Binomial Pricing Model Binomial Pricing Outcome Trees Example

Binomial Pricing Model

Binomial Pricing Outcome Trees Example - one month option Price = $20 Possible outcomes = 22 or 18 21 call = ? Monthly risk free rate = 1% Intrinsic Value @ 22 = 1 Intrinsic Value @ 18 = 0

Binomial Pricing T 0 T 1 Value Pa=22 22 x -1 Pb=18 18 x P=20 22 x - 1 = 18 x x=. 25 at. 25 shares A=B X Shares

Binomial Pricing at. 25 shares A=B T 1 Value = 22(. 25) - 1 = 4. 5 T 0 Value = 20 (. 25) - Call = 5 - Call (T 0 Value) (1+ r) = 4. 5 (5 -call) (1. 01) = 4. 5 call =. 5446

Binomial Pricing Probability Up = a= er. D t d (a - d) (u - d) . 5 -s [D t] =e Prob Down = 1 - p u =es [D Dt = time intervals as % of year t]. 5

Binomial Pricing Example Price = 36 s =. 40 t = 90/365 D t = 30/365 Strike = 40 r = 10% a = 1. 0083 u = 1. 1215 d =. 8917 Pu =. 5075 Pd =. 4925

Binomial Pricing 40. 37 36 32. 10

Binomial Pricing 45. 28 50. 78 = price 36 40. 37 36 32. 10 28. 62 25. 52

Binomial Pricing 45. 28 50. 78 = price 10. 78 = intrinsic value 40. 37 36 32. 10 28. 62 0 25. 52 0

Binomial Pricing 45. 28 50. 78 = price 5. 60 10. 78 = intrinsic value 40. 37 36 36 . 37 32. 10 28. 62 0 25. 52 0

Binomial Pricing 45. 28 50. 78 = price 5. 60 10. 78 = intrinsic value 40. 37 2. 91 36 . 37 . 19 36 1. 51 32. 10 28. 62 0 0 25. 52 0

Project • • • Select a Call option (w/ high vol & expires next month) Use spreadsheet to calc BS value for this Friday Calc volatility (include div if necessary) Calc Expected Return Probability Intervals Use spreadsheet to calc Binomial value. Use weekly intervals. Chart Black Scholes position Create a cross section price chart (showing time value decay) - Calculate option price at various stock prices for 0, 30, 60, 90 days. Print and hand in the Bloomberg profile of the option Include 1 page executive summary. Explain difference between market implied volatility and your calculated volatility.

Option Strategies Bullish Strategies Call purchase Synthetic long stock Bull spread Protective Put Bullish calendar spread Covered call Naked put write Risk limited unlimited Reward unlimited limited

Option Strategies Bearish Strategies Put purchase Synthetic Put Synthetic short sale Bear spread Covered put write Bearish calendar spread Naked call write Risk limited unlimited Reward unlimited limited unlimited

Covered Call Long Stock, Short Call

Covered Call Long Stock, Short Call Profit = S + call - P BE = P - call

Protective Put Long Stock, Long Put

Protective Put Long Stock, Long Put Profit = P - put - S

Syhthetic Long Put Short Stock, Long Call

Synthetic Short Call Short Stock, Short Put

Synthetic Stock Short Put, Long Call

Bull Spread Long Call @ s 1 Short Call @ s 2 s 1 < s 2 Max Profit = s 2 - s 1 - c 1 + c 2 Break Even = s 2 - MP = s 1 - c 2 + c 1

Bull Spread Example Price = 32 Oct 30 C = 3 Oct 35 C = 1 t=60 days/365 v =. 24 Buy Oct 30 C = -3 Sell Oct 35 C = +1 Max Profit = 35 -30 -3+1 = 3 BE = 30 -1+3 = 32 Net Debit = -3 + 1 = -2

Bull Spread

Bull Spread Compute probability of bull spread Example Vt =. 24 (60/365). 5 =. 097

Bull Spread Compute probability of bull spread Example Vt =. 24 (60/365). 5 =. 097 Prob (<32) = N[ln(32/32) /. 097] =. 5000

Bull Spread Compute probability of bull spread Example Vt =. 24 (60/365). 5 =. 097 Prob (<32) = N[ln(32/32) /. 097] =. 5000 Prob (>32) = 1 -. 500 =. 5000

Bull Spread Compute probability of bull spread Example Vt =. 24 (60/365). 5 =. 097 Prob (<32) = N[ln(32/32) /. 097] =. 5000 Prob (>32) = 1 -. 500 =. 5000 Max Profit = $300 Max Loss = -$200

Bull Spread Compute probability of bull spread Example Vt =. 24 (60/365). 5 =. 097 Prob (<32) = N[ln(32/32) /. 097] =. 5000 Prob (>32) = 1 -. 500 =. 5000 Max Profit = $300 Max Loss = -$200 • at 50% odds, makes good sense

Bull Spread

Aggressive Bull Spread s 1 < P << s 2 Good probablility, good profit potential

Extremely Aggr. Bull Spread P < s 1 < s 2 Small Cost, high profit, low prob

Least Aggr. Bull Spread S 1 < s 2 < P Low profit, high prob

Put Bull Spread Long Put @ s 1 Short put @ s 2 s 1 < s 2 example (Credit Spread) Price = 55 Jan 50 P = 2 Jan 60 P = 7 Net Credit = p 2 - p 1 = + 7 - 2 = + 5 Break Even = S 2 - credit = 60 - 5 = 55

Put Bull Spread

Call Bear Spread Short Call @ s 1 Long Call @ s 2 s 1 < s 2 credit spread

Call Bear Spread Short Call @ s 1 Long Call @ s 2 s 1 < s 2 credit spread Example P = 55 Jan 60 C = 2 Jan 50 C = 7 Net Credit = 7 - 2 = 5 BE = 50 + 5 = 55

Put Bear Spread Long Put @ s 1 Short Put @ s 2 s 1 > s 2 debit spread

Put Bear Spread Long Put @ s 1 Short Put @ s 2 s 1 > s 2 debit spread Example P = 55 Jan 50 P = 2 Jan 60 P = 7 Net Debit = 7 - 2 = 5 BE = 60 - 5 = 55

Call Bear vs. Put Bear +Credit spread - assignment risk ? What causes assignment -Large Credit = P well above lower strike

Call Bear vs. Put Bear +Credit spread - assignment risk ? What causes assignment -Large Credit = P well above lower strike Example: p = 59, Jan 60 C=1, Jan 50 C=9

Bull Spread - Roll Down Long Stock, Long Call, Short 2 Calls Example Own stock @ $48 Price = 42 Oct 40 Call = 4 (buy) Oct 45 Call = 2 (sell 2) Net Credit = 0 BE = 44

Bull Spread - Roll Down

Bull Spread - Roll Down Price 35 38 40 42 44 45 48 50 P/LSt -1300 -1000 -800 -600 -400 -300 0 +200 P/L Sh C +400 +400 -200 -600 P/L Lg C -400 -200 0 +100 +400 +600 Net P/L -1300 -1000 -800 -400 0 +200

Synthetic Covered Call Bull 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. Example Price = 49 Sell Apr 50 C = 3 Buy Apr 35 C = 14

Synthetic Covered Call Bull spread

Butterfly Spread • A nuetral position that combines both a bear spread and a bull spread Long call @ s 1 < s 2 < s 3 Short 2 calls @ s 2 Long call @ s 3 Example Price = 60 buy July 50 C = 12 short 2 July 60 C = 6 buy July 70 C = 3 1200 debit 1200 credit 300 debit 300 Net Debit

Butterfly Spread

Put Butterfly Spread Multiple ways to create the butterfly spread example Strike Call Put 50 12 1 60 6 5 70 2 11 Butterfly Positions Buy 50 C / sell 2 60 C / buy 70 C Buy 50 C/sell 60 C/buy 70 P/sell 60 P Buy 50 P/sell 60 P/Buy 70 C/sell 60 C Buy 50 P / sell 2 60 P / buy 70 P Net Position 2 debit 12 debit 8 credit 2 debit

Ratio Call Write Long stock, short multiple calls example 2: 1 ratio call write Price = 49 Oct 50 C = 6 sell 2 calls and long 100 stock

Ratio Call Write

Ratio Call Roll Down example 2: 1 ratio call write Price = 49 Oct 50 C = 6 sell 2 calls and long 100 stock Price drops to 40 Oct 50 C = 1 Oct 40 C = 4 Buy 2 Oct 50 C = profit = 12 - 2 = 10 Sell 2 Oct 40 C apply to stock price & pretend we onw stock at $39

Ratio Call Roll Down

Variable Ratios Max Profit = m(S-P) + n. C Upside BE = S + MP/(n-m) Downside BE = S - MP / m m = # stock lots n = # of Call ks Example Max Profit = 1 (50 -49) + 2 (6) = 13 Upside BE = 50 + 13/ (2 -1) = 63 Downside BE = 50 - 13/1 = 37

Ratio Call Write Example 3: 1 Buy 1 lot stock @ 49 sell 3 oct 50 c@18 Max Profit = 1 (50 -49) + 3 (6) = 19 Upside BE = 50 + 19/ (3 -1) = 59. 5 Downside BE = 50 - 19/1 = 31

Variable Ratio Write Long stock, short in money call (s 1), short out of money call (s 2) Max Profit = c 1 + c 2 + s 1 - P Downside BE = s 1 - MP Upside BE = s 2 + MP Example Price = 65 Oct 60 C = 8 Oct 70 C = 3 s 1 < P < s 2

Variable Ratio Write

Ratio Put Write Don’t do - because

Ratio Spread Long call @ s 1 Short X calls @ s 2 Example 2: 1 Price = 44 Apr 40 C = 5 buy 1 Apr 45 C = 3 sell 2 BE = 51 MP = 6 s 1 < s 2

Ratio Spread Step 1

Ratio Spread Step 2

Ratio spread 3: 1 example increase profit lower BE 2: 1

Ratio spread 3: 1 example increase profit lower BE 3: 1

Naked Straddle Write Short Put Short Call Example Price = 45 Jan 45 C = 4 Jan 45 P =3

Naked Straddle Write Same Example - But, sell 4 of each Price = 45 Jan 45 C = 4 Jan 45 P =3

Covered Straddle Write Long Stock Short Call Short Put example Price = 51 Jan 50 C = 5 Jan 50 P = 4 buy 100 shares sell 1 call sell 1 put Max Profit = Premium + S - P = 9 + 50 - 51 = 8 BE = (P+S-Prem)/2 = 46

Covered Straddle Write

Covered Straddle vs Covered call

Combination Write or Strangle Write Short put (out of money) Short call (out of money) example price = 65 Jan 70 C = 4 Jan 60 P = 3 Downside BE = Sp - put - call = 60 -3 -4 = 53 Upside BE = Sc + put + call = 70+3+4 = 77 Max Profit = put + call = 3+4 = 7

Combination Write or Strangle Write

Strangle Straddle Conversion same example price = 65 (price rises to 70) Jan 70 C = 4 Jan 60 P = 3 Put falls to 1 Jan 70 P = 4 action: buy back the 60 put & sell the 70 put

Strangle Straddle Conversion

Splitting The Strikes & Synthetic Stocks Short out of money put Long out of money call example (Bullish Strike Split) price = 53 Jan 50 P = 2 Jan 60 C = 1 BE = 48

Bullish Strike Split

Bearish Strike Split

Calendar Spread Short near term option Long distant term option example (Bull Calendar Spread) Price = 50 Today Apr 50 C = 5 short = +5 (Jan) July 50 C = 8 long = -8 Net Debit = -3 Price = 50 April Apr 50 C = 0 July 50 C = 5

Bull Calendar Spread

Bull Calendar Spread April Profit/Loss Table Price 40 45 48 50 52 55 60 Apr 50 C/PL 0/+500 2/+300 5/0 10/-500 July 50 C/PL. 5/-750 2. 5/-550 4/-400 5/-300 6/-200 8/0 10. 5/+250 Net Profit -250 -50 +100 +200 +100 0 +250

Put Calendar Spread (Bearish) Same as call short near term & long distant term ex - price = 50, Jan 50 P = 2, Apr 50 P = 3

Reverse Spread Opposite of all other common positions Example (Reverse ratio - backspread) 2: 1 Short call @ s 1<s 2 Long x calls @ s 2 Price = 43 July 40 C = 4 July 45 C = 1

Reverse Ratio Backspread Step 1

Reverse Ratio Backspread

Reverse Butterfly

Diagonal Spread diff strikes & diff exp example (Diagonal Bull Spread) Price = 32 Apr 30 C = 3 Apr 35 C = 1 July 30 C = 4 Long July 30 C July 35 C = 1. 5 Short Apr 35 C Normal Bull Spread - Long Apr 30 C Short Apr 35 C

Diagonal Spread vs Normal Bull Spread