Financial Engineering
description
Transcript of Financial Engineering
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Financial EngineeringLecture 4
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Option StrategiesBullish 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
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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
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Covered CallLong Stock, Short Call
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Covered CallLong Stock, Short Call
Profit = S + call - P BE = P - call
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Protective PutLong Stock, Long Put
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Protective PutLong Stock, Long Put
Profit = P - put - S
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Synthetic Long Put Short Stock, Long Call
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Synthetic Long Put Short Stock, Long Call
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Synthetic Short Call Short Stock, Short Put
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Synthetic Short Call Short Stock, Short Put
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Synthetic Stock Short Put, Long Call
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Synthetic Stock Short Put, Long Call
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Synthetic Stock Short Put, Long Call
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Bull Spread Long Call @ s1 s1 < s2 Short Call @ s2
Max Profit = s2 - s1 - c1 + c2 Break Even = s2 - MP = s1 - c2 + c1
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Bull SpreadExamplePrice = 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
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Bull Spread
+3
-2
+1
-330 32 35
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Bull Spread
+3
-2
+1
-330 32 35
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Bull Spread
+3
-2
+1
-330 32 35
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Bull Spread
+3
-2
+1
-330 32 35
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Bull Spread Profit / Loss Diagram Table
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Bull Spread Compute probability of bull spread
Example
Vt = .24 (60/365).5 = .097Prob (<32) = N[ln(32/32) /.097] = .5000Prob (>32) = 1 - .500 = .5000
Max Profit = $300Max Loss = -$200
• at 50% odds, makes good sense
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Bull Spread
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Aggressive Bull Spread s1 < P << s2 Good probability, good profit potential
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Extremely Aggr. Bull Spread P < s1 < s2 Small Cost, high profit, low prob
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Least Aggr. Bull Spread S1 < s2 < P Low profit, high prob
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Put Bull SpreadLong 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
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Put Bull Spread+7
-2
+5
-5 50 55 60
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Put Bull Spread+7
-2
+5
-5 50 55 60
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Put Bull Spread+7
-2
+5
-5 50 55 60
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Call Bear SpreadShort Call @ s1 s1 < s2Long Call @ s2 credit spread
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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
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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
-5 50 55 60
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Put Bear SpreadLong Put @ s1 s1 > s2Short Put @ s2 debit spread
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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
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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
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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
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Bull Spread - Roll DownLong Stock, Long Call, Short 2 Calls
ExampleOwn stock @ $48Price = 42Oct40Call = 4 (buy)Oct45Call = 2 (sell 2)Net Credit = 0BE = 44
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Bull Spread - Roll Down
+400
-400
+200
-800 40 44 48
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Bull Spread - Roll Down
+400
-400
+200
-800 40 44 48
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+400
-400
+200
-800 40 44 48
Bull Spread - Roll Down
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Bull Spread - Roll Down
+400
-400
+200
-800 40 44 48
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Bull Spread - Roll Down
+400
-400
+200
-800 40 44 48
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Bull Spread - Roll DownPrice 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
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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
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Synthetic Covered CallBull spread
+3
+11
35 46 50
+4
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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
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Butterfly Spread
+12+7
-12 50 53 60 67 70
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Butterfly Spread
+12+7
-12 50 53 60 67 70
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Butterfly Spread
+12+7
-12 50 53 60 67 70
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Butterfly Spread
+12+7
-12 50 53 60 67 70
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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
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Ratio Call WriteLong stock, short multiple calls
example 2:1 ratio call writePrice = 49Oct50C = 6sell 2 calls and long 100 stock
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Ratio Call Write
+13+12
-12 37 49 50 63
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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
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Ratio Call Roll Down
+9+8
31 49 40 49
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Variable RatiosMax Profit = m(S-P) + nC m = # stock
lotsUpside BE = S + MP/(n-m) n = # of Call
ksDownside BE = S - MP / m
Example
Max Profit = 1 (50-49) + 2 (6) = 13Upside BE = 50 + 13/ (2-1) = 63Downside BE = 50 - 13/1 = 37
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Ratio Call WriteExample 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
-12 37 49 50 63
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Ratio Call WriteExample 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
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Variable Ratio WriteLong 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
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Variable Ratio Write
+8
+3
54 60 65 70 76
+6
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Variable Ratio Write
+8
+3
54 60 65 70 76
+6
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Variable Ratio Write
+8
+3
54 60 65 70 76
+6
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Ratio Put Write
+13+12
-12 37 49 50 63
Don’t do - because
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Ratio SpreadLong call @ s1 s1 < s2Short X calls @ s2
Example 2:1Price = 44Apr40C = 5 buy 1Apr45C = 3 sell 2
BE = 51MP = 6
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Ratio Spread
+ 3
-2
-5 40 42 45
Step 1
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Ratio Spread
+ 3
-2
-5 40 42 45 48 51
Step 2
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Ratio Spread
+ 3
-2
40 42 45 48 51
Step 2
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Ratio Spread
+ 3
-2
+6
40 42 45 48 51
+1
Step 2
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Ratio spread3:1 exampleincrease profitlower BE 2:1
+ 6+9
40 45 51
+1
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Ratio spread3:1 exampleincrease profitlower BE
+ 6+9
40 45 49.5
+4
3:1
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Naked Straddle WriteShort PutShort Call
ExamplePrice = 45Jan45C = 4Jan45P =3
+7
+4+3
38 45 52 55
-3
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Naked Straddle WriteSame Example - But, sell 4 of eachPrice = 45Jan45C = 4Jan45P =3
+28
-12 38 45 52 55
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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
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Covered Straddle Write
+8
+5+4
46 50 51
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Covered Straddle vs Covered call
+8
+4
46 50 51
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Combination Writeor Strangle WriteShort 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
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Combination Writeor Strangle Write
+7
+3
53 60 65 70 77
+4
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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
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Strangle Straddle Conversion
+7
53 60 70 77
-1
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Strangle Straddle Conversion
+7
53 60 70 77
-1+4
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Strangle Straddle Conversion
+7
53 60 70 77 80
-1+4
+10
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Splitting The Strikes& Synthetic StocksShort out of money putLong out of money call
example (Bullish Strike Split)price = 53Jan50P = 2Jan60C = 1
BE = 48
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Bullish Strike Split
+2
50 60
-1+1
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Bearish Strike Split
+2
50 60
-1+1
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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
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Bull Calendar Spread
+2
X 50 Y
-3
+5
-8
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Bull Calendar Spread
+2
X 50 Y
-3
+5
-8
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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
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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
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Reverse SpreadOpposite of all other common positions
Example (Reverse ratio - backspread) 2:1Short call @ s1 s1<s2Long x calls @ s2
Price = 43July40C = 4July45C = 1
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Step 1
+ 3
-2
+4
40 43 45 48
-1
Reverse Ratio Backspread
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Reverse Ratio Backspread
+ 3
-2
+2
40 43 45 48
-1
-3
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Reverse Butterfly
+12+7
-12 50 53 60 67 70
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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
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Diagonal Spreadvs Normal Bull Spread
+ 3
-2
30 32 35
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Diagonal Spreadvs Normal Bull Spread
+ 3
-2
30 32 35