Options Summary

Option strategies:
c = call, p = put
X = strike price, t = expiration date, S = stock price
prem = price of options




Options Summary S&P500
1/70-1/98
rr sd 10k:
b+h 9.0% 15.1% 112.6k
16% m stop 9.3 14.8 120.9k
long atm -7.4% 9.6 1.1k
1% otm -7.8 8.5 1.0k
10% itm 6.8% 14.5% 63.0k
short:
ATM 23.5% 9.6% 3.650m
1% OTM 18.5% 8.5% 1.151m
10% OTM 9.5 1.5 127.2k
Spread:
5% ITM - 3% OTM 14.3 9.3 425k
10% ITM - 3% 21.2% 10.8% 2.162m
5% ITM - ATM 14.4% 5.7% 433k


Options: Black-Scholes
option_P =
stock_P * prob_d1
-
strike_P * exp ( -rf * yrs_to_exp) * prob_d2

d1 =
(ln(stock_P/strike_P) + (rf + SD^2/2)*yrs_to_exp) /
( SD * sqrt(yrs_to_exp) )

d2 =
(ln(stock_P/strike_P) + (rf + SD^2/2)*yrs_to_exp) /
( SD * sqrt(yrs_to_exp) )
- SD* sqrt(yrs_to_exp)

Options: Butterfly Spread
b call(X1), s 2 calls(X2), b call(X3),
X3 > X2 > X1, X3 - X2 = X2 - X1
payoff = 0 if S <> X3
max = S = S - X2 - prem(X1) + prem(X2) - prem(X3)
min = o
risk = prem(X3) + prem(X1) - 2*prem(X2)

Options: Calls per Cook
only b if
- nd <= 6% ch in stock P to double money
- t val < 50% of val of option val
insure open interest of at least 100


Options: COVERED CALL
demand min of 1% per mo if stock ds nothing
strive for 10% downside protection
calculate rtn if xwercised, rtm if flat, downside
protectn
- s call option on stock you own (naked = don't own)
- payoff =
S + prem if S <= X,
X + prem if S > X <= capped payoff for prem today

x x = stock ownership
x
-x---------------
-x
-x
-x
-x
x
- risk = S - prem
- in-th-$ call always offers > dnside prot than out of $




Options: Covered Call per Cook
try to sell so that option P = 8% of stock P
=> 16% profit if b on margin
eg stock = $10, option = .80
20, option = 1.60
30 => 2.40
use stocks in $5-18 range for max profit
try not to sell < $500 worth of calls
b stock on dip, s call on strength

eg b 1000 XYZ @ 7 on margin = $3,500 cost
s 10 .50 calls = $500 inc =
14% profit in 1 mo = 289% annualized
must choose bw larger premium now and less cap gain later
(if get called out) or larger cap gain later, smaller
premium now

Options: Quick Pricing
atm option = 2/3 SD

Assume 6% risk free rr
ATM call as % of underlying: 13m p if inv
IV: 1m 2m 3m 13m @ 5%, s in 12 m
10% 1.4% 2.2% 2.8% 7.6% 3.0% 1.6%
15% 1.9 2.9 3.7 9.9 4.5% 2.6%
20% 2.5 3.7 4.6 11.6 7.2% 4.7%
25 3.0 4.5 5.5 13.4 9.1% 6.1%
30 3.6 5.2 6.4 15.2 10.9% 7.3%
40 4.7 6.8 8.3 19.0 15.0% 10.3%
50 5.8 8.4 10.2 22.8 18.9% 13.1%
60 6.9 10.0 12.2 26.6 22.9% 16.0%

Long 13m, Short 1m:
P/L if no change in underlying:
20%: 20.9%
25% 25.6
50 52.6%


Options: Quick Pricing
For ATM call as % of stock p:
Implied Volatilitu:
%: 1m 2m 3m 13m (LEAP)
1% 6% - - -
2% 15% 9% - -
3% 25% 16 11%
4 34% 22 17%
5 43% 29 22%* (7%=7%)
10 88% 60 49% 15%
11 (6=28%) 19
12 21
13 24
14 27
15 30
20 43
25% 56

Options: Quick Pricing 20%
% out of $ v. X (of call) as % of S
1m 2m 3m 13m 12m 11m 10m 9m
-20 22.2 21.8 21.5 21.1
-15 19.5 18.9 18.2 17.5
-10% 16.7 16.2 15.7 15.1
-5% 6.3% 7.0 7.6 14.0%13.4 12.8 12.2 11.6
-2% 3.9 5.0 5.9 12.9 12.4 11.7 11.1 10.5
-1% 3.1 4.3 5.2 12.3 11.7 11.1 10.4 9.8
ATM 2.5 3.7 4.6 11.6 11.0 10.4 9.8 9.1
1% 2.0 3.2 4.0 11.0
2% 1.6 2.7 3.6 10.4
3 1.4 2.4 3.2 9.8
4 0.8 2.1 2.8 9.3
5 0.7 1.9 2.6 8.8 8.1 7.5 6.9 6.3
10 - 0.3 1.3 6.7 5.9 5.5 5.0 4.6
15 - - 0.5 5.5 3.8 3.1 2.5 2.3
20% - - - 3.4 2.7 2.7 2.2 1.2

P/L if long 13m ATM, short 1m:
-10% 0% +10% +20%
ATM 20.9 20.9 20.9% 20.9%
1% 14.4 14.4 24.4 27.4%
2% 9.2 9.2 19.2 29.2%
3% 6.6 6.6 16.6 26.6



Options: Quick Pricing 25%
% out of $ v. X (of call) as % of S
1m t prem: 2m 3m 13m t prem:
-20 20.3 .3 20.7 21.1 25.9 5.9
-15 15.4 .4 15.9 16.5 22.1 7.1
-10% 10.6 .6 11.4 12.2 18.7 8.7
-5% 6.3% 1.3 7.5 8.5 15.6% 10.6
-2% 4.2 2.2 5.6 6.7 14.0 12.0
-1% 3.6 2.6 5.0 6.1 13.4 12.4
ATM 3.1 3.1 4.5 5.6 12.9 12.9
1% 2.6 2.6 4.0 5.1 12.4 12.4
2% 2.2 2.2 3.5 4.6 12.0 12.0
3 1.8 1.8 3.1 4.2 11.5 11.5
4 1.5 1.5 2.8 3.8 11.0 11.0
5 1.2 1.2 2.4 3.4 10.6 10.6
10 0.4 0.4 1.2 2.0 8.6
15 0.1 0.1 0.5 1.1 6.9
20% - - 0.5 5.5


Options: Spread
SPREAD (574-5, Investments)
- b c(X1), s c(X2), X2>X1 = BULLISH SPREAD
- payoff = X2 - X1 - prem MAX; no addl proft aft S > X2
-------------
-
0---------------------
-
------
X1 X2
- risk = prem (P of c(X1) - P of c(X2); finite; no addl
loss if S < X1
- good if target profit in mind w/ finite risk tolerance


Options: Spread Strategies
For 25% Volatility:
Price as %age of underlying:
Summary: 15-5 = 14.2 10-5 = 9.4 5-5 = 5.1
10-ATM = 7.5 5-ATM = 3.2

Short leg
OTM:
ATM 1% 2 3 4 5
ITM: 3.1% 2.6 2.2 1.8 1.5 1.2
Long 20% 20.3 17.2 17.7 18.1 18.5 18.8 19.1
P/L +2.8 3.3 3.9 4.5 5.2 +5.9
15 15.4 12.3 12.8 13.2 13.6 13.9 14.2
P/L +2.7 3.2 3.8 4.4 5.1 +5.8
10 10.6 7.5 8.0 8.4 8.8 9.1 9.4
P/L +2.5 3.0 3.6 4.2 4.9 +5.6
5 6.3 3.2 3.7 4.1 4.5 4.8 5.1
P/L +1.8 2.3 2.9 3.5 4.2 +4.9
2 4.2 1.1 1.6 2.0 2.4 2.7 3.0
P/L +0.9
1 3.6 0.5 1.0 1.4 1.8 2.1 2.4
P/L +0.5
ATM 3.1 0.0 0.5 0.9 1.3 1.6 1.9

eg long 20% ITM @ 20.3%, short 1% OTM @ 2.6% = 17.7% cost
-max profit = 20 + 3 - 17.7 = 5.3%
-if no change = 20 - 17.7 = 2.3%
-bkeven = 17.7 - 20 = -2.3%

Options: Spreads, Analysis
%ile: 5% 10% 25% 50% 75% 90% 95%
P/L if +/-: -5% -4% -1.5 +1% 3% 5% 7%
Long: Short:
10% ITM ATM -2.5%-1.5 +1.3 +2.8 +2.8 +2.8 +2.8
10% ITM 3% -3.8 -2.8 -0.3 +2.2 +4.2 +4.2 +4.2
10% ITM 5% -4.4 -3.4 -0.9 +1.6 +3.6 +5.6 +5.6
5% ITM ATM -3.2 -2.2 +0.3 +1.8 +1.8 +1.8 +1.8
5% ITM 3% -4.5 -3.5 -1.0 +1.5 +3.5 +3.5 +3.5
5% ITM 5%

OTM:
ATM 1% 2 3 4 5
ITM: 3.1% 2.6 2.2 1.8 1.5 1.2
Long 20% 20.3 17.2 17.7 18.1 18.5 18.8 19.1
P/L +2.8 3.3 3.9 4.5 5.2 5.9
15 15.4 12.3 12.8 13.2 13.6 13.9 14.2
P/L +2.7 3.2 3.8 4.4 5.1 5.8
10 10.6 7.5 8.0 8.4 8.8 9.1 9.4
P/L +2.5 3.0 3.6 4.2 4.9 5.6
5 6.3 3.2 3.7 4.1 4.5 4.8 5.1
P/L +1.8 2.3 2.9 3.5 4.2 4.9
2 4.2 1.1 1.6 2.0 2.4 2.7 3.0
P/L +0.9
1 3.6 0.5 1.0 1.4 1.8 2.1 2.4
P/L +0.5


Options: STD
STD(1m)
x 3.54 = STD(1 yr)
x 1.41 = STD(2m)
x 1.73 = STD(3m)

Options: Straddle
STRADDLE b c + p w/ same X + t (pp 572-3, Investments)
- payoff = abs(S-X) - prem

- -
- -
0---------
-

- risk = finite (premium) + only if X = S xactly @ xpir
- bet on volatility; no $ if dS < price of prem
- make same $ if stock rises or falls
- lose if stock stays in range

FOLLOW-UP: eg XYZ @ 45, b 45 straddle @ 7
- if XYZ rises to 50, s 45 put, buy 50 put =>
now own COMBINATION; can never b < $500 so dec risk
b maintain profit pot
- if XYZ falls to 40, s 45 c, b 40 call, etc.


Options: SuperCharts Formula
Option_Price =
BlackScholes((32-DayOfMonth(date)),(MonthlyClose(offset)*
(1+gain)),price,int_rate,vola,1)