Lecture 8: Quanttatve Opton trateges Marco Avellaneda G63.936.001 prng emester 009
Equty Optons Markets ngle-name optons Electronc tradng n 6 exchanges, cross-lstng of many stocks, penny-wde bd ask spreads for many contracts Index Optons &P 500, NDX, Mns. Traded on the hcago Mercantle Exchange. VIX optons & futures trade n ME as well. ETF Optons Most of the large ETFs are optonable. Traded lke stocks n multple exchanges. PY, QQQQ, XLF are among the most traded optons n the U.
Optons Markets Hallburton (HAL) Aprl 09 ALL PUT ymbol Last hange Bd Ask Volume Open Int trke ymbol Last hange Bd Ask Volume Open Int HALDA.X 1.65 0 11.15 11.3 0 0 5 HALPA.X 0.03 0 N/A 0.04 100 10 HALDU.X 8.5 0 8.65 8.85 7.5 HALPU.X 0.05 0 0.01 0.06 1,37 HALDB.X 5. 0 6.3 6.35 57 116 10 HALPB.X 0.15 0 0.1 0.1 5 3,775 HALDZ.X 4. 0.15 4.05 4.15 0 944 1.5 HALPZ.X 0.4 0.1 0.39 0.4 185 10,48 HALD.X.31 0.1.3.33 0 4,94 15 HALP.X 1.06 0.33 1.09 1.11 5 10,59 HALDP.X 1.11 0.18 1.09 1.11 495 8,044 17.5 HALPP.X.4 0.34.36.37 196 8,48 HALDD.X 0.43 0.05 0.4 0.44 57 10,693 0 HALPD.X 4.59 0 4.15 4.5 50 1,440 HALDQ.X 0.15 0.0 0.14 0.16 3 7,646.5 HALPQ.X 7.5 0 6.4 6.45 5,770 HALDE.X 0.05 0.01 0.05 0.06 13 4,060 5 HALPE.X 9.95 0 8.8 8.85 4 1,111 HALDR.X 0.03 0 0.01 0.03 8 5,784 7.5 HALPR.X 1.35 0 11.5 11.35 18 977 HALDF.X 0.01 0 N/A 0.0 0 8,399 30 HALPF.X 14.8 0 13.7 13.9 18 5,77 HALD.X 0.04 0 N/A 0.04 1 1,698 3.5 HALP.X 15.5 0 16. 16.4 0 150 HALDG.X 0.08 0 N/A 0.04 1,470 35 HALPG.X 18.93 0 18.7 18.9 5 514 HALDT.X 0.0 0 N/A 0.04 9 604 37.5 HALPT.X 0.59 0 1. 1.35 40 151 HALDH.X 0.0 0 N/A 0.03 10 1,593 40 HALPH.X 0.6 0 3.7 3.85 10 139 HALDV.X 0.0 0 N/A 0.0 4,805 4.5 HALPV.X 6.1 0 6. 6.4 75 311 HALDI.X 0.0 0 N/A 0.0 1 63 45 HALPI.X 8.6 0 8.7 9 15 0 HALDW.X 0.0 0 N/A 0.0 1 45 47.5 HALPW.X 31.1 0 31. 31.4 5 13 HALDJ.X 0.0 0 N/A 0.0 7 733 50 HALPJ.X 4.55 0 33.7 33.9 0 0 HALDX.X 0.04 0 N/A 0.0 10 34 5.5 HALPX.X 14.8 0 36. 36.4 0 0 HALDK.X 0.0 0 N/A 0.0 10 376 55 HALPK.X 19.1 0 38.7 39 0 HAL $16.36 Avalable expratons: Mar09, Apr09, Jul09, Oct09, Jan10, Jan11 front months, LEAP, quarterly cycle (Jan cycle for HAL).
Put-all Party P e dt Ke rt Put-call party holds for Amercan optons whch are ATM, to wthn reasonable approxmaton. ALL PUT (-P+K*(1-r*40/5))/ d_mp HALD.X.3.33 15 H ALP.X 1.09 1.11 0.988473167 7.6% HALDP.X 1.09 1.11 17.5 H ALPP.X.36.37 0.989451906 6.65% Hal pays dvdend of 9 cents at the end of Feb, May, Aug, Nov There are no ex-dvdend dates between now and Aprl 0, 009. Opton markets gve an mpled cost of carry for the stock (mpled forward prce), whch may be dfferent from the nomnal cost of carry. Ths s due to stock-loan consderatons.
DIA Optons Apr 18, 009 ymbol Last hange Bd Ask Volume OpenInt TRIKE ymbol Last hange Bd Ask Volume Open Int DIHDX.X N/A 0 18.1 18. 0 0 50 DIHPX.X 0.37 0 0.15 0.19 18 45 DIHDY.X 1 0 17.3 17.4 51 DIHPY.X 0.39 0 0.17 0. 105 370 DIHDZ.X 16.3 0 16.3 16.4 1 93 5 DIHPZ.X 0.6 0. 0.3 0.6 7 5 DIHDA.X N/A 0 15. 45 15. 55 0 0 53 DIHPA.X 0.3 0.6 0.8 0.31 5 68 DIHDB.X N/A 0 14. 5 14. 35 0 0 54 DIHPB.X 0.4 0.4 0.34 0.37 4 39 DIHD. X 11.94 0 13. 45 13. 55 4 14 55 DIHP.X 0.4 0.38 0.41 0.44 5 765 DIHDD. X 1.35 0. 17 1. 55 1. 65 40 56 DIHPD.X 0.51 0.46 0.49 0.5 0 870 DIHDE.X 10.3 0. 47 11.6 11. 75 10 48 57 DIHPE.X 0.61 0.53 0.59 0.6 7 414 DIHDF.X 8.6 0 10. 75 10. 85 0 58 DIHPF.X 0.73 0.53 0.71 0.73 3 689 DIHDG.X 8.4 0 9. 85 9. 95 33 11 59 DIHPG.X 0.86 0.54 0.83 0.87 18 658 DIHDH. X 8.4 1. 35 9 9.1 48 06 60 DIHPH.X 1 0.75 1 1.0 165 11, 734 DIJDI.X 7.7 1. 8. 15 8.3 1 16 61 DIJPI.X 1.1 0.75 1.17 1. 61 510 DIJDJ.X 7. 0.8 7.4 7. 45 34 8 6 DIJPJ.X 1.43 0.9 1.38 1.4 41 916 DIJDK.X 6.7 1. 65 6.6 6.7 137 8 63 DIJPK.X 1.65 0.94 1.61 1.63 108 1, 347 DIJDL.X 6 1.6 5.9 5. 95 60 444 64 DIJPL.X 1.93 1.03 1.89 1.91 305 1, 138 DIJDM.X 5.5 1. 41 5. 5. 5 10 85 65 DIJPM.X.7 1.18.19.1 583 1, 735 DIJDN.X 4.55 1. 3 4.5 4.6 69 1,14 66 DIJPN.X.64 1.1.5.56 13 1, 919 DIJDO.X 3.96 1. 5 3.9 4 134 945 67 DIJPO.X 3.05 1.4.91.95 450, 115 DIJDP.X 3.4 1. 08 3. 35 3.4 343 1,788 68 DIJPP.X 3.46 1.44 3.3 3.4 17, 505 DIJDQ.X.85 0. 91. 84. 87 168 1,709 69 DIJPQ.X 3.8 1.85 3.8 3.9 116 1, 688 DIJDR.X.41 0. 8. 37.4 399 9,896 70 DIJPR.X 4.54 1.61 4.35 4.4 144, 89 DIJD.X 1.9 0. 64 1. 94 1. 98 117 1,465 71 DIJP.X 5.14 1.86 4.9 5 51 3, 035 DIJDT.X 1.58 0. 58 1. 57 1.6 6 1,998 7 DIJPT.X 5.6. 5.55 5.65 7, 58 DIJDU.X 1.7 0.5 1. 5 1. 9 15 1,94 73 DIJPU.X 6.8.37 6. 6.35 1, 580 DIJDV.X 1 0.4 0. 99 1. 0 35 1,761 74 DIJPV.X 7.1.05 6.95 7.05 1, 53 DIJDW.X 0.78 0.3 0. 77 0. 79 18 3,41 75 DIJPW.X 7.8.8 7.75 7.85 9 1, 9 DIJDX.X 0.6 0. 16 0. 58 0. 61 6,65 76 DIJPX.X 10.3 0 8.55 8.65 9 1, 008 DIJDY.X 0.44 0. 14 0. 44 0. 47 7,055 77 DIJPY.X 9.5.36 9.4 9.5 5 943 DIJDZ.X 0.3 0. 05 0. 3 0. 35 81 1,800 78 DIJPZ.X 10.65 0.75 10.3 10.4 4 1, 90 DIJDA.X 0.6 0. 09 0. 4 0. 6 140 1,147 79 DIJPA.X 11.83 1.37 11. 11.3 3 1, 006 DIJDB.X 0.19 0. 08 0. 17 0. 48 8,568 80 DIJPB.X 13.57 1.9 1.15 1.5 3 1, 35 DIJD.X 0.11 0 0. 1 0. 15 9 3,494 81 DIJP.X 15.13 0 13.1 13. 6 5, 989 DAVDD.X 0.1 0 0. 09 0. 1 9,455 8 DAVPD.X 16.6 0 14.3 14.45 10 1, 184 DAVDE.X 0.07 0. 01 0. 06 0. 09 3 3,18 83 DAVPE.X 16.44 1. 15.3 15.4 1 1, 016 DAVDF.X 0.05 0 0. 05 0. 08 3 1,470 84 DAVPF.X 16.85 1.8 16.3 16.4 3 843 DAVDG.X 0.04 0 0. 03 0. 07 11 4,03 85 DAVPG.X 17. 1.55 17.3 17.4 30 496 DAVDH.X 0.0 0 0. 0 0. 06 3 841 86 DAVPH.X 17.7 0 18.5 18.4 1 91 DAVDI.X 0.04 0 N/A 0. 05 10 617 87 DAVPI.X 1.78 0 19.5 19.35 3 305 DAVDJ.X 0.04 0 N/A 0. 05 8 748 88 DAVPJ.X 19.5 0 0.5 0.35 10 14 DAVDK.X 0.04 0. 01 N/A 0. 04 30 450 89 DAVPK.X 15.9 0 1.5 1.35 15 56 DAVDL. X 0.04 0 N/A 0. 04 30 97 90 DAVPL.X 16.95 0..35 5 58 DAVDM.X 0.03 0 N/A 0. 04 4 787 91 DAVPM. X 17.5 0 3. 3.35 78
Impled Dvdend Yeld for DIA Aprl 18, 009 Optons ALL PUT (-P+K*(1-r*40/5))/ d_mp DIJDP.X 3.35 3.4 68 DIJPP.X 3.3 3.4 0.99567636.98% DIJDQ.X.84.87 69 DIJPQ.X 3.8 3.9 0.9949519 3.18% Dvdend Yeld from Yahoo.com 3.30% Actual payments are approx 15 cents / month ~ $1.80 ~.60% tep1 n understandng optons markets: fnd the mpled dvdend from the market. If the mpled dvdend s dfferent from the nomnal dvdend then -- check for HTB f d mp > d nom -- check for dvdend reductons f d mp < d nom
alculaton of d_{nom}, d_{mp} d nom T ln n 1 1 D e rt Dvdend payment dates d mp 1 atm Patm + ln T K atm e rt
Impled Volatlty HAL Aprl 09 ALL PUT ymbol Last B d Ask IVOL Delta trke ymbol Last Bd Ask IVOL Del ta HALDU.X 8.5 8.65 8.85 na 1.00 7.5 HALPU.X 0.05 0.01 0.06 11 0.00 HALDB.X 5. 6.3 6.35 141 0.99 10 HALPB.X 0.15 0.1 0.1 144-0.01 HALDZ.X 4. 4.05 4.15 108 0.94 1.5 HALPZ.X 0.4 0.39 0.4 109-0.05 HALD.X.31.3.33 9.4 0.76 15 HALP.X 1.06 1.09 1.11 93-0.4 HALDP.X 1.11 1.09 1.11 85.1 0.36 17.5 HALPP.X.4.36.37 85-0.63 HALDD.X 0.43 0.4 0.44 8.4 0.09 0 HALPD.X 4.59 4.15 4.5 84-0.90 HALDQ.X 0.15 0.14 0.16 89.3 0.0.5 HALPQ.X 7.5 6.4 6.45 90-0.97 50 Impled Volatlty 00 150 100 50 ALL PUT 0 7.5 10 1.5 15 17.5 0.5 trke
DIA Volatlty urface, March 10 009, 1:00 noon DIA, Mar09 DIA, Jun 30, 09 50 39 48 46 44 4 40 38 36 34 3 38 37 36 35 34 33 3 31 call put call put 30 30 64 65 66 67 68 69 70 71 7 73 64 65 66 67 68 69 70 71 7 73 DIA, Apr09 DIA, ep 30, 09 4 37 40 36 38 36 34 35 34 33 3 call put call put 3 31 30 64 65 66 67 68 69 70 71 7 73 30 64 65 66 67 68 69 70 71 7 73 These curves move and provde tradng opportuntes.
Many dfferent trades possble -- arry trades usng optons (mpled dvdend vs. actual dvdend, HTB) -- Volatlty surface trades (non-drectonal): tradng dfferent strkes on the same underlyng asset -- hstorcal vol vs mpled vol -- Relatve-value trades across names (non-drectonal) -- sngle-name opton versus far-value -- dsperson tradng (ndex opton versus components) -- Drectonal volatlty trades (long vol/ short vol, etc)
kewness -- For equtes, the mpled volatlty curve s decreasng n the strke prce around ATM -- The effect s more pronounced for ndces and etfs than for sngle names
Mechancs of opton tradng -- Open poston (long or short) and trade the stock so as to be delta-neutral. -- Adjust the Delta of the opton as the stock/opton prces move ( ) + + + + + + + + + + + dt d d dt r d r t dt d r dt d d d rdt ddt rdt d d L P d d d dt t d ) ( &... 1
Book-keepng: proft/loss from a delta-hedged opton poston P/L θ ( n 1) + V d or P/L 1 Γ ( di ) I dt + V d
1-day P/L for Long all/hort tock (onstant volatlty16%) 50 40 30 0 10 0 950 975 1000 105 1050 1075 1100 115 1150 1175 100 15 150 175-10 P/L θ ( n 1) θ daly tme - decay, n percent ndex change expected daly volatlty
Assumng an mpled volatlty drop of 1% Vol15% 50 40 30 0 10 0 950 975 1000 105 1050 1075 1100 115 1150 1175 100 15 150 175-10 3.80 loss f stock does not move and volatlty drops 1%
A closer look at the proft-loss due to a change n volatlty 6 5 4 3 1 0-1 1075 1100 115 1150 1175 - -3-4 -5 1% move n vol > 8% move n premum for a 6m ATM opton
Measurng the Rsk of a Portfolo (assumng delta neutralty) Portfolo of optons on N stocks n j contracts of opton wth underlyng stock, expraton T j, volatlty j Π j j n n j j ( +, T, K, + ) (, T, K, ) ( ( ) ( ) j + + (1 R, Tj, Kj, j 1 R, Tj, Kj, j R j j j j j j j j j Need to defne a jont dstrbuton of stock returns and volatlty returns to calculate statstcs of PNL
Factor Model onsder only parallel vol shfts and use 30-day ATM volatltes k m k k k m k k F R F R ς γ ε β + + 1 1 N N j j j R R R E R R D R R j j j ',, M E D D M Extract factors from PA of augmented matrx
Alternatve Approach usng ETFs d d d ETF ( ) β + γ + ς, ETF ( ) ETF( ) ETF assocated wth stock Model the ATM volatlty returns as a functon of the stock return and changes n the volatlty of the sector. onjecture: there are fewer systematc factors that explan volatlty returns than n the case of stock returns. (m<0) Possble project: do the PA on the Nasdaq 100 optonable stocks analyzng the matrx M for ths case.
Modelng the Volatlty kew x ln( K / ) mp ( x, t) mp (0, t) ( 1+ γx + δx +...) Proposton: Under reasonable assumptons on prce process (stoch. vol), If d atm atm d β + ε Then γ β
Evoluton of the slope of the 30-day mpled volatlty curve, 1996-004 Avellaneda & Lee, 005
Evoluton of rato [slope/leverage coeffcent] The ``roarng 90 s! Far value lne (V) γ β / Avellaneda & Lee, 005