adv. fine. man. put options

adv. fine. man. put options - W5 15“\Mwé’(axhq Venkat...

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Unformatted text preview: W5 15“ \Mwé’ \(axhq Venkat Subramaniam Lecture Notes Put Options and Portfolio Insurance - Buy Stock and Buy 3 Put Option with exercise mice of $70 - Irrespective of the current stock price this portfolio is at least worth $70 Stock + Put M ‘i’ 85 ago “A 90%“ o {DSMTCMNCQ CDD’K‘CLCJr DDWfiWSM 63 “VS Q)? “U $413 ‘h how? who?! 060w (\rxms’r MK (1 goAA oQ’WJH (games o\% gbmv a) L Chapter 22, Part A — Page 11 g :5; 3 SL9 O O 1?) ’1: 55 55 1E '20 {I 70 70 O “I O ’13 75 ~ 0 "75 \DO 100 / O /OO 40m N (SLSSL/K‘V‘idK b4: (1* 01064? $10 g) do; RM mag/a3 ( W \Mps'icfihl @Wfi on) (g {Ckph Oh WIFE?“ $1C§LQ> \ . ”MTNWWEWW 3% s F“: b E; 9 PC 5,. g ”C 5% 35, I 3 To ‘5 O 55 O WK“ 7 55 is 0 W99 (‘83;739 O 0”ng (95 (95 5 N 6sz0? 70 l $9 0 WW 70 {N 70 "{D O O 5‘31; {3 UJ‘N “\3 7% “O O 33 agémt \J» D f my, 60— 23; %s — O M g (83 is”? O\O OH? «O 5&303" 100 {(30 Fwo “(5 83 :figww zoo LOO '0 «H5 C35 \ Oi/Qk/M 63' Venkar Stfbramaniam, Lecture Notes 155% (3. OK “'4‘- An In-Class Exampie 95‘ (732) c. 5?“ Consider the following portfolio. You m a put option with an exercise price of ‘/ $40, and you have written a call option on he same stock with the same time to P fl C 82 expiration but with an exercise price of $50.6‘Thol, _ u 000“ W S‘fbflt} é -’ 1 Compute the payoff from the portfolio for different stock price ranges. (Consider stock prices in the ranges $0 to $40, $40 to $50, and $50 to $90). Draw the payoff diagram for the payoff on the expiration date on this portfolio. ”<57 . Solution \K r. ..= .7 . — a: Stock $ Put Payoff Payoff from writing ' Portfom Payoff {PLAT ”3°96 E = $40 CallwithE = $50 Wu 0030??) $0 $40 — $0 $40 $25 $15 ~ $0 $15 $35 $5 —— $0 $5 $40 $0 - $0 $5 $45 $0 - $0 $0 $50 $0 — $0 $0] $55 $0 — $5 —- $5 $60 $0 — $10 — $10 $65 $0 - $15 — $15 / $90 $0 — $40 _ $40 / :29 »< O . 5 29 Portfolio Payoff 0—) O ( Q ox Q< 40 0 O 0" O 50 (9‘ ’é 44 ‘5‘ 0 40 Stock Price $9 \ ' 0 Chapter 22, Part A —— Page 12 @293— E: O *r‘$”'+0 38 + 7. 4o “0" 4F). “of 4’7 —0’ Sb ~O’ 55 #0, [OO ”O” {05* M 100$ 13% M thb n) qovjbfi; .., S; 51(5) (wmswwrz ' ekSrc {Xerox}: 3 MW mu?)=~7 w (,0 O mitt , LUM- sf‘ @4— ( 0 lorctan O 0 PFC ,5 ”j - WED ”“0 ’1 N0 5) Drug O ofim bfi 0 lg OULJ‘T‘" '3“: O W EQS‘WCV‘ O ( u CQ-n wowa 636* ‘ S O D( [08%) F3) This {Jusen was (bom‘ SM 5 m puf op‘honj, (Wm PUfi-nqhe bDSEil Qaurhqheibgwgl amaniam, Lecture Notes No Arbitrafie Condition: Securities that offer Identical stream of cash flows will be priced the 6" 9 same in the financial markets. {30 fit}? (WAS)f :2 xvii—55%? - If a strategy is riskless then it :5“ offer only the riskless rate of return. / DVQ 0% «W‘ l 5 5'5 eiaear eeee= 5+P-‘Ca H E.g.: Buy the Stock (Current price = 44) \j Cutie _ $5 BuythePut (E=55) 9% ”2* CL : 33th Write the Call (E = 55) T /" it: Wat" W 7 u - 58 ' not—m to‘ t e‘. 13- {made up Stock Price 09 #5) OM . \lr magnum: 34 \ICiiK/ii’x Ol’LQ \{em' 603m 5L4 1-2.! -o~' 55 indwdr - (1832/th Value of the Portfolio if ‘6"me £0 n‘ C Q 5 ; n Q U}; state Down State Ff— \BGOLV C VOUfl Ci 0 m 6 Stock Value = $58 $34 + Put Value = $0 + $21 - Call Value = $3 - $0 Net: E x $55 $55 A ho matte/r megs So your initial investment strategy was a riskless strategy! Hence, the return on that investment must only be the riskless rate. Initial Investment was: Price of Stock + Price of Put - Price of Call So, (S + P - C) (1+rf) = E or S + P — C m E/(l+rf) .. . L~m4 This 18 the Put—Call Parity. or \C e, +OC\O\.S-4i O :1. m S i— P— C E (WlU‘flO’r Ch (in 9 ”(3 :9 73w matter Mow mange} m , E L Chapter 22, Part A — Page 13 E M Hi? 3+?—C: UH?) LTCM ’_______.__ MAOJQ. hmd “ 5 “name (No 93350” ,H won Nobe\ \Dfiabt W263 5’ - 0.53 W i ./ 8*?” b 0-9 W CT E LT ”21%) yew-rm ’k 0“ v mm ‘M K W Venkat Sttbmmanfam, Lecture Notes Put Call Parity Example — 2 (data from around August 22nd) The case of Goldman Sachs September Options With E = $80. W The current market price of the underlying stock S = $79. The exercise price on the options E = $80. m \&’r 3;) The time to expiration t a September = 4/52 years C 7’ ‘ 35 Put option price P = $3.20. The annual risk—free rate rF =2 1.5%. Call Option Price C m ? Using put-call parity: 3 + r = E/(i + rF)‘+ c 79 + 3.20 m 80/(1.015)‘”52 + (3 => C = 82.20—79.91 = $2.29 Call is overvalued! Using put—call parity the price of the call option is $2.29. Since the call option price in the market is $2.35 which is more than the price determined through put—call parity, the call option is overvalued in the market. Chapter 22, PartA — Page 15 Venice! Subramaniam, Lecture Notes g. 2 Put Call Parity Example — 1 (data from around August 22nd) The ease of IBM October Options with E = $80. WSJL The current market price of the underlying stock S = $86.20. The exercise price on the options E = $80. The t' to ex ' at‘o t = October = 8:52 ears ;: . line plr 1n y (3 QH'O sum/VS OR Call option price C = $8.70. %0 0,03“ ‘c; K \’\ The annual risk-free rate IF = 1.5%. 9 C 1-;— CK\ 03? S + Pd C H— r) l: Put Option Price P = ? Mfiau‘rfl ow: a shank! Wm. m Using put—call parity: 3 +PL=E/(1+rF) + C \ tit—5 we —> 86.20+P = 30/(1.015)3’52+8.70 (at 3 h find Pm pm Ce) :> P : 79.82+8.70—86.20 = $2.32 Put is overvalued! Using put-call parity the price of the put option is $2.32. Since the put option price in the market is $2.40 which ‘ more than the price determined through put-call parity, the put option is‘n the market. $0 , 08 Chapter 22, PartA — Page 14 -Ccu\s , 906:5 how WW8 "V‘COKM "W bug] wr‘vre ,gggLJQKLQe/rcmc (0C mm) 9693 09‘? w'0%m\qn5 rcombo CSACKA‘CQm 'MCM} Lhflfl» defermim 0mm #5 wow ’Okrvp“3_i%[email protected] h) Hod whoa» M (”Km 9’? WWW/Comm S‘I/Loutcfiba (3: 3%:‘10 watt/,— how) (om @ (ER: SC \qujAU LM—m—w WM“ Ll,» 1 can opfl on “x ...
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  • Spring '14
  • VenkatSubramaniam

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