THE COST-OF-CARRY FORMULA TO DETERMINE FUTURES PRICES: HOW WRONG CAN YOU BE? *
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1 Jonal o Conmpoay I in in Rach Volm I No 03 Jonal o Conmpoay I in in Rach IN Onlin 03 Vol No Copyigh o h Acamic Jonal JCIR All igh HE CO-OF-CARRY FORLA O DEERINE FRE PRICE: HO RONG CAN YO E? * NORRE LINDE Nowgian niiy o cinc an chnology ARAC In hi no w analyz h picing o o ing h co-o-cay omla o min pic hn h nlying a i a ha o ock h ign o h picing o i baically min by h ign o h colaion bwn h ock n an ho-m ik- in a hn h nlying a i a zocopon bon h owa pic i an pp bon o h picing o Kywo: Co-o-cay Fomla; Fowa Pic; F Pic; Picing Eo JEL Claiicaion: G G3 INRODCION I i wll known i in a a miniic ha owa- an pic coinci g Cox Ingoll an Ro 98 How h i plny o mpiical inc howing ha in a ol anomly o im poibly caing owa- an pic o i Fowa pic can in hoy aily b min om h pic o a a ing h co-o-cay omla In many i no mo inocoy xbook in inanc h co-o-cay omla i alo o min pic h qion w lik o a in hi no i How wong can yo b i yo apply h co-o-cay omla o min pic?" hi no conib o h lia on conac in wo way Fi w i o bon o h pic whn i i ima by h co-o-cay omla h o bon inica ha h picing o can b lag conly w illa wih wo nmical xampl ing aliic paam al ha h picing o a likly o b mall ECONOIC E-P am a compl an abiag- mak wh aing ak plac in conino im olo chnical coniion h hn xi an qialn maingal ma Q wh pic poc o non-iin paying a a maingal whn icon wih h bank accon Fo analyical impliciy w am ha h olion o in a can b cib by a Gaian ion o h Hah Jaow an oon amwok Hah Jaow an oon 99 h hom ik- in a a om poin in im n Q i hn gin by wh i h inanano owa a o im pailing a im i a woimnional co o miniic olailiy ncion an i a wo-imnional co o * h iw o opinion xp in hi mancip a ho o h aho an o no ncaily lc h poiion iw o opinion o h io h ioial boa o h pblih Coponing aho nolin@nnno 39
2 Jonal o Conmpoay I in in Rach Volm I No ana ownian moion h accmla n on h bank accon o om im pio o i ln wh i h im al o a zo-copon bon maing a im an A bank accon wih im poi will a im ha al In h ollowing w coni wo nlying a; a non-iin paying ock wih pic an a zocopon bon maing a im wih pic n h qialn maingal ma Q h im pic < < a gin by wh i a wo-imnional co o miniic olailiy ncion an CO-OF-CARRY FORLA AND HE FRE PRICE L F b h owa pic yo can ag pon a im o liy a im an h coponing pic I i wll known g Cox al 98 an ila an Rkowki 997 ha ] [ Q E an ] [ Q E F h co-o-cay omla H E i h coniional xpcaion opao i h po pic o h nlying a an Q i a pobabiliy ma qialn o Q an i min by h Raon- Nikoym iai Q Q ih h am pic poc in hi no h pic o h ock i 0 0 F h pic i qal o h owa pic mlipli by a cocion o h aianc o accmla ho-m in a an h coaianc bwn n on h nlying
3 Jonal o Conmpoay I in in Rach Volm I No 03 a an h bank accon ha miniic in a whn impli ha F h wo pic alo coinci i 0 an hn hi qaliy can only hol i h n n Q on h nlying a in xc o h n on h bank accon an h n on h bank accon a ngaily cola h coponing pic o h zo-copon bon maing a im > i F o b g an naning o h qaniai inc bwn owa- an pic w a pciicaion o h olailiy ncion ha ha omim bn in h lia g iln an Pon 999 am ha an 0 wh an a conan L h b h xponn in : h i m o h i non-ngai o hi coni h an i alway non-ngai Fo > 0 alo h con m i x x x 0 x i h oc-o-gaiaion in a x man-ing poc an i poii no ha 0 0 an x > 0 o x > 0 h ncion x i ho poii imilaly bca an a non-ngai h con m o h ha h am ign a L L wh L i lag" Fo < 0 h owa pic F i an pp bon o h o in h pic by ing h co-o-cay omla Fo > 0 h i no pp bon o h o in h n ha ci paib L gi a lag o han L In pacic boh an ha moa al ypically l han an h picing o hby bcom laily mall illa h picing o wih a nmical xampl Am ha h conac ma in ix monh 05 an ha h iniial m c o in a i la an qal o 396% ih 00 hi m c gi a owa pic o F 0 h am 0 In ig w plo pic a a ncion o o h wo ca an h owa pic 4
4 Jonal o Conmpoay I in in Rach Volm I No 03 i alo plo o nc h hoizonal lin Claly h mol pic a aily mo picing o 0300 FIGRE h ig how h owa pic hoizonal lin a 0 an pic o in choic o Paam al a an 05 h o pic wih h p inclinaion i o 05 an 004 whil h con o pic i o 05 an 00 h a no calna c in h in a mol in hi no an o omwha impliy xpion w can ho wiho lo o gnaliy 0 L g b h ingan o h o ingal in h xponn in : g ha ha g 0 Fhmo g 0 o 0 h h ingan i poii 0 o 0 in h aa o ingaion an h xponn in i ngai F pic a ho low han owa pic an h owa pic i an pp bon o h picing o hi obaion i in lin wih h hoical icion in [?] hi pag 35 In ig w plo pic a a ncion o h inc bwn an o wo ca 00 an 0 owa pic a alo plo b hy canno b iingih om h pic o h ca 00 Fo aliic paam al h o ma by ing h co-o-cay omla o min pic i mall 4
5 Jonal o Conmpoay I in in Rach Volm I No FIGRE Fig : h ig how pic o in choic o Paam al a an 05 h high pic o lin a o 00 an h low o 0 Fowa pic a high han h pic b in h ig hy canno b iingih om h high pic Faco ha may b lan o xplaining any inc bwn owa- an pic ha w ha xcl om h analyi h incl anacion co collaal an conpay ik CONCLION In hi no w analyz pic in an conomy wih ochaic in a an a-picing mol o i o bon o h pic whn i i ima by h co-ocay omla h o bon a no igh implying ha h picing o can b lag h magni o h o pn on h paam o h mol How aliic paam al in combinaion wih h ho im nill xpaaion o conac on l han h o ix monh la o mo picing o illa hi ac wih nmical xampl o conac on a non-iin paying ock an on a zo-copon bon REFERENCE Cox J Ingoll J & Ro 98 h Rlaion bwn Fowa Pic an F Pic Jonal o Financial Economic Fnch K R 983 A Compaion o F an Fowa Pic Jonal o Financial Economic Hah D Jaow R & oon A 99 on Picing an h m c o In Ra: A Nw hoology o Coningn Claim Valaion Economica iln K & Pon A 999 Picing Ra o Rn Gaanin a Hah-Jaow-oon Famwok Inanc: ahmaic an Economic ila & Rkowki 997 aingal ho in Financialoling ping Vlag lin Hilbg 43
Journal of Contemporary Issues in Business Research USING THE COST-OF-CARRY FORMULA TO DETERMINE FUTURES PRICES: HOW WRONG CAN YOU BE?
Jonal o Conmpoay I in in Rach ING HE CO-OF-CARRY FORLA O DEERINE FRE PRICE: HO RONG CAN YO E? NORRE LINDE Nowgian niiy o cinc an chnology Dp o Economic Dagoll 749 onhim Noway ARAC In hi no w analyz h picing
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