Mercados de futros y opciones

OCTAVA EDICIÓN INTRODUCCIÓN A LOS MERCADOS DE FUTUROS Y OPCIONES John Hull 8QLYHUVLGDGGH7RURQWR 75$'8&&,Ï1 Jaime Gómez-Mont Araiza 7UDGXFWRUSURIHVLRQDO (VSHFLDOLVWDHQWHPDVGHDGPLQLVWUDFLyQ\¿QDQ]DV 5(9,6,Ï17e&1,&$ Arturo Morales Castro 8QLYHUVLGDG1DFLRQDO$XWyQRPDGH0p[LFR José Antonio Morales Castro ,QVWLWXWR3ROLWpFQLFR1DFLRQDO0p[LFR -RKQ+XOO Introducción a los mercados de futuros y opciones. 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GHUHXQERQRGHOJRELHUQRDFLQFRDxRVTXHRIUHFHXQFXSyQGH(OSUHFLRGHHVWHERQRQRGHWHUPLQD SRUVtPLVPRODWDVDFHURGHO7HVRURDFLQFRDxRVSRUTXHXQDSDUWHGHOUHQGLPLHQWRVREUHHOERQRVH REWLHQHHQODIRUPDGHFXSRQHVDQWHVGHO¿QDOGHODxR0iVDGHODQWHHQHVWHFDStWXORH[SRQGUHPRV FyPRSRGHPRVGHWHUPLQDUODVWDVDVFHURGHO7HVRURDSDUWLUGHORVSUHFLRVGHERQRVTXHWLHQHQFXSRQHV 4.4 VALUACIÓN DE BONOS /DPD\RUtDGHORVERQRVSDJDQFXSRQHVDVXWHQHGRUHQIRUPDSHULyGLFD(OFDSLWDORSULQFLSDOGHOERQR HOFXDOVHFRQRFHWDPELpQFRPRVXYDORUDODSDURYDORUQRPLQDO VHSDJDDO¿QDOGHVXYLGD(OSUHFLR WHyULFRGHXQERQRVHFDOFXODFRPRHOYDORUSUHVHQWHGHWRGRVORVÀXMRVGHHIHFWLYRTXHUHFLELUiHOGXHxR GHOERQR$OJXQDVYHFHVORVQHJRFLDQWHVGHERQRVXVDQODPLVPDWDVDGHGHVFXHQWRSDUDWRGRVORVÀXMRV GHHIHFWLYRSURYHQLHQWHVGHXQERQRSHURXQHQIRTXHPiVH[DFWRFRQVLVWHHQXVDUODWDVDFHURDGHFXDGD SDUDFDGDÀXMRGHHIHFWLYR 3DUDLOXVWUDUHVWRFRQVLGHUHODVLWXDFLyQHQTXHODVWDVDVFHURGHO7HVRURPHGLGDVFRQXQDFDSLWDOL]D FLyQFRQWLQXDVRQFRPRVHPXHVWUDHQODWDEOD 0iVDGHODQWHH[SOLFDUHPRVFyPRVHFDOFXODQGLFKDV WDVDV 6XSRQJDTXHXQERQRGHO7HVRURDGRVDxRVFRQXQFDSLWDOGHGDFXSRQHVDODWDVDGH SRUDxRHQIRUPDVHPHVWUDO3DUDFDOFXODUHOYDORUSUHVHQWHGHOSULPHUFXSyQGHORGHVFRQWDPRVDO GXUDQWH VHLV PHVHV SDUD FDOFXODU HO YDORU SUHVHQWH GHO VHJXQGR FXSyQ GH OR GHVFRQWDPRV DOGXUDQWHXQDxR\DVtVXFHVLYDPHQWH(OSUHFLRWHyULFRGHOERQRHVSRUORWDQWR R H231H231 H231H235 7DVDVGHLQWHUpV Tabla 4.2 7DVDVFHURGHO7HVRUR 9HQFLPLHQWR DxRV 7DVDFHUR FDSLWDOL]DFLyQFRQWLQXD Rendimiento de los bonos (OUHQGLPLHQWRGHXQERQRHVODWDVDGHGHVFXHQWRLQGLYLGXDOTXHFXDQGRVHDSOLFDDWRGRVORVÀXMRVGH HIHFWLYRLJXDODHOYDORUGHOERQRDVXSUHFLRGHPHUFDGR6XSRQJDTXHHOSUHFLRWHyULFRGHOERQRTXH KHPRVHVWDGRFRQVLGHUDQGRWDPELpQHVVXYDORUGHPHUFDGR HVGHFLUHOSUHFLRGHPHUFDGR GHOERQRHVWiHQFRQFRUGDQFLDH[DFWDFRQORVGDWRVGHODWDEOD 6L\HVHOUHQGLPLHQWRVREUHHOERQR H[SUHVDGRFRQXQDFDSLWDOL]DFLyQFRQWLQXDGHEHVHUYHUGDGTXH 3ey0:5 þ 3ey1:0 þ 3ey1:5 þ 103ey2:0 ¼ 98:39 (VWDHFXDFLyQVHUHVXHOYHXVDQGRXQSURFHGLPLHQWRLWHUDWLYR ³HQVD\R\HUURU´ SDUDORJUDUTXH\5 Rendimiento a la par (OUHQGLPLHQWRDODSDUSDUDXQFLHUWRYHQFLPLHQWRGHXQERQRHVODWDVDFXSyQTXHSURGXFHTXHHOSUH FLRGHOERQRVHDLJXDODVXYDORUDODSDU (OYDORUDODSDUHVHOPLVPRTXHHOYDORUGHOSULQFLSDO 3RU ORJHQHUDOVHVXSRQHTXHHOERQRGDFXSRQHVVHPHVWUDOHV6XSRQJDTXHHOFXSyQVREUHXQERQRDGRV DxRVGHQXHVWURHMHPSORHVGHFSRUDxR RGHFSRUVHLVPHVHV 8VDQGRODVWDVDVFHURGHODWDEOD HOYDORUGHOERQRHVLJXDODVXYDORUQRPLQDOGHFXDQGR c 0:050:5 c 0:0581:0 c 0:0641:5 c e þ e þ e þ 100 þ e0:0682:0 ¼ 100 2 2 2 2 (VWDHFXDFLyQVHUHVXHOYHGHXQDPDQHUDGLUHFWDSDUDGDUF5(OUHQGLPLHQWRDODSDUDGRVDxRV HVSRUORWDQWRGHDQXDO 'HXQDPDQHUDPiVJHQHUDOVLGHVHOYDORUSUHVHQWHGHDUHFLELUVHDOYHQFLPLHQWRGHOERQR$HVHO YDORUGHXQDDQXDOLGDGTXHSDJDXQGyODUHQFDGDIHFKDGHSDJRGHFXSRQHV\PHVHOQ~PHURGHSDJRV GHFXSyQSRUDxRHQWRQFHVHOUHQGLPLHQWRDODSDUFGHEHVDWLVIDFHU GHPRGRTXH c þ 100d m ð100 100dÞm c¼ A 100 ¼ A (QQXHVWURHMHPSOR m ¼ 2, d ¼ e0:0682 ¼ 0:87284, \ A ¼ e0:050:5 þ e0:0581:0 þ e0:0641:5 þ e0:0682:0 ¼ 3:70027 /DIyUPXODFRQ¿UPDTXHHOUHQGLPLHQWRDODSDUHVGHDQXDO(VWDHVODWDVDH[SUHVDGDFRQXQD FDSLWDOL]DFLyQVHPHVWUDOFRQXQDFDSLWDOL]DFLyQFRQWLQXDVHUtDGH 4.5 &$3Ë78/2 DETERMINACIÓN DE LAS TASAS CERO DEL TESORO 8QDIRUPDGHGHWHUPLQDUODVWDVDVFHURGHO7HVRURFRPRODVGHODWDEODFRQVLVWHHQREVHUYDUORV UHQGLPLHQWRVVREUHORVERQRV³HQIUDQMDV´(VWRVVRQERQRVFRQFXSRQHVFHURTXHORVQHJRFLDQWHVFUHDQ GHDOJXQDPDQHUDDUWL¿FLDOFXDQGRYHQGHQFXSRQHVVREUHXQERQRGHO7HVRURHQIRUPDVHSDUDGDGHO SULQFLSDO 2WUDIRUPDGHGHWHUPLQDUODVWDVDVFHURGHO7HVRURHVDSDUWLUGHODVOHWUDV\ORVERQRVTXHOOHYDQFXSR QHV(OHQIRTXHPiVFRP~QHVHOTXHVHFRQRFHFRPRPpWRGRGHUHPXHVWUHR ERRWVWUDS 3DUDLOXVWUDU ODQDWXUDOH]DGHHVWHPpWRGRFRQVLGHUHORVGDWRVGHODWDEODVREUHORVSUHFLRVGHFLQFRERQRV&RPR ORVSULPHURVWUHVERQRVQRSDJDQFXSRQHVODVWDVDVFHURFRUUHVSRQGLHQWHVDORVYHQFLPLHQWRVGHHVWRV WUHVERQRVVHFDOFXODQFRQIDFLOLGDG(OERQRDWUHVPHVHVWLHQHHOHIHFWRGHFRQYHUWLUXQDLQYHUVLyQGH DWUHVPHVHVGHVSXpV/DWDVD5DWUHVPHVHVFDSLWDOL]DEOHHQIRUPDFRQWLQXDVHREWLHQHSRUOR WDQWRPHGLDQWHODUHVROXFLyQGH 5H53 (VGHDQXDO'HPDQHUDVLPLODUODWDVDDVHLVPHVHVHVWiGDGDSRUODVROXFLyQGH 5H53 (VGHDQXDOFRQXQDFDSLWDOL]DFLyQFRQWLQXD(QIRUPDVLPLODUODWDVDDXQDxRFRQXQDFDSL WDOL]DFLyQFRQWLQXDHVWiGDGDSRUODVROXFLyQGH 5H53 (VGHDQXDO (OFXDUWRERQRGXUDDxRV/RVSDJRVVRQORVVLJXLHQWHV PHVHV DxR DxRV 3DUWLHQGRGHQXHVWURVFiOFXORVDQWHULRUHVVDEHPRVTXHODWDVDGHGHVFXHQWRSDUDHOSDJRDO¿QDOGHVHLV PHVHVHVGH\TXHODWDVDGHGHVFXHQWRSDUDHOSDJRDO¿QDOGHXQDxRHVGH7DPELpQ VDEHPRVTXHHOSUHFLRGHOERQRGHEHVHULJXDODOYDORUSUHVHQWHGHWRGRVORVSDJRVTXHUHFLEDHO WHQHGRUGHOERQR6XSRQJDTXHODWDVDFHURDDxRVVHGHQRWDFRQ5'HORDQWHULRUVHGHVSUHQGHTXH H231H231 H2535 Tabla 4.3 'DWRVSDUDHOPpWRGRGHUHPXHVWUHR 3ULQFLSDOGHO ERQR 3OD]RDOYHQFLPLHQWR DxRV &XSyQDQXDO 3UHFLRGHOERQR 6HVXSRQHTXHODPLWDGGHFXSyQGHFODUDGRVHSDJDFDGDVHLVPHVHV 7DVDVGHLQWHUpV Tabla 4.4 7DVDVFHURFRQFDSLWDOL]DFLyQFRQWLQXD\ GHWHUPLQDGDVDSDUWLUGHORVGDWRVGHODWDEOD 9HQFLPLHQWR DxRV 7DVDFHUR FDSLWDOL]DFLyQFRQWLQXD (VWRVHUHGXFHD e1:5R ¼ 0:85196 R R¼ lnð0:85196Þ ¼ 0:10681 1:5 /DWDVDFHURDDxRVHVSRUORWDQWRGH(VWDHVOD~QLFDWDVDFHURTXHHVFRQJUXHQWHFRQOD WDVDDVHLVPHVHVODWDVDDXQDxR\ORVGDWRVGHODWDEOD /DWDVDFHURDGRVDxRVVHFDOFXODHQIRUPDVLPLODUDODVWDVDVFHURDVHLVPHVHVDXQDxR\DDxRV MXQWRFRQODLQIRUPDFLyQVREUHHO~OWLPRERQRHQODWDEOD6L5HVODWDVDFHURDGRVDxRVHQWRQFHV H231H231H231H2535 Tasas de interés (% por año) (VWRQRVGD55R /DVWDVDVTXHKHPRVFDOFXODGRVHUHVXPHQHQODWDEOD8QDJUi¿FDTXHPXHVWUHODWDVDFHURFRPR XQDIXQFLyQGHOYHQFLPLHQWRVHFRQRFHFRPRFXUYDFHUR8QVXSXHVWRFRP~QHVTXHODFXUYDFHURHV OLQHDOHQWUHORVSXQWRVGHWHUPLQDGRVXVDQGRHOPpWRGRGHUHPXHVWUHR (VWRVLJQL¿FDTXHODWDVDFHURD DxRVHVGH3135HQQXHVWURHMHPSOR 7DPELpQVHVXSRQH SRUORJHQHUDOTXHODFXUYDFHURHVKRUL]RQWDODQWHVGHOSULPHUSXQWR\KRUL]RQWDOPiVDOOiGHO~OWLPR SXQWR/D¿JXUDPXHVWUDODFXUYDFHURSDUDQXHVWURVGDWRVXVDQGRHVWRVVXSXHVWRV0HGLDQWHHOXVR GHERQRVFRQXQFUHFLPLHQWRPiVSURORQJDGRODFXUYDFHURVHGHWHUPLQDUtDGHXQDPDQHUDPiVSUHFLVD PiVDOOiGHGRVDxRV 11 10 Vencimiento (años) 1 Figura 4.1 7DVDVFHURTXHSURGXFHHOPpWRGRGHUHPXHVWUHR 2 &$3Ë78/2 (QODSUiFWLFDSRUORJHQHUDOQRWHQHPRVERQRVFRQYHQFLPLHQWRVLJXDOHVDH[DFWDPHQWHDxRV DxRVDxRVHWFpWHUD(OHQIRTXHTXHXVDQFRQIUHFXHQFLDORVDQDOLVWDVFRQVLVWHHQKDFHUXQDLQWHU SRODFLyQHQWUHORVGDWRVGHORVSUHFLRVGHORVERQRVDQWHVGHXWLOL]DUORVSDUDFDOFXODUODFXUYDFHUR3RU HMHPSORVLORVDQDOLVWDVVDEHQTXHXQERQRDDxRVFRQXQFXSyQGHVHYHQGHHQ\TXHXQERQR DDxRVFRQXQFXSyQGHVHYHQGHHQSRGUtDQVXSRQHUTXHXQERQRDDxRVFRQXQFXSyQ GHVHYHQGHUtDHQ 4.6 TASAS A PLAZO /DVWDVDVGHLQWHUpVDSOD]RVRQDTXHOODVTXHHVWiQLPSOtFLWDVHQODVWDVDVFHURDFWXDOHVSDUDYDULRVSHULR GRVHQORIXWXUR3DUDLOXVWUDUFyPRVHFDOFXODQVXSRQHPRVTXHODVWDVDVFHUROLEUHVGHULHVJRVRQFRPR VHPXHVWUDHQODVHJXQGDFROXPQDGHODWDEOD6HVXSRQHTXHODVWDVDVVHFDSLWDOL]DQHQIRUPDFRQWL QXD'HHVWHPRGRODWDVDDQXDOGHSDUDXQDxRVLJQL¿FDTXHDFDPELRGHXQDLQYHUVLyQGHHO GtDGHKR\VHUHFLEHXQPRQWRGHH35HQXQDxRODWDVDGHSDUDGRVDxRVVLJQL¿FD TXHDFDPELRGHXQDLQYHUVLyQGHHOGtDGHKR\VHUHFLEHXQPRQWRGHH35HQ GRVDxRV\DVtVXFHVLYDPHQWH /DWDVDGHLQWHUpVDSOD]RHQODWDEODSDUDHODxRHVGHDQXDO(VWDHVODWDVDGHLQWHUpVTXHVH HQFXHQWUDLPSOtFLWDHQODVWDVDVFHURSDUDHOSHULRGRHQWUHHO¿QDOGHOSULPHUDxR\HO¿QDOGHOVHJXQGR DxR6HSXHGHFDOFXODUDSDUWLUGHODWDVDGHLQWHUpVFHURDXQDxRGHDQXDO\ODWDVDGHLQWHUpVFHURD GRVDxRVGHDQXDO(VODWDVDGHLQWHUpVSDUDHODxRTXHFXDQGRVHFRPELQDFRQXQDQXDOSDUD HODxRQRVGDHQWRWDOSDUDORVGRVDxRV3DUDGHPRVWUDUTXHODUHVSXHVWDFRUUHFWDHVGHDQXDO VXSRQJDTXHVHLQYLHUWHQ8QDWDVDGHSDUDHOSULPHUDxR\GHSDUDHOVHJXQGRDxRQRVGD H3H35 DO¿QDOGHOVHJXQGRDxR8QDWDVDGHDQXDOSDUDGRVDxRVQRVGD H3 ORFXDOHVWDPELpQ(VWHHMHPSORLOXVWUDHOUHVXOWDGRJHQHUDOGHTXHFXDQGRODVWDVDVGHLQWHUpV VHFDSLWDOL]DQHQIRUPDFRQWLQXD\ODVWDVDVGHSHULRGRVVXFHVLYRVVHFRPELQDQODWDVDJHQHUDOHTXLYD OHQWHHVVLPSOHPHQWHODWDVDSURPHGLRGXUDQWHODWRWDOLGDGGHOSHULRGR (VWRVHH[SOLFDHQHODSpQGL FHGHHVWHFDStWXOR (QQXHVWURHMHPSORSDUDHOSULPHUDxR\SDUDHOVHJXQGRDxRGDQXQSUR PHGLRGHSDUDORVGRVDxRV(OUHVXOWDGRHVWDQVRORDSUR[LPDGDPHQWHYHUGDGHURFXDQGRODVWDVDV QRVHFDSLWDOL]DQGHXQDPDQHUDFRQWLQXD Tabla 4.5 &iOFXORGHODVWDVDVDSOD]R $xR Q 7DVDFHURSDUDXQD LQYHUVLyQDQDxRV DQXDO 7DVDDSOD]RSDUD HODxRQ DQXDO 7DVDVGHLQWHUpV Panorámica de los negocios 4.2 (VWUDWHJLDVGHFXUYDVGHUHQGLPLHQWRGHOFRQGDGRGH 2UDQJH 6XSRQJDTXHXQJUDQLQYHUVLRQLVWDSXHGHVROLFLWDURFRQFHGHUSUpVWDPRVDODVWDVDVGHODWDEOD\ FRQVLGHUDTXHODVWDVDVGHLQWHUpVDXQDxRQRFDPELDUiQPXFKRHQORVFLQFRDxRVVLJXLHQWHV(OLQYHU VLRQLVWDSXHGHVROLFLWDUIRQGRVHQSUpVWDPRDXQDxRHLQYHUWLUORVGXUDQWHFLQFRDxRV/RVSUpVWDPRV DXQDxRVHSXHGHQUHQRYDUSRUSHULRGRVPiVODUJRVGHXQDxRDO¿QDOGHOSULPHURVHJXQGRWHUFHUR \FXDUWRDxRV6LODVWDVDVGHLQWHUpVVLJXHQVLHQGRDSUR[LPDGDPHQWHODVPLVPDVHVWDHVWUDWHJLDGDUi FRPRUHVXOWDGRXQDXWLOLGDGGHFHUFDGHSRUDxRSRUTXHORVLQWHUHVHVVHUHFLELUiQDO\VH SDJDUiQDO(VWHWLSRGHHVWUDWHJLDGHQHJRFLDFLyQVHFRQRFHFRPRHVWUDWHJLDGHODFXUYDGHUHQ GLPLHQWR(OLQYHUVLRQLVWDHVWiHVSHFXODQGRTXHODVWDVDVGHOIXWXURVHUiQPX\GLVWLQWDVGHODVWDVDVD SOD]RTXHVHKDQREVHUYDGRHQHOPHUFDGRHOGtDGHKR\ (QQXHVWURHMHPSORODVWDVDVDSOD]RTXHVH KDQREVHUYDGRHQHOPHUFDGRHOGtDGHKR\SDUDSHULRGRVIXWXURVGHXQDxRVRQGH \ 5REHUW&LWURQWHVRUHURGHOFRQGDGRGH2UDQJHXVyFRQPXFKRp[LWRHQ\ORVMXHJRV GHODFXUYDGHUHQGLPLHQWRVLPLODUHVDOTXHDFDEDPRVGHGHVFULELU/DVXWLOLGDGHVSURYHQLHQWHVGH 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GRQGH4HVODFRWL]DFLyQ'HHVWHPRGRHOSUHFLRGHSDUDXQFRQWUDWRDGLFLHPEUHGHHQOD WDEODFRUUHVSRQGHDXQSUHFLRGHFRQWUDWRGH 10,000 ½100 0:25 ð100 99:570Þ ¼ $998,925 (QODWDEODHOSUHFLR¿QDOGHOFRQWUDWRHV 10;000 ½100 0:25 ð100 99:500Þ ¼ $998,750 \ODGLIHUHQFLDHQWUHHOSUHFLRLQLFLDO\¿QDOGHOFRQWUDWRHVGH(VWRHVFRQJUXHQWHFRQODSpUGLGD TXHVHFDOFXOyHQODWDEODXVDQGRODUHJODGH³SRUPRYLPLHQWRGHSXQWREDVH´ /DWDEODPXHVWUDTXHODHVWUXFWXUDGHSOD]RVGHODWDVDGHLQWHUpVHQ(VWDGRV8QLGRVWXYRXQD SHQGLHQWHDVFHQGHQWHHQMXOLRGH/DWDVDGHOLTXLGDFLyQDIXWXURSDUDHOSHULRGRGHWUHVPHVHV TXHFRPHQ]yHOGHVHSWLHPEUHGHHUDGHSDUDHOSHULRGRGHWUHVPHVHVTXHLQLFLy HOGHGLFLHPEUHGHHUDGH\SDUDHOSHULRGRGHWUHVPHVHVTXHFRPLHQ]DHOGH GLFLHPEUHGHVHUtDGH (OHMHPSORPXHVWUDODPDQHUDHQTXHXQLQYHUVLRQLVWDLQWHUHVDGRHQFXEULUHOLQWHUpVTXHVHJDQDUi GXUDQWHXQSHULRGRGHWUHVPHVHVDIXWXURHPSH]DQGRHOGHGLFLHPEUHGHSRGUtDXVDUORVFRQ WUDWRVGHHXURGyODUHVDIXWXUR2EVHUYHTXHODSHULRGLFLGDGGHORVÀXMRVGHHIHFWLYRSURYHQLHQWHVGHOD FREHUWXUDQRFRLQFLGHHQIRUPDH[DFWDFRQODSHULRGLFLGDGGHORVÀXMRVGHHIHFWLYRGHOLQWHUpV(VWRHV DVtSRUTXHHOFRQWUDWRDIXWXURVHOLTXLGDGLDULDPHQWH$GHPiVODOLTXLGDFLyQ¿QDOHVHOGHVHSWLHP EUHGHPLHQWUDVTXHORVSDJRVGHLQWHUHVHVVREUHODLQYHUVLyQVHUHFLEHQWUHVPHVHVGHVSXpVGHHVWD IHFKD&RPRVHLQGLFDHQHOHMHPSORHVSRVLEOHKDFHUXQSHTXHxRDMXVWHSDUDFXEULUODSRVLFLyQFRPR XQLQWHQWRSDUDSHUPLWLUHVWHVHJXQGRDVSHFWR 2WURVFRQWUDWRVVLPLODUHVDORVFRQWUDWRVGHHXURGyODUHVDIXWXURGHO&0(VHQHJRFLDQVREUHODVWDVDV GHLQWHUpVHQRWURVSDtVHV(O&0(QHJRFLDFRQWUDWRVGHHXUR\HQHV3RUVXSDUWH/RQGRQ,QWHUQDWLRQDO )LQDQFLDO)XWXUHVDQG2SWLRQV([FKDQJH SDUWHGH(XURQH[W QHJRFLDFRQWUDWRV(XULERUDWUHVPHVHV HV GHFLUFRQWUDWRVVREUHODWDVD/O%25DWUHVPHVHVSDUDHOHXUR \(XURVZLVVFRQWUDWRVDIXWXURDWUHVPHVHV )XWXURVGHODVWDVDVGHLQWHUpV Ejemplo 6.3 8VRGHORVIXWXURVGHHXURGyODUHVSDUDFREHUWXUDVGHULHVJR 8QLQYHUVLRQLVWDTXLHUH¿MDUODWDVDGHLQWHUpVSRUXQSHULRGRGHWUHVPHVHVDSDUWLUGHOGHVHSWLHP EUHGHVREUHXQFDSLWDOGHPLOORQHV6XSRQHPRVTXHODFRWL]DFLyQDIXWXURGHHXURGyODUHV DOPHVGHVHSWLHPEUHGHHVGHORFXDOLQGLFDTXHHOLQYHUVLRQLVWDSXHGH¿MDUXQDWDVDGH LQWHUpVGH2RGHDQXDO(OLQYHUVLRQLVWDWRPDODFREHUWXUDPHGLDQWHODFRPSUDGH FRQWUDWRV6XSRQJDTXHHOGHVHSWLHPEUHGHODWDVDGHHXURGyODUHVDWUHVPHVHVUHVXOWDVHUGH /DOLTXLGDFLyQ¿QDOGHOFRQWUDWRVHUHDOL]DHQWRQFHVDXQSUHFLRGH(OLQYHUVLRQLVWDJDQD 100 25 ð9,740 9,650Þ ¼ 225,000 RVREUHORVFRQWUDWRVGHHXURGyODUHVDIXWXUR/DWDVDGHLQWHUpVTXHVHJDQDVREUHOD LQYHUVLyQDWUHVPHVHVHVGH 100,000,000 0:25 0:026 ¼ 650,000 R/DJDQDQFLDVREUHORVIXWXURVGHHXURGyODUHVOOHYDHVWRKDVWDHOQLYHOGHTXH HVORTXHODWDVDGHLQWHUpVVHUtDD 335 3DUHFHVHUTXHODQHJRFLDFLyQDIXWXURWLHQHHOHIHFWRGH¿MDUHQIRUPDH[DFWDXQDWDVDGHLQWHUpV GHHQWRGDVODVFLUFXQVWDQFLDV'HKHFKRODFREHUWXUDHVPHQRVTXHSHUIHFWDSRUTXHD ORV FRQWUDWRVDIXWXURVHOLTXLGDQGLDULDPHQWH \QRHQVXWRWDOLGDGDO¿QDO \E ODOLTXLGDFLyQ¿QDOHQ HOFRQWUDWRDIXWXURVXFHGHHOGHVHSWLHPEUHGHPLHQWUDVTXHHOSDJRGHLQWHUHVHVVREUH ODLQYHUVLyQVHUHDOL]DWUHVPHVHVPiVWDUGH8QDIRUPDGHKDFHUDMXVWHVSDUDHOVHJXQGRDVSHFWR 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(VWUDWHJLDVGHQHJRFLDFLyQUHODFLRQDGDVFRQRSFLRQHV Ejemplo 11.3 'LIHUHQFLDOEDMLVWD EHDUVSUHDG PHGLDQWHHOXVRGHRSFLRQHVGHYHQWD 8QLQYHUVLRQLVWDFRPSUDHQXQDRSFLyQGHYHQWDDWUHVPHVHVFRQXQSUHFLRGHHMHUFLFLRGH \YHQGHHQXQDRSFLyQGHYHQWDDWUHVPHVHVFRQXQSUHFLRGHHMHUFLFLRGH(OEHQH¿FLR SURYHQLHQWHGHHVWDHVWUDWHJLDGHXQGLIHUHQFLDOEDMLVWD EHDUVSUHDG HVFHURVLHOSUHFLRGHODDFFLyQ HVWiSRUDUULEDGH\GHVLHVWiSRUGHEDMRGH6LHOSUHFLRGHODDFFLyQVHHQFXHQWUDHQWUH \HOEHQH¿FLRHVGH267/DVRSFLRQHVFXHVWDQ25HQIRUPDDGHODQWDGD 3RUORWDQWRODXWLOLGDGHV ,QWHUYDORGHYDULDFLyQGHOSUHFLRGHODDFFLyQ 8WLOLGDG 67< ,67, 67> 1 267 2 Utilidad Opción de compra con posición corta, precio de ejercicio K1 K1 K2 ST Opción de compra con posición larga, precio de ejercicio K2 Figura 11.5 8WLOLGDGGHULYDGDGHXQGLIHUHQFLDOEDMLVWDFUHDGRPHGLDQWHHOXVRGHRSFLRQHVGHFRPSUD DFFLyQHVPD\RUTXH.HOUHQGLPLHQWRHVFHUR6LHOSUHFLRGHODDFFLyQHVLQIHULRUD.HOEHQH¿FLRHV GH.±.6LHOSUHFLRGHODDFFLyQVHHQFXHQWUDHQWUH.\.HOEHQH¿FLRHVGH.267/DXWLOLGDG VHFDOFXODVXVWUD\HQGRHOFRVWRLQLFLDOGHOEHQH¿FLR(OHMHPSORSUHVHQWDXQDLOXVWUDFLyQQXPpULFD $OLJXDOTXHORVGLIHUHQFLDOHVEDMLVWDV EHDUVSUHDGV ORVGLIHUHQFLDOHVDOFLVWDV EXOOVSUHDGV OLPLWDQ WDQWRHOSRWHQFLDOGHDXPHQWRHQODXWLOLGDGFRPRHOULHVJRGHXQDGLVPLQXFLyQ/RVGLIHUHQFLDOHVEDMLVWDV VHSXHGHQFUHDUXVDQGRRSFLRQHVGHFRPSUDHQOXJDUGHRSFLRQHVGHYHQWD(OLQYHUVLRQLVWDDGTXLHUHXQD RSFLyQGHFRPSUDFRQXQDOWRSUHFLRGHHMHUFLFLR\YHQGHXQDRSFLyQGHFRPSUDFRQXQEDMRSUHFLRGH HMHUFLFLRFRPRVHLOXVWUDHQOD¿JXUD/RVGLIHUHQFLDOHVEDMLVWDV EHDUVSUHDGV FUHDGRVFRQRSFLRQHV GHFRPSUDLPSOLFDQXQÀXMRLQLFLDOGHHQWUDGDGHHIHFWLYR LJQRUDQGRORVUHTXLVLWRVGHPDUJHQ Diferenciales de conjunto (box spreads) 8QGLIHUHQFLDOGHFRQMXQWR ER[VSUHDG HVXQDFRPELQDFLyQGHXQGLIHUHQFLDODOFLVWD EXOOVSUHDG GH XQDRSFLyQGHFRPSUDFRQSUHFLRVGHHMHUFLFLRGH.\.\XQGLIHUHQFLDOEDMLVWD EHDUVSUHDG GHXQD Tabla 11.3 %HQH¿FLRGHULYDGRGHXQGLIHUHQFLDOGHFRQMXQWR ,QWHUYDORGHYDULDFLyQ GHOSUHFLRGHODDFFLyQ %HQH¿FLRGHULYDGRGHXQGLIHUHQFLDO DOFLVWDFRQXQDRSFLyQGHFRPSUD 67<. .,67,. 67>. 672. .2. %HQH¿FLRGHULYDGRGHXQGLIHUHQFLDO %HQH¿FLR EDMLVWDFRQXQDRSFLyQGHYHQWD WRWDO .2. .267 .2. .2. .2. &$3Ë78/2 Panorámica de los negocios 11.1 3pUGLGDGHGLQHURFRQGLIHUHQFLDOHVGHFRQMXQWR ER[VSUHDGV 6XSRQJDTXHXQDDFFLyQWLHQHXQSUHFLRGH\YRODWLOLGDGGHO1RVHHVSHUDQGLYLGHQGRV\ ODWDVDOLEUHGHULHVJRHVGH8QQHJRFLDQWHOHRIUHFHDXVWHGODRSRUWXQLGDGGHYHQGHUHQHO&KL FDJR%RDUG2SWLRQV([FKDQJH &%2( XQGLIHUHQFLDOGHFRQMXQWRDGRVPHVHVGRQGHORVSUHFLRVGH HMHUFLFLRVRQGH\SRU¢/HFRQYLHQHOOHYDUDFDERODQHJRFLDFLyQ" 6LQGXGDODRSRUWXQLGDGVXHQDDWUDFWLYD(QHVWHFDVR.5.5\HOEHQH¿FLRVHUiFRQ FHUWH]DGHGHQWURGHGRVPHVHV$OYHQGHUHOGLIHUHQFLDOGHFRQMXQWRHQHLQYHUWLUORVIRQGRV GXUDQWHGRVPHVHVXVWHGWHQGUtDPiVTXHVX¿FLHQWHSDUDVDWLVIDFHUHOEHQH¿FLRGHHQGRVPHVHV (OYDORUWHyULFRGHOGLIHUHQFLDOGHFRQMXQWRDOGtDGHKR\HVGH3H235 3RUGHVJUDFLDKD\XQLQFRQYHQLHQWH/DVRSFLRQHVVREUHDFFLRQHVGHO&%2(VRQHVWDGRXQLGHQVHV \HOEHQH¿FLRGHSURYHQLHQWHGHOGLIHUHQFLDOGHFRQMXQWRVHFDOFXODVREUHHOVXSXHVWRGHTXHODV RSFLRQHVTXHFRQIRUPDQHOFRQMXQWRVRQHXURSHDV/RVSUHFLRVGHODVRSFLRQHVSDUDHVWHHMHPSOR ORVFXDOHVVHFDOFXODURQXVDQGRHOSURJUDPD'HULYD*HP VHPXHVWUDQHQODWDEODTXHVHSUHVHQWD PiVDGHODQWH8QGLIHUHQFLDODOFLVWD EXOOVSUHDG VREUHXQDRSFLyQGHFRPSUDGRQGHORVSUHFLRV GHHMHUFLFLRVRQGH\WLHQHXQFRVWRGH25 (VWRHVHOPLVPRSDUDODV RSFLRQHVWDQWRHXURSHDVFRPRHVWDGRXQLGHQVHVSRUTXHFRPRYLPRVHQHOFDStWXORHOSUHFLRGH ODRSFLyQGHFRPSUDHXURSHDHVLJXDOTXHHOSUHFLRGHXQDRSFLyQGHFRPSUDHVWDGRXQLGHQVHFXDQGR QRKD\GLYLGHQGRV 8QGLIHUHQFLDOEDMLVWD EHDUVSUHDG VREUHXQDRSFLyQGHYHQWDFRQORVPLVPRV SUHFLRVGHHMHUFLFLRWLHQHXQFRVWRGH25VLODVRSFLRQHVVRQHXURSHDV\GH 25VLVRQHVWDGRXQLGHQVHV(OYDORUFRPELQDGRGHDPERVGLIHUHQFLDOHVFXDQGRVHFUHDQ FRQRSFLRQHVHXURSHDVHVGH15(VWHHVHOSUHFLRWHyULFRGHOGLIHUHQFLDOGHFRQMXQ WR ER[VSUHDG TXHVHFDOFXOyPiVDUULED(OYDORUFRPELQDGRGHODFRPSUDGHDPERVGLIHUHQFLDOHV FXDQGRVHWUDWDGHRSFLRQHVHVWDGRXQLGHQVHVHVGH15/DYHQWDGHXQGLIHUHQFLDO GHFRQMXQWRFUHDGRFRQRSFLRQHVHVWDGRXQLGHQVHVSRUQRVHUtDXQDEXHQDQHJRFLDFLyQ8VWHG REWHQGUtDHVWRFDVLGHLQPHGLDWRSXHVWRTXHODQHJRFLDFLyQLPSOLFDODYHQWDGHXQDRSFLyQGHYHQWD FRQXQSUHFLRGHHMHUFLFLRGH\HVWRVHHMHUFHUtDFRQWUDXVWHG£FDVLWDQSURQWRFRPRODYHQGLHUD 7LSRGHRSFLyQ 3UHFLRGHHMHUFLFLR 3UHFLRGHODRSFLyQHXURSHD 3UHFLRGHODRSFLyQHVWDGRXQLGHQVH 2SFLyQGHFRPSUD 2SFLyQGHFRPSUD 2SFLyQYHQWD 2SFLyQYHQWD RSFLyQGHYHQWDFRQORVPLVPRVGRVSUHFLRVGHHMHUFLFLR&RPRVHPXHVWUDHQODWDEODHOEHQH¿FLR SURYHQLHQWHGHXQGLIHUHQFLDOGHFRQMXQWRVLHPSUHHV.±.3RUORWDQWRHOYDORUGHXQGLIHUHQFLDOGH FRQMXQWR ER[VSUHDG VLHPSUHHVHOYDORUSUHVHQWHGHHVWHEHQH¿FLRR .2. 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(VLPSRUWDQWHFRPSUHQGHUTXHXQDUELWUDMHVREUHXQGLIHUHQFLDOGHFRQMXQWR ER[VSUHDG WDQVROR IXQFLRQDFRQODVRSFLRQHVHXURSHDV0XFKDVGHODVRSFLRQHVTXHVHQHJRFLDQHQEROVDVRQHVWDGRXQL GHQVHV&RPRVHGHVFULEHHQHOUHFXDGUR³3DQRUiPLFDGHORVQHJRFLRVÓRVQHJRFLDQWHVFRQSRFD H[SHULHQFLDTXHWUDWDQODVRSFLRQHVHVWDGRXQLGHQVHVFRPRHXURSHDVHVWiQH[SXHVWRVDSHUGHUGLQHUR (VWUDWHJLDVGHQHJRFLDFLyQUHODFLRQDGDVFRQRSFLRQHV Estrategia con opciones de tipo mariposa (butterfly spread) 8QDHVWUDWHJLDFRQRSFLRQHVGHWLSRPDULSRVD EXWWHUÀ\VSUHDG LPSOLFDSRVLFLRQHVHQDFFLRQHVFRQWUHV GLIHUHQWHVSUHFLRVGHHMHUFLFLR6HSXHGHFUHDUPHGLDQWHODDGTXLVLFLyQGHXQDRSFLyQGHFRPSUDHXURSHD FRQXQSUHFLRGHHMHUFLFLRUHODWLYDPHQWHEDMR.ODDGTXLVLFLyQGHXQDRSFLyQGHFRPSUDHXURSHDFRQXQ SUHFLRGHHMHUFLFLRUHODWLYDPHQWHDOWR.\ODYHQWDGHGRVRSFLRQHVGHFRPSUDHXURSHDVFRQXQSUHFLRGH HMHUFLFLR.VLWXDGRDODPLWDGHQWUH.\.*HQHUDOPHQWH.HVWiFHUFDQRDOSUHFLRDFWXDOGHODDFFLyQ (OSDWUyQGHXWLOLGDGHVSURYHQLHQWHGHODHVWUDWHJLDVHPXHVWUDHQOD¿JXUD8QDHVWUDWHJLDFRQRSFLR QHVGHWLSRPDULSRVDFRQGXFHDXQDXWLOLGDGVLHOSUHFLRGHODDFFLyQHVWiFHUFDQRD.SHURGDOXJDUDXQD SHTXHxDSpUGLGDVLKD\XQPRYLPLHQWRVLJQL¿FDWLYRHQHOSUHFLRGHODDFFLyQHQFXDOTXLHUGLUHFFLyQ3RU ORWDQWRHVXQDHVWUDWHJLDDGHFXDGDSDUDXQLQYHUVLRQLVWDTXHFRQVLGHUHTXHORVPRYLPLHQWRVIXHUWHVHQHO SUHFLRGHODVDFFLRQHVVRQLPSUREDEOHV/DHVWUDWHJLDUHTXLHUHXQDSHTXHxDLQYHUVLyQLQLFLDO(OEHQH¿FLR GHULYDGRGHXQDHVWUDWHJLDFRQRSFLRQHVGHWLSRPDULSRVDVHPXHVWUDHQODWDEOD 6XSRQJDTXHFLHUWDDFFLyQWLHQHDFWXDOPHQWHXQYDORUGH&RQVLGHUHDXQLQYHUVLRQLVWDTXHSLHQ VDTXHXQPRYLPLHQWRVLJQL¿FDWLYRHQHOSUHFLRGHODVDFFLRQHVGHQWURGHORVVHLVPHVHVVLJXLHQWHVHV LPSUREDEOH6XSRQJDTXHORVSUHFLRVGHPHUFDGRGHODVRSFLRQHVGHFRPSUDHXURSHDVDVHLVPHVHVVRQ ORVVLJXLHQWHV 3UHFLRGHHMHUFLFLR 3UHFLRGHODRSFLyQGHFRPSUD (OLQYHUVLRQLVWDSRGUtDFUHDUXQDHVWUDWHJLDFRQRSFLRQHVGHWLSRPDULSRVDPHGLDQWHODDGTXLVLFLyQGH XQDRSFLyQGHFRPSUDFRQXQSUHFLRGHHMHUFLFLRGHODDGTXLVLFLyQGHXQDRSFLyQGHFRPSUDFRQ XQSUHFLRGHHMHUFLFLRGH\ODYHQWDGHGRVRSFLRQHVGHFRPSUDFRQXQSUHFLRGHHMHUFLFLRGH /DFUHDFLyQGHODHVWUDWHJLDWHQGUtDXQFRVWRGH12 3 56LHOSUHFLRGHODDFFLyQ GHQWURGHVHLVPHVHVHVPD\RUTXHRPHQRUTXHHOEHQH¿FLRWRWDOHVGHFHUR\HOLQYHUVLRQLVWD LQFXUUHHQXQDSpUGLGDQHWDGH6LHOSUHFLRGHODDFFLyQHVWiHQWUH\VHREWLHQHXQDXWLOLGDG /DXWLOLGDGPi[LPDRFXUUHFXDQGRHOSUHFLRGHODDFFLyQGHQWURGHVHLVPHVHVHVGH /DVHVWUDWHJLDVFRQRSFLRQHVGHWLSRPDULSRVDVHSXHGHQFUHDUPHGLDQWHHOXVRGHRSFLRQHVGHYHQWD (OLQYHUVLRQLVWDFRPSUDGRVRSFLRQHVGHYHQWDHXURSHDVXQDFRQXQEDMRSUHFLRGHHMHUFLFLR\RWUDFRQ XQDOWRSUHFLRGHHMHUFLFLR\YHQGHGRVRSFLRQHVGHYHQWDHXURSHDVFRQXQSUHFLRGHHMHUFLFLRLQWHUPH Utilidad Posición corta sobre 2 opciones de compra, precio de ejercicio K2 K1 K2 K3 ST Posición larga sobre una opción de compra, precio de ejercicio K3 Posición larga sobre una opción de compra, precio de ejercicio de K1 Figura 11.6 8WLOLGDGSURYHQLHQWHGHXQDHVWUDWHJLDFRQRSFLRQHVGHWLSRPDULSRVDPHGLDQWHHOXVRGHRSFLRQHV GHFRPSUD &$3Ë78/2 Tabla 11.4 %HQH¿FLRGHXQDHVWUDWHJLDFRQRSFLRQHVGHWLSRPDULSRVD ,QWHUYDORGHYDULDFLyQ GHOSUHFLRGHODDFFLyQ %HQH¿FLRGHULYDGRGH ODSULPHUDRSFLyQGH FRPSUDFRQSRVLFLyQ ODUJD %HQH¿FLRGHULYDGRGH ODVHJXQGDRSFLyQGH FRPSUDFRQSRVLFLyQ ODUJD 67<. .,67<. .,67,. 67>. 672 . 672 . 672 . 672. %HQH¿FLRGHULYDGR GHODVRSFLRQHVGH FRPSUDFRQSRVLFLyQ %HQH¿FLR FRUWD WRWDO 2 672 . 2 672 . 672 . .2 67 (VWRVEHQH¿FLRVVHFDOFXODQXVDQGRODUHODFLyQ.5 .1. GLRFRPRVHPXHVWUDHQOD¿JXUD/DVHVWUDWHJLDVFRQRSFLRQHVGHWLSRPDULSRVDGHOHMHPSORTXH VHDFDEDGHFRQVLGHUDUVHFUHDUtDQPHGLDQWHODFRPSUDGHGRVRSFLRQHVGHYHQWDXQDFRQXQSUHFLRGH HMHUFLFLRGH\RWUDFRQXQSUHFLRGHHMHUFLFLRGH\ODYHQWDGHGRVRSFLRQHVGHYHQWDFRQXQ SUHFLRGHHMHUFLFLRGH (OXVRGHODVRSFLRQHVGHYHQWDGDFRPRUHVXOWDGRH[DFWDPHQWHHOPLVPRGLIHUHQFLDOTXHHOXVRGH ODVRSFLRQHVGHFRPSUD/DSDULGDGYHQWDFRPSUDVHSXHGHXVDUSDUDGHPRVWUDUTXHODLQYHUVLyQLQLFLDO HVODPLVPDHQDPERVFDVRV 8QEXWWHUÀ\VSUHDGVHSXHGHYHQGHURFRPSUDUVLJXLHQGRODHVWUDWHJLDLQYHUVD6HYHQGHQODVRSFLRQHV FRQSUHFLRVGHHMHUFLFLR.\.\VHFRPSUDQODVGRVRSFLRQHVFRQHOSUHFLRGHHMHUFLFLRLQWHUPHGLR. (VWDHVWUDWHJLDJHQHUDXQDXWLOLGDGPRGHVWDVLKD\XQPRYLPLHQWRVLJQL¿FDWLYRHQHOSUHFLRGHODDFFLyQ Margen de calendario (calendar spread) +DVWDDKRUDKHPRVVXSXHVWRTXHWRGDVODVRSFLRQHVTXHVHXVDQSDUDFUHDUXQGLIHUHQFLDOH[SLUDQDO PLVPRWLHPSR$FRQWLQXDFLyQQRVRFXSDUHPRVGHORVPiUJHQHVGHFDOHQGDULR FDOHQGDUVSUHDGV HQ ORVFXDOHVODVRSFLRQHVWLHQHQHOPLVPRSUHFLRGHHMHUFLFLRSHURGLIHUHQWHVIHFKDVGHH[SLUDFLyQ 6HSXHGHFUHDUXQPDUJHQGHFDOHQGDULRPHGLDQWHODYHQWDGHXQDRSFLyQGHFRPSUDHXURSHDFRQ FLHUWRSUHFLRGHHMHUFLFLR\ODDGTXLVLFLyQGHXQDRSFLyQGHFRPSUDHXURSHDFRQXQSOD]RGHYHQFLPLHQ WRPiVODUJRFRQHOPLVPRSUHFLRGHHMHUFLFLR&XDQWRPiVODUJRVHDHOSOD]RGHYHQFLPLHQWRGHXQD RSFLyQSRUORJHQHUDOVHUiPiVFRVWRVDGLFKDRSFLyQ3RUORWDQWRXQPDUJHQGHFDOHQGDULRJHQHUDO PHQWHUHTXLHUHGHXQDLQYHUVLyQLQLFLDO/RVGLDJUDPDVGHXWLOLGDGHVGHORVPiUJHQHVGHFDOHQGDULRVH SURGXFHQSRUORJHQHUDOGHWDOPRGRTXHPXHVWUHQODXWLOLGDGFXDQGRH[SLUDODRSFLyQFRQXQSOD]RGH YHQFLPLHQWRFRUWRVREUHHOVXSXHVWRGHTXHODSRVLFLyQGHODRSFLyQFRQXQSOD]RGHYHQFLPLHQWRODUJR VHFLHUUDHQHVHPRPHQWR(OSDWUyQGHXWLOLGDGHVGHXQGLIHUHQFLDOGHFDOHQGDULRSURGXFLGRDSDUWLUGH RSFLRQHVGHFRPSUDVHPXHVWUDHQOD¿JXUD(OSDWUyQHVVLPLODUDODXWLOLGDGGHODHVWUDWHJLDFRQ Utilidad Posición corta sobre dos opciones de venta, precio de ejercicio K2 K1 K2 K3 ST Posición larga sobre una opción de venta, precio de ejercicio K1 Posición larga sobre una opción de venta, precio de ejercicio K3 Figura 11.7 8WLOLGDGGHULYDGDGH XQDHVWUDWHJLDFRQRSFLRQHV GHWLSRPDULSRVDPHGLDQWH HOXVRGHRSFLRQHVGHYHQWD (VWUDWHJLDVGHQHJRFLDFLyQUHODFLRQDGDVFRQRSFLRQHV Utilidad Posición corta sobre una opción de compra, con vencimiento T1 ST K Figura 11.8 8WLOLGDGGHULYDGDGH XQPDUJHQGHFDOHQGDULRFUHDGR PHGLDQWHHOXVRGHGRVRSFLRQHV GHFRPSUDFXDQGR7.7FDOFXODGD HQHOPRPHQWRHQTXHH[SLUDOD RSFLyQGHFRPSUDFRQXQSOD]R GHYHQFLPLHQWRFRUWR Posición larga sobre una opción de compra, con vencimiento T2 RSFLRQHVGHWLSRPDULSRVDGHOD¿JXUD(OLQYHUVLRQLVWDREWLHQHXQDXWLOLGDGVLHOSUHFLRGHODDFFLyQ HQODIHFKDGHH[SLUDFLyQGHODRSFLyQFRQXQSOD]RGHYHQFLPLHQWRFRUWRHVWiFHUFDQRDOSUHFLRGHHMHU FLFLRGHODRSFLyQFRQXQSOD]RGHYHQFLPLHQWRFRUWR6LQHPEDUJRVHLQFXUUHHQXQDSpUGLGDFXDQGRHO SUHFLRGHODDFFLyQHVWiVLJQL¿FDWLYDPHQWHSRUDUULEDRSRUGHEDMRGHHVWHSUHFLRGHHMHUFLFLR 3DUDHQWHQGHUHOSDWUyQGHXWLOLGDGHVGHULYDGRGHXQPDUJHQGHFDOHQGDULRFRQVLGHUHSULPHURORTXH VXFHGHVLHOSUHFLRGHODDFFLyQHVPX\EDMRFXDQGRH[SLUDODRSFLyQFRQSOD]RGHYHQFLPLHQWRFRUWR /DRSFLyQFRQSOD]RGHYHQFLPLHQWRFRUWRFDUHFHGHYDORU\HOYDORUGHODRSFLyQFRQSOD]RGHYHQFL PLHQWRODUJRHVWiFHUFDQRDFHUR3RUORWDQWRHOLQYHUVLRQLVWDLQFXUUHHQXQDSpUGLGDTXHHVWiFHUFDQD DOFRVWRGHFRQ¿JXUDUHOGLIHUHQFLDOLQLFLDOPHQWH&RQVLGHUHDFRQWLQXDFLyQORTXHVXFHGHVLHOSUHFLR GHODDFFLyQ67HVPX\DOWRFXDQGRH[SLUDODRSFLyQFRQXQSOD]RGHYHQFLPLHQWRFRUWR/DRSFLyQFRQ SOD]RGHYHQFLPLHQWRFRUWROHFXHVWDDOLQYHUVLRQLVWD672.\ODRSFLyQFRQXQSOD]RGHYHQFLPLHQWR ODUJRYDOHXQSRFRPiVTXH672.GRQGH.HVHOSUHFLRGHHMHUFLFLRGHODVRSFLRQHV8QDYH]PiVHO LQYHUVLRQLVWDLQFXUUHHQXQDSpUGLGDQHWDTXHHVWiFHUFDQDDOFRVWRGHHVWDEOHFHUHOGLIHUHQFLDOLQLFLDO PHQWH6L67HVWiFHUFDQRD.ODRSFLyQFRQXQSOD]RGHYHQFLPLHQWRFRUWROHFXHVWDDOLQYHUVLRQLVWD\D VHDXQDSHTXHxDFDQWLGDGRQDGD6LQHPEDUJRODRSFLyQFRQXQSOD]RGHYHQFLPLHQWRODUJRHVWRGDYtD PX\YDOLRVD(QHVWHFDVRVHREWLHQHXQDXWLOLGDGQHWDVLJQL¿FDWLYD (QXQPDUJHQGHFDOHQGDULRQHXWUDOVHHOLJHXQSUHFLRGHHMHUFLFLRFHUFDQRDOSUHFLRDFWXDOGHOD DFFLyQ8QPDUJHQGHFDOHQGDULRDOFLVWDLPSOLFDXQSUHFLRGHHMHUFLFLRPiVDOWRPLHQWUDVTXHXQPDU JHQGHFDOHQGDULREDMLVWDLPSOLFDXQSUHFLRGHHMHUFLFLRPiVEDMR Utilidad Posición corta sobre una opción de venta, plazo de vencimiento T1 ST K Posición larga sobre una opción de venta, plazo de vencimiento T2 Figura 11.9 8WLOLGDGGHULYDGDGHXQ PDUJHQGHFDOHQGDULRFUHDGRPHGLDQWH HOXVRGHGRVRSFLRQHVGHYHQWDFXDQGR 7.7FDOFXODGDHQHOPRPHQWRHQTXH H[SLUDODRSFLyQGHYHQWDFRQXQSOD]RGH YHQFLPLHQWRFRUWR &$3Ë78/2 /RV PiUJHQHV GH FDOHQGDULR VH SXHGHQ FUHDU WDQWR FRQ RSFLRQHV GH YHQWD FRPR FRQ RSFLRQHV GH FRPSUD(OLQYHUVLRQLVWDDGTXLHUHXQDRSFLyQGHYHQWDFRQXQSOD]RGHYHQFLPLHQWRODUJR\YHQGHXQD RSFLyQGHYHQWDFRQXQSOD]RGHYHQFLPLHQWRFRUWR&RPRVHPXHVWUDHQOD¿JXUDHOSDWUyQGH XWLOLGDGHVHVVLPLODUDOTXHVHREWLHQHPHGLDQWHHOXVRGHRSFLRQHVGHFRPSUD 8QPDUJHQGHFDOHQGDULRLQYHUVRHVORRSXHVWRGHORTXHVHPXHVWUDHQODV¿JXUDV\(O LQYHUVLRQLVWDDGTXLHUHXQDRSFLyQFRQXQSOD]RGHYHQFLPLHQWRFRUWR\YHQGHXQDRSFLyQFRQXQSOD]R GHYHQFLPLHQWRODUJR6XUJHXQDXWLOLGDGSHTXHxDVLHOSUHFLRGHODDFFLyQHQODH[SLUDFLyQGHODRSFLyQ FRQSOD]RGHYHQFLPLHQWRFRUWRVHHQFXHQWUDPX\SRUDUULEDRPX\SRUGHEDMRGHOSUHFLRGHHMHUFLFLR GHODRSFLyQFRQSOD]RGHYHQFLPLHQWRFRUWR6LQHPEDUJRVHJHQHUDXQDSpUGLGDVLJQL¿FDWLYDVLVH HQFXHQWUDFHUFDQRDOSUHFLRGHHMHUFLFLR Combinación de opciones en diagonal (diagonal spreads) /RVGLIHUHQFLDOHVDOFLVWDVEDMLVWDV\ORVPiUJHQHVGHFDOHQGDULRVHSXHGHQFUHDUDSDUWLUGHXQDSRVLFLyQ ODUJDHQXQDRSFLyQGHFRPSUD\XQDSRVLFLyQFRUWDHQRWUDRSFLyQGHFRPSUD(QHOFDVRGHORVGLIH UHQFLDOHVDOFLVWDV\EDMLVWDVODVRSFLRQHVGHFRPSUDWLHQHQGLIHUHQWHVSUHFLRVGHHMHUFLFLR\ODPLVPD IHFKDGHH[SLUDFLyQ(QHOFDVRGHORVPiUJHQHVGHFDOHQGDULRODVRSFLRQHVGHFRPSUDWLHQHQHOPLVPR SUHFLRGHHMHUFLFLR\GLIHUHQWHVIHFKDVGHH[SLUDFLyQ(QXQDFRPELQDFLyQGHDFFLRQHVHQGLDJRQDO GLD JRQDOVSUHDG WDQWRODIHFKDGHH[SLUDFLyQFRPRHOSUHFLRGHHMHUFLFLRGHODVRSFLRQHVGHFRPSUDVRQ GLIHUHQWHV(VWRDXPHQWDHOLQWHUYDORGHYDULDFLyQGHORVSDWURQHVGHXWLOLGDGTXHVRQSRVLEOHV 11.4 COMBINACIONES 8QDFRPELQDFLyQHVXQDHVWUDWHJLDGHQHJRFLDFLyQGHRSFLRQHVTXHLPSOLFDHOKHFKRGHWRPDUXQDSRVL FLyQWDQWRHQODVRSFLRQHVGHFRPSUDFRPRHQODVRSFLRQHVGHYHQWDVREUHXQDPLVPDDFFLyQ&RQVLGHUD UHPRVODVFRPELQDFLRQHVDOWHUQDWLYDVGHFRPSUD\YHQWD VWUDGGOHV ORVVWULSVORVVWUDSV\ORVVWUDQJOHV Combinación alternativa de compra y venta (straddle) 8QD FRPELQDFLyQ FRP~Q HV DTXHOOD TXH LQFOX\H XQD FRPELQDFLyQ DOWHUQDWLYD GH FRPSUD \ YHQWD VWUDGGOH ORFXDOLPSOLFDDGTXLULUXQDRSFLyQGHFRPSUD\XQDRSFLyQGHYHQWDHXURSHDVFRQHOPLVPR SUHFLRGHHMHUFLFLRHLJXDOIHFKDGHH[SLUDFLyQ(OSDWUyQGHXWLOLGDGHVVHPXHVWUDHQOD¿JXUD (OSUHFLRGHHMHUFLFLRVHGHQRWDFRQ.6LHOSUHFLRGHODDFFLyQVHHQFXHQWUDFHUFDQRDHVWHSUHFLRGH HMHUFLFLR HQ OD H[SLUDFLyQ GH ODV RSFLRQHV OD FRPELQDFLyQ DOWHUQDWLYD GH FRPSUD \ YHQWD FRQGXFH D XQDSpUGLGD6LQHPEDUJRVLKD\XQPRYLPLHQWRORVX¿FLHQWHPHQWHJUDQGHHQFXDOTXLHUGLUHFFLyQVH SURGXFLUiXQDXWLOLGDGVLJQL¿FDWLYD(OEHQH¿FLRGHULYDGRGHXQDFRPELQDFLyQDOWHUQDWLYDGHFRPSUD\ YHQWDVHFDOFXODHQODWDEOD 8QDFRPELQDFLyQDOWHUQDWLYDGHFRPSUD\YHQWDHVDGHFXDGDFXDQGRXQLQYHUVLRQLVWDHVWiHVSHUDQGR XQPRYLPLHQWRIXHUWHHQHOSUHFLRGHXQDDFFLyQSHURQRVDEHHQTXpGLUHFFLyQVHUiGLFKRPRYLPLHQWR Utilidad K Posición larga en una opción de compra, precio de ejercicio K ST Posición larga en una opción de venta, precio de ejercicio K Figura 11.10 8WLOLGDGSURYHQLHQWHGHXQD FRPELQDFLyQDOWHUQDWLYDGHFRPSUD\YHQWD (VWUDWHJLDVGHQHJRFLDFLyQUHODFLRQDGDVFRQRSFLRQHV Tabla 11.5 %HQH¿FLRSURYHQLHQWHGHXQDFRPELQDFLyQDOWHUQDWLYDGHFRPSUD\YHQWD ,QWHUYDORGHYDULDFLyQ GHOSUHFLRGHODDFFLyQ %HQH¿FLRGHULYDGRGHOD RSFLyQGHFRPSUD %HQH¿FLRGHULYDGRGHOD RSFLyQGHYHQWD %HQH¿FLRWRWDO 67<. 67.. 672 . .2 67 .2 67 672 . &RQVLGHUH D XQ LQYHUVLRQLVWD TXH SLHQVD TXH HO SUHFLR GH FLHUWD DFFLyQ DFWXDOPHQWH YDOXDGR HQ SRUHOPHUFDGRVHGHVSOD]DUiGHXQDPDQHUDVLJQL¿FDWLYDHQORVWUHVPHVHVVLJXLHQWHV(OLQYHUVLRQLV WDSRGUtDFUHDUXQDFRPELQDFLyQDOWHUQDWLYDGHFRPSUD\YHQWDDGTXLULHQGRWDQWRXQDRSFLyQGHYHQWD FRPRXQDGHFRPSUDFRQXQSUHFLRGHHMHUFLFLRGH\XQDIHFKDGHH[SLUDFLyQGHQWURGHWUHVPHVHV 6XSRQJDTXHODRSFLyQGHFRPSUDWLHQHXQFRVWRGH\ODRSFLyQGHYHQWDWLHQHXQFRVWRGH6LHO SUHFLRGHODDFFLyQSHUPDQHFHHQHVIiFLOYHUTXHODHVWUDWHJLDFXHVWDDOLQYHUVLRQLVWD VHUHTXLHUH XQDLQYHUVLyQDQWLFLSDGDGHODRSFLyQGHFRPSUDH[SLUDVLQQLQJ~QYDORU\ODRSFLyQGHYHQWDH[SLUD FRQXQYDORUGH 6LHOSUHFLRGHODDFFLyQVHGHVSOD]DKDVWDVHH[SHULPHQWDXQDSpUGLGDGH HVWRHVORSHRUTXHSXHGHVXFHGHU 6LQHPEDUJRVLHOSUHFLRGHODDFFLyQVDOWDDVHREWLHQHXQD XWLOLGDGGHVLODDFFLyQGLVPLQX\HDVHREWLHQHXQDXWLOLGDGGH\DVtVXFHVLYDPHQWH&RPR VHLQGLFDHQHOUHFXDGUR³3DQRUiPLFDGHORVQHJRFLRV´XQLQYHUVLRQLVWDGHEHUtDFRQVLGHUDUFRQ WRGRFXLGDGRVLHOVDOWRTXHKDDQWLFLSDGR\DVHUHÀHMDHQORVSUHFLRVGHODVRSFLRQHVDQWHVGHSRQHUXQD FRPELQDFLyQDOWHUQDWLYDGHFRPSUD\YHQWDHQODPHVDGHQHJRFLDFLRQHV /DFRPELQDFLyQDOWHUQDWLYDGHFRPSUD\YHQWDGHOD¿JXUDDOJXQDVYHFHVVHGHQRPLQDFRP ELQDFLyQDOWHUQDWLYDLQIHULRURFRPSUDGHXQDFRPELQDFLyQDOWHUQDWLYD8QDFRPELQDFLyQDOWHUQDWLYD VXSHULRURYHQWDGHXQDFRPELQDFLyQDOWHUQDWLYDHVODSRVLFLyQRSXHVWD6HFUHDPHGLDQWHODYHQWDGHXQD RSFLyQGHFRPSUD\XQDRSFLyQGHYHQWDFRQHOPLVPRSUHFLRGHHMHUFLFLRHLJXDOIHFKDGHH[SLUDFLyQ (VXQDHVWUDWHJLDDOWDPHQWHULHVJRVD6LHOSUHFLRGHODDFFLyQHQODIHFKDGHH[SLUDFLyQHVWiFHUFDGHO SUHFLRGHHMHUFLFLRVHUHJLVWUDXQDSpUGLGDVLJQL¿FDWLYD6LQHPEDUJRODSpUGLGDTXHSURYLHQHGHXQ PRYLPLHQWRFRQVLGHUDEOHHVLOLPLWDGD Bandas (strips) y correas (straps) 8QDEDQGDRVWULSFRQVLVWHHQXQDSRVLFLyQODUJDHQXQDRSFLyQGHFRPSUDHXURSHD\HQGRVRSFLRQHV GHYHQWDHXURSHDVFRQHOPLVPRSUHFLRGHHMHUFLFLRHLJXDOIHFKDGHH[SLUDFLyQ8QDFRUUHDRVWUDS FRQVLVWHHQXQDSRVLFLyQODUJDHQGRVRSFLRQHVGHFRPSUDHXURSHDV\HQXQDRSFLyQGHYHQWDHXURSHDFRQ HOPLVPRSUHFLRGHHMHUFLFLRHLJXDOIHFKDGHH[SLUDFLyQ/RVSDWURQHVGHXWLOLGDGHVSURYHQLHQWHVGHORV VWULSV\VWUDSVVHPXHVWUDQHQOD¿JXUD(QXQVWULSHOLQYHUVLRQLVWDHVWiDSRVWDQGRTXHKDEUiXQ JUDQPRYLPLHQWRHQHOSUHFLRGHXQDDFFLyQ\FRQVLGHUDTXHXQGHFUHPHQWRHQHOSUHFLRGHODDFFLyQ Utilidad Utilidad K Strip (una opción de compra + dos opciones de venta) ST K Strap (dos opciones de compra + una opción de venta) ST Figura 11.11 8WLOLGDGHV SURYHQLHQWHVGH XQVWULS\GHXQ VWUDS &$3Ë78/2 Panorámica de los negocios 11.2 &yPR JDQDU GLQHUR D SDUWLU GH ODV FRPELQDFLRQHV DOWHUQDWLYDVGHFRPSUD\YHQWD VWUDGGOHV 6XSRQJDTXHVHHVSHUDXQJUDQPRYLPLHQWRHQHOSUHFLRGHODVDFFLRQHVGHXQDFRPSDxtDSRUTXH H[LVWHXQDRIHUWDS~EOLFDGHFRPSUDSDUDOD¿UPDRSRUTXHHVWiDSXQWRGHDQXQFLDUVHHOUHVXOWDGRGH XQSOHLWROHJDOPD\RUTXHLPSOLFDDODFRPSDxtD¢6HGHEHUtDQHJRFLDUXQDFRPELQDFLyQDOWHUQDWLYD GHFRPSUD\YHQWD" (QHVWHFDVRXQDFRPELQDFLyQDOWHUQDWLYDGHFRPSUD\YHQWDSDUHFHVHUXQDHVWUDWHJLDQDWXUDO GHQHJRFLDFLyQ6LQHPEDUJRVLVXSHUVSHFWLYDGHODVLWXDFLyQGHODFRPSDxtDHVPX\VLPLODUDODGH RWURVSDUWLFLSDQWHVGHOPHUFDGRHVWDSHUVSHFWLYDVHUHÀHMDUiHQORVSUHFLRVGHODVRSFLRQHV/DVRS FLRQHVVREUHODVDFFLRQHVVHUiQVLJQL¿FDWLYDPHQWHPiVFRVWRVDVTXHODVRSFLRQHVVREUHXQDDFFLyQ VLPLODUSDUDODFXDOQRVHHVSHUDQLQJ~QDXPHQWR(OSDWUyQGHXWLOLGDGHVHQIRUPDGH9SURYHQLHQWH GHODFRPELQDFLyQDOWHUQDWLYDGHFRPSUD\YHQWDHQOD¿JXUDVHKDEUiGHVSOD]DGRKDFLDDEDMRGH PRGRTXHVHUiQHFHVDULRTXHKD\DXQPRYLPLHQWRPD\RUHQHOSUHFLRGHODVDFFLRQHVSDUDTXHXVWHG REWHQJDXQDXWLOLGDG 3DUDTXHXQDFRPELQDFLyQDOWHUQDWLYDGHFRPSUD\YHQWDVHDXQDHVWUDWHJLDHIHFWLYDXVWHGGHEHFUHHU TXHHVSUREDEOHTXHKD\DPRYLPLHQWRVQRWDEOHVHQHOSUHFLRGHODVDFFLRQHVVLQTXHORVGHPiVLQYHU VLRQLVWDVFRPSDUWDQHVDFUHHQFLD/RVSUHFLRVGHPHUFDGRLQFRUSRUDQODVFUHHQFLDVGHORVSDUWLFLSDQWHV GHOPHUFDGR3DUDJDQDUGLQHURDSDUWLUGHXQDHVWUDWHJLDGHLQYHUVLyQXVWHGGHEHDGRSWDUXQDSHUV SHFWLYDTXHVHDGLIHUHQWHGHODPD\RUSDUWHGHOUHVWRGHOPHUFDGR\GHVGHOXHJR£GHEHWHQHUODUD]yQ HV PiV SUREDEOH TXH XQ LQFUHPHQWR (Q XQ VWUDS HO LQYHUVLRQLVWD WDPELpQ HVWi DSRVWDQGR TXH KDEUi XQPRYLPLHQWRLPSRUWDQWHHQHOSUHFLRGHODDFFLyQ6LQHPEDUJRHQHVWHFDVRVHFRQVLGHUDTXHXQ LQFUHPHQWRHQHOSUHFLRGHODDFFLyQHVPiVSUREDEOHTXHXQGHFUHPHQWR Cunas de acciones (strangles) (QXQDFXQDGHDFFLRQHVRVWUDQJOHTXHDOJXQDVYHFHVVHGHQRPLQDFRPELQDFLyQLQIHULRUYHUWLFDOXQ LQYHUVLRQLVWDDGTXLHUHXQDRSFLyQGHYHQWDHXURSHD\XQDRSFLyQGHFRPSUDHXURSHDFRQODPLVPDIHFKD GHH[SLUDFLyQSHURGLIHUHQWHVSUHFLRVGHHMHUFLFLR(OSDWUyQGHXWLOLGDGHVVHLOXVWUDHQOD¿JXUD (OSUHFLRGHHMHUFLFLRGHODRSFLyQGHFRPSUD.HVPiVDOWRTXHHOSUHFLRGHHMHUFLFLRGHODRSFLyQGH YHQWD./DIXQFLyQGHOEHQH¿FLRGHXQVWUDQJOHVHFDOFXODHQODWDEOD 8QVWUDQJOHHVXQDHVWUDWHJLDVLPLODUDXQDFRPELQDFLyQDOWHUQDWLYDGHFRPSUD\YHQWD(OLQYHUVLR QLVWDHVWiDSRVWDQGRTXHKDEUiXQPRYLPLHQWRLPSRUWDQWHHQHOSUHFLRSHURQRVDEHVLVHUiXQDXPHQWR RXQDGLVPLQXFLyQ$OFRPSDUDUODV¿JXUDV\REVHUYDPRVTXHHOSUHFLRGHODDFFLyQWLHQH TXHDOHMDUVHPiVHQXQVWUDQJOHTXHHQXQDFRPELQDFLyQDOWHUQDWLYDGHFRPSUD\YHQWDSDUDTXHHOLQYHU VLRQLVWDREWHQJDXQDXWLOLGDG6LQHPEDUJRHOULHVJRGHGLVPLQXFLyQGHYDORUVLHOSUHFLRGHODDFFLyQ WHUPLQDHQHOYDORUFHQWUDOHVPHQRUSDUDXQVWUDQJOH Utilidad K1 K2 ST Posición larga sobre una opción de compra, precio de ejercicio K2 Posición larga sobre una opción de venta, precio de ejercicio K1 Figura 11.12 8WLOLGDGSURYHQLHQWHGHXQ VWUDQJOH (VWUDWHJLDVGHQHJRFLDFLyQUHODFLRQDGDVFRQRSFLRQHV Tabla 11.6 8WLOLGDGSURYHQLHQWHGHXQVWUDQJOH ,QWHUYDORGHYDULDFLyQ GHOSUHFLRGHODDFFLyQ %HQH¿FLRGHULYDGRGHXQD RSFLyQGHFRPSUD %HQH¿FLRGHULYDGRGHXQD RSFLyQGHYHQWD %HQH¿FLRWRWDO 67<. .,67,. 67>. .267 .267 672 . 672 . 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QHVGHWLSRPDULSRVDVHFUHDDODGTXLULURSFLRQHVFRQSUHFLRVGHHMHUFLFLR.\.\DOYHQGHUGRVRSFLRQHV FRQSUHFLRGHHMHUFLFLR.GRQGH.,.,.\.±.5.2./D¿JXUDPXHVWUDHOEHQH¿FLR GHXQDHVWUDWHJLDFRQRSFLRQHVGHWLSRPDULSRVD(OSDWUyQVHSRGUtDGHVFULELUFRPRXQDHVSLJD&RQIRU PH.\.VHDFHUFDQHQWUHVtODHVSLJDVHYXHOYHPiVSHTXHxD$WUDYpVGHXQDFRPELQDFLyQMXLFLRVD GHXQDJUDQFDQWLGDGGHHVSLJDVPX\SHTXHxDVHVSRVLEOHDSUR[LPDUFXDOTXLHUIXQFLyQGHEHQH¿FLRV RESUMEN /RVSDJDUpVSURWHJLGRVSRUHOFDSLWDOVHFUHDQDSDUWLUGHXQERQRFXSyQFHUR\XQDRSFLyQGHFRPSUDHXUR SHD6RQDWUDFWLYRVSDUDDOJXQRVLQYHUVLRQLVWDVSRUTXHHOHPLVRUGHOSURGXFWRWLHQHODFDSDFLGDGGHJDUDQ WL]DUTXHHOFRPSUDGRUUHFXSHUHVXFDSLWDOVLQLPSRUWDUHOGHVHPSHxRGHODFWLYRVXE\DFHQWHGHODRSFLyQ &LHUWDVHVWUDWHJLDVGHQHJRFLDFLyQFRPXQHVLPSOLFDQXQDVRODRSFLyQ\ODDFFLyQVXE\DFHQWH3RU HMHPSORODHPLVLyQGHXQDRSFLyQGHFRPSUDFXELHUWDLPSOLFDODFRPSUDGHXQDDFFLyQ\ODYHQWDGHOD RSFLyQGHFRPSUDVREUHHVDDFFLyQXQDRSFLyQGHYHQWDGHSURWHFFLyQLPSOLFDODFRPSUDGHXQDRSFLyQ GHYHQWD\ODDGTXLVLFLyQGHODDFFLyQ/RSULPHURHVVLPLODUDODYHQWDGHXQDRSFLyQGHYHQWDOR~OWLPR 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6XSRQJDTXHXQtQGLFHEXUViWLOHVDFWXDOPHQWHGH\TXHWLHQHXQDYRODWLOLGDGGH\XQUHQ GLPLHQWRGHGLYLGHQGRVGHO/DWDVDGHLQWHUpVOLEUHGHULHVJRHVGH/D¿JXUDTXHVHPXHV WUD PiV DEDMR SUHVHQWD HO UHVXOWDGR GHO VRIWZDUH 'HULYD*HP SDUD YDOXDU XQD RSFLyQ GH FRPSUD HXURSHDDVHLVPHVHVFRQXQSUHFLRGHHMHUFLFLRGHXVDQGRXQiUEROGHGRVSDVRV(QHVWHFDVR t ¼ 0:25; pffiffiffiffiffiffi u ¼ e0:20 0:25 ¼ 1:1052; a ¼ eð0:050:02Þ0:25 ¼ 1:0075; p¼ (OYDORUGHODRSFLyQHVGH Resultado con DerivaGem: En cada nodo: Valor superior = Precio del activo subyacente Valor inferior = Precio de la opción El área sombreada indica dónde se ejerce la opción Precio de ejercicio = 800 Factor de descuento por intervalo = 0.9876 Intervalo de tiempo, dt = 0.2500 años, 91.25 días Factor de crecimiento por intervalo, a = 1.0075 Probabilidad de un movimiento ascendente, p = 0.5126 Tamaño de un paso ascendente, u = 1.1052 Tamaño de un paso descendente, d = 0.9048 989.34 189.34 895.19 100.66 810.00 53.39 810.00 732.92 5.06 663.17 0.00 Tiempo del nodo: 0.0000 0.2500 0.5000 d ¼ 1=u ¼ 0:9048; 1:0075 0:9048 ¼ 0:5126 1:1052 0:9048 &$3Ë78/2 Ejemplo 12.2 2SFLyQVREUHXQDGLYLVD 6XSRQJDTXHHOGyODUDXVWUDOLDQRWLHQHDFWXDOPHQWHXQYDORUGHGyODUHVHVWDGRXQLGHQVHV\ TXHHVWHWLSRGHFDPELRWLHQHXQDYRODWLOLGDGGH/DWDVDDXVWUDOLDQDOLEUHGHULHVJRHVGH \ODWDVDHVWDGRXQLGHQVHOLEUHGHULHVJRHVGH/D¿JXUDTXHVHPXHVWUDPiVDEDMRSUHVHQWDHO UHVXOWDGRGHOVRIWZDUH'HULYD*HPSDUDYDOXDUXQDRSFLyQGHFRPSUDHVWDGRXQLGHQVHDWUHVPHVHV FRQXQSUHFLRGHHMHUFLFLRGHXVDQGRXQiUEROGHWUHVSDVRV(QHVWHFDVR t ¼ 0:08333; pffiffiffiffiffiffiffiffiffiffiffi u ¼ e0:12 0:08333 ¼ 1:0352; a ¼ eð0:050:07Þ0:08333 ¼ 0:9983; p¼ (OYDORUGHODRSFLyQHV Resultado con DerivaGem: En cada nodo: Valor superior = Precio del activo subyacente Valor inferior = Precio de la opción El área sombreada indica dónde se ejerce la opción Precio de ejercicio = 0.6 Factor de descuento por intervalo = 0.9958 Intervalo de tiempo, dt = 0.0833 años, 30.42 días Factor de crecimiento por intervalo, a = 0.9983 Probabilidad de un movimiento ascendente, p = 0.4673 Tamaño de un paso ascendente, u = 1.0352 Tamaño de un paso descendente, d = 0.9660 0.677 0.077 0.654 0.054 0.632 0.033 0.610 0.019 0.632 0.032 0.610 0.015 0.589 0.007 0.589 0.000 0.569 0.000 0.550 0.000 Tiempo del nodo 0.0000 0.0833 0.1667 0.2500 d ¼ 1=u ¼ 0:9660; 0:9983 0:9660 ¼ 0:4673 1:0352 0:9660 ,QWURGXFFLyQDORViUEROHVELQRPLDOHV Ejemplo 12.3 2SFLyQVREUHIXWXURV 8QSUHFLRDIXWXURHVDFWXDOPHQWHGH\WLHQHXQDYRODWLOLGDGGH/DWDVDGHLQWHUpVOLEUHGH ULHVJRHVGH/D¿JXUDTXHVHSUHVHQWDPiVDEDMRSUHVHQWDHOUHVXOWDGRGHOVRIWZDUH'HULYD*HP SDUDYDOXDUXQDRSFLyQGHYHQWDHVWDGRXQLGHQVHDQXHYHPHVHVFRQXQSUHFLRGHHMHUFLFLRGH XVDQGRXQiUEROGHWUHVSDVRV(QHVWHFDVR t ¼ 0:25; pffiffiffiffiffiffi u ¼ e0:3 0:25 ¼ 1:1618; a ¼ 1; p¼ d ¼ 1=u ¼ 1=1:1618 ¼ 0:8607; 1 0:8607 ¼ 0:4626 1:1618 0:8607 (OYDORUGHODRSFLyQHVGH Resultado con DerivaGem: En cada nodo: Valor superior = Precio del activo subyacente Valor inferior = Precio de la opción El área sombreada indica dónde se ejerce la opción Precio de ejercicio = 30 Factor de descuento por intervalo = 0.9876 Intervalo de tiempo, dt = 0.2500 años, 91.25 días Factor de crecimiento por intervalo, a = 1.000 Probabilidad de un movimiento ascendente, p = 0.4626 Tamaño de un paso ascendente, u = 1.1618 Tamaño de un paso descendente, d = 0.8607 48.62 0.00 41.85 0.00 36.02 0.93 31.00 2.84 36.02 0.00 31.00 1.76 26.68 4.54 26.68 3.32 22.97 7.03 19.77 10.23 Tiempo del nodo: 0.0000 0.2500 0.5000 0.7500 &$3Ë78/2 RESUMEN (VWHFDStWXORGLRXQSULPHUYLVWD]RDODYDOXDFLyQGHODVRSFLRQHVVREUHDFFLRQHV\VREUHRWURVDFWLYRV PHGLDQWHHOXVRGHiUEROHV(QODVLWXDFLyQVHQFLOODHQTXHORVPRYLPLHQWRVHQHOSUHFLRGHXQDDFFLyQ GXUDQWHHOSHULRGRGHYLGDGHXQDRSFLyQVHULJHQSRUXQiUEROELQRPLDOGHXQSDVRHVSRVLEOHFRQ¿ JXUDUXQSRUWDIROLROLEUHGHULHVJRTXHFRQVLVWDHQDGRSWDUXQDSRVLFLyQFRQUHVSHFWRDODRSFLyQVREUH ODDFFLyQ\XQDSRVLFLyQFRQUHVSHFWRDODDFFLyQ(QXQPXQGRVLQRSRUWXQLGDGHVGHDUELWUDMHORVSRU WDIROLRVOLEUHVGHULHVJRGHEHQJDQDUODWDVDGHLQWHUpVOLEUHGHULHVJR(VWRKDFHSRVLEOHTXHODRSFLyQ 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ODUHGXFFLyQHQHOSUHFLRGHXQDDFFLyQHQODIHFKDGHH[GLYLGHQGRVRFDVLRQDGDSRUHOGLYLGHQGR'HHVWHPRGRVLVHDQWLFLSD XQGLYLGHQGRGHSRUDFFLyQ\VLHOSUHFLRGHXQDDFFLyQQRUPDOPHQWHGLVPLQX\HHQHOGHOGLYLGHQGRHQODIHFKDGHH[ GLYLGHQGRVHQWRQFHVVHGHEHUtDVXSRQHUTXHHOGLYLGHQGRHVGHSDUDORVSURSyVLWRVGHODQiOLVLV 9DOXDFLyQGHRSFLRQHVVREUHDFFLRQHV(OPRGHOR%ODFN6FKROHV\0HUWRQ Ejemplo 13.6 )RUPDGHXVDUODVIyUPXODVGH%ODFN6FKROHV\0HUWRQFXDQGRKD\GLYLGHQGRV &RQVLGHUHXQDRSFLyQGHFRPSUDHXURSHDVREUHXQDDFFLyQFRQIHFKDVGHH[GLYLGHQGRVGHQWURGH GRVPHVHV\GHQWURGHFLQFRPHVHV(QFDGDIHFKDGHH[GLYLGHQGRVVHHVSHUDTXHHOGLYLGHQGRVHD GH(OSUHFLRDFWXDOSRUDFFLyQHVGHHOSUHFLRGHHMHUFLFLRHVGHODYRODWLOLGDGHQHO SUHFLRGHODDFFLyQHVGHDQXDOODWDVDGHLQWHUpVOLEUHGHULHVJRHVGHDQXDO\HOSOD]RDO YHQFLPLHQWRHVGHVHLVPHVHV(OYDORUSUHVHQWHGHORVGLYLGHQGRVHV 0:5e0:092=12 þ 0:5e0:095=12 ¼ 0:9741 3RUORWDQWRHOSUHFLRGHODRSFLyQVHFDOFXODDSDUWLUGHODIyUPXODGH%ODFN6FKROHV\0HUWRQFRQ 6⫽⫺⫽.⫽U⫽ı⫽\7⫽ d1 ¼ lnð39:0259=40Þ þ ð0:09 þ 0:32 =2Þ 0:5 pffiffiffiffiffiffiffi ¼ 0:2020 0:3 0:5 d2 ¼ lnð39:0259=40Þ þ ð0:09 0:32 =2Þ 0:5 pffiffiffiffiffiffiffi ¼ 0:01012 0:3 0:5 8VDQGRODIXQFLyQ1250',67GH([FHOREWHQHPRV Nðd1 Þ ¼ 0:5800 \ Nðd2 Þ ¼ 0:4959 <GHDFXHUGRFRQODHFXDFLyQ HOSUHFLRGHODRSFLyQGHFRPSUDHV 39:0259 0:5800 40e0:090:5 0:4959 ¼ 3:67 R RSHUDFLRQDOPHQWHHVWRVLJQL¿FDTXHODIyUPXODGH%ODFN6FKROHV\0HUWRQVHSXHGHXVDUVLHPSUH\ FXDQGRHOSUHFLRGHXQDDFFLyQVHUHGX]FDHQXQDFDQWLGDGLJXDODOYDORUSUHVHQWHGHWRGRVORVGLYLGHQ GRVGXUDQWHHOSHULRGRGHYLGDGHODRSFLyQUHDOL]iQGRVHHOGHVFXHQWRGHVGHODVIHFKDVGHH[GLYLGHQGRV DODWDVDOLEUHGHULHVJR&RPRVHPHQFLRQyVHLQFOX\HXQGLYLGHQGRHQORVFiOFXORVWDQVRORVLODIHFKD GHH[GLYLGHQGRVRFXUUHGXUDQWHHOSHULRGRGHYLGDGHODRSFLyQ(OHMHPSORLOXVWUDORVFiOFXORV &RQHVWHSURFHGLPLHQWRıHQODIyUPXODGH%ODFN6FKROHV\0HUWRQGHEHUtDVHUODYRODWLOLGDGGHO FRPSRQHQWHULHVJRVRGHOSUHFLRGHODDFFLyQ\QRODYRODWLOLGDGGHOSUHFLRGHODDFFLyQHQVtPLVPR(Q ODSUiFWLFDSRUORJHQHUDOVHVXSRQHTXHVRQLJXDOHV(QWHRUtDODYRODWLOLGDGGHOFRPSRQHQWHULHVJRVR HVDSUR[LPDGDPHQWH6 6⫺' PXOWLSOLFDGRSRUODYRODWLOLGDGGHOSUHFLRGHODDFFLyQGRQGH'HVHO 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