Financial Engineering Lecture 4
Dec 14, 2015
Option Strategies
Bullish Strategies Risk RewardCall purchase limited
unlimitedSynthetic long stock unlimited
unlimitedBull spread limited limitedProtective Put limited
unlimitedBullish calendar spread limited
unlimitedCovered call unlimited limitedNaked put write unlimited limited
Option StrategiesBearish Strategies Risk RewardPut purchase limited
unlimitedSynthetic Put limited
unlimitedSynthetic short sale unlimited
unlimitedBear spread limited limitedCovered put write unlimited limitedBearish calendar spread limited
unlimitedNaked call write unlimited limited
Bull Spread Long Call @ s1 s1 < s2 Short Call @ s2
Max Profit = s2 - s1 - c1 + c2 Break Even = s2 - MP = s1 - c2 + c1
Bull Spread
ExamplePrice = 32 Oct35C = 1 t=60days/365Oct30C = 3 v = .24
Buy Oct30C = -3Sell Oct35C = +1Max Profit = 35-30-3+1 = 3BE = 30-1+3 = 32Net Debit = -3 + 1 = -2
Bull Spread Compute probability of bull spread
Example
Vt = .24 (60/365).5 = .097
Prob (<32) = N[ln(32/32) /.097] = .5000Prob (>32) = 1 - .500 = .5000
Max Profit = $300Max Loss = -$200
• at 50% odds, makes good sense
Put Bull Spread
Long Put @ s1 s1 < s2Short put @ s2
example (Credit Spread)Price = 55Jan50P = 2Jan60P = 7
Net Credit = p2 - p1 = + 7 - 2 = + 5Break Even = S2 - credit = 60 - 5 = 55
Call Bear SpreadShort Call @ s1 s1 < s2Long Call @ s2 credit spread
ExampleP = 55 Jan60C = 2 Jan50C = 7Net Credit = 7 - 2 = 5 BE = 50 + 5 = 55
Call Bear SpreadShort Call @ s1 s1 < s2Long Call @ s2 credit spread
ExampleP = 55 Jan60C = 2 Jan50C = 7Net Credit = 7 - 2 = 5 BE = 50 + 5 = 55
+7
-2
+5
-550 55 60
Put Bear SpreadLong Put @ s1 s1 > s2Short Put @ s2 debit spread
ExampleP = 55 Jan50P = 2 Jan60P = 7Net Debit = 7 - 2 = 5 BE = 60 - 5 = 55
Put Bear SpreadLong Put @ s1 s1 > s2Short Put @ s2 debit spread
ExampleP = 55 Jan50P = 2 Jan60P = 7Net Debit = 7 - 2 = 5 BE = 60 - 5 = 55
-7
+2
+5
-5
50 55 60
Call Bear vs. Put Bear +Credit spread- assignment risk? What causes assignment-Large Credit = P well above lower strike
Example: p = 59, Jan60C=1, Jan50C=9
+9
-1
50 60
Bull Spread - Roll Down
Long Stock, Long Call, Short 2 Calls
ExampleOwn stock @ $48Price = 42Oct40Call = 4 (buy)Oct45Call = 2 (sell 2)Net Credit = 0BE = 44
Bull Spread - Roll Down
Price P/LSt P/L Sh C P/L Lg C Net P/L35 -1300 +400 -400 -130038 -1000 +400 -400 -100040 -800 +400 -400 -80042 -600 +400 -200 -40044 -400 +400 0 045 -300 +400 +100 +20048 0 -200 +400 +20050 +200 -600 +600 +200
Synthetic Covered CallBull spread
If call is deep in the money and has no time to exp, a bull spread can be used to simulate a covered call.
ExamplePrice = 49Sell Apr50C = 3Buy Apr35C = 14
Butterfly SpreadA neutral position that combines both a bear spread and a
bull spreadLong call @ s1 s1 < s2 < s3Short 2 calls @ s2Long call @ s3
ExamplePrice = 60buy July50C = 12 1200 debitshort2 July60C = 6 1200 creditbuy July70C = 3 300 debit 300 Net Debit
Put Butterfly SpreadMultiple ways to create the butterfly spread
exampleStrike 50 60 70Call 12 6 2Put 1 5 11
Butterfly Positions Net PositionBuy 50C / sell 2 60C / buy 70C 2 debitBuy50C/sell 60C/buy70P/sell60P 12 debitBuy50P/sell60P/Buy70C/sell60C 8 creditBuy50P / sell 2 60P / buy 70P 2 debit
Ratio Call Write
Long stock, short multiple calls
example 2:1 ratio call writePrice = 49Oct50C = 6sell 2 calls and long 100 stock
Ratio Call Roll Downexample 2:1 ratio call writePrice = 49Oct50C = 6sell 2 calls and long 100 stock
Price drops to 40Oct50C = 1Oct40C = 4Buy 2 Oct50C = profit = 12 - 2 = 10Sell 2 Oct40C
apply to stock price & pretend we own stock at $39
Variable Ratios
Max Profit = m(S-P) + nC m = # stock lots
Upside BE = S + MP/(n-m) n = # of Call ks
Downside BE = S - MP / m
Example
Max Profit = 1 (50-49) + 2 (6) = 13Upside BE = 50 + 13/ (2-1) = 63Downside BE = 50 - 13/1 = 37
Ratio Call Write
Example 3:1Buy 1 lot stock @ 49sell 3 oct50c@18Max Profit = 1 (50-49) + 3 (6) = 19Upside BE = 50 + 19/ (3-1) = 59.5Downside BE = 50 - 19/1 = 31
+13+12
-1237 49 50 63
Ratio Call Write
Example 3:1Buy 1 lot stock @ 49sell 3 oct50c@18Max Profit = 1 (50-49) + 3 (6) = 19Upside BE = 50 + 19/ (3-1) = 59.5Downside BE = 50 - 19/1 = 31
+19+18
-12 31 49 50 59.5
Variable Ratio Write
Long stock, s1 < P < s2short in money call (s1), short out of money call (s2)
Max Profit = c1 + c2 + s1 - PDownside BE = s1 - MPUpside BE = s2 + MP
ExamplePrice = 65Oct60C = 8Oct70C = 3
Ratio Spread
Long call @ s1 s1 < s2Short X calls @ s2
Example 2:1Price = 44Apr40C = 5 buy 1Apr45C = 3 sell 2
BE = 51MP = 6
Naked Straddle WriteSame Example - But, sell 4 of eachPrice = 45Jan45C = 4Jan45P =3
+28
-12
38 45 52 55
Covered Straddle WriteLong StockShort CallShort Put
examplePrice = 51 buy 100 sharesJan50C = 5 sell 1 callJan50P = 4 sell 1 put
Max Profit = Premium + S - P = 9 + 50 - 51 = 8BE = (P+S-Prem)/2 = 46
Combination Writeor Strangle Write
Short put (out of money)Short call (out of money)
exampleprice = 65Jan70C = 4Jan60P = 3Downside BE = Sp - put - call = 60-3-4 = 53Upside BE = Sc + put + call = 70+3+4 = 77Max Profit = put + call = 3+4 = 7
Strangle Straddle Conversionsame exampleprice = 65 (price rises to 70)Jan70C = 4Jan60P = 3 Put falls to 1Jan70P = 4action: buy back the 60 put & sell the 70 put
+7
53 60 70 77
Splitting The Strikes& Synthetic StocksShort out of money putLong out of money call
example (Bullish Strike Split)price = 53Jan50P = 2Jan60C = 1
BE = 48
Calendar SpreadShort near term optionLong distant term option
example (Bull Calendar Spread)Price = 50Today Apr50C = 5 short = +5(Jan) July50C = 8 long = -8 Net Debit = -3Price = 50April Apr50C = 0 July50C = 5
Price Apr50C/PL July50C/PL Net Profit40 0/+500 .5/-750-25045 0/+500 2.5/-550 -5048 0/+500 4/-400 +10050 0/+500 5/-300 +20052 2/+300 6/-200 +10055 5/0 8/0 060 10/-500 10.5/+250 +250
Bull Calendar SpreadApril Profit/Loss Table
Put Calendar Spread(Bearish)Same as callshort near term & long distant termex - price = 50, Jan50P = 2, Apr50P = 3
+1
X 50 Y
-1
+2
-3
Reverse SpreadOpposite of all other common positions
Example (Reverse ratio - backspread) 2:1Short call @ s1 s1<s2Long x calls @ s2
Price = 43July40C = 4July45C = 1
Diagonal Spreaddiff strikes & diff exp
example (Diagonal Bull Spread)Price = 32Apr30C = 3Apr35C = 1July30C = 4 Long July30CJuly35C = 1.5 Short Apr35C
Normal Bull Spread - Long Apr30C Short Apr35C