.00
$101.00
lognormal Mean =
$1.00 $0.90 $0.80 $0.70 $0.60 $0.50 $0.40 $0.30 $0.20
Err:502 'Expected' Gains Err:502 Price
$0.00
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Density
Distn
Distn
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0.00%
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$0.10
Cum
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