06. index futures pricing
TRANSCRIPT
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Index Futures Pricing
RAVI -IBA
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Index Futures
• Index Futures is a contract whoseunderlying asset is a stock marketindex.
• It is an agreement to buy or sell theportolio o stocks in the stockmarket index with in a speci!ed
uture period at a pre-determinedrate.
• "he rate# thus agreed upon or the
uture transaction is reerred to as
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• In any utures contract# the uture pricedepends upon the spot price# also knownas # as the cash price# o the underlying
asset and $aries with changes in cashprice o the underlying asset.
• In Index utures# the cash price o theunderlying asset is the $alue o theunderlying stock market index or themonetary $alue o the stock market index.
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• %hat is the relationship between theutures price o an index uture and the$alue o the stock market index &
• F'#t ( )' *+,
• %here F'#t ( utures price at t ( ' or
deli$ery at time t
• )' ( spot price at t ('• ( the percentage cost o carrying the
asset rom t(' to time t
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• "he cost o carry model by modi!ed as below
• F'#t ( )' *+, ( /i(+#0 1t *+, ri
• %here F'#t ( index utures price at t (' or the contract
expiring at time t
• )' ( )pot price at t( ' *stock index $alue at t ('• ( percentage cost o carrying the portolio o stocks rom t
( ' to time t
• 1i( the ith di$idend
• ri ( the interest rate on in$estment o di$idend rom its time
o receipt till time t
• It may be noted that /1i *+,ri represents the sum o
di$idends recei$ed rom stocks with interest earned onin$estment o such di$idends till contract maturity.
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• "he excess o the !nancing cost o$erthe di$idend income constitutes thenet cost-of-carry.
• "he utures price is expected to bee2ual to the spot index $alue plusthe net cost-o-carry.
• In other words# the utures prices isexpected to be at premium to thespot price# the premium being e2ual
to the net cost-o-carry.
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• Futures premium may be calculated by usingthe ollowing ormula.
• FP ( I x 3 *r 4 y5+'' 6 7 3d 589:6
• FP ( utures premium• I ( )pot price
• r ( annual percentage interest rate *!nancingcost
• y( annual ; di$idend yield on the indexportolio
• d( no. o days in the unding period
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'' *'.'=7 '.'>
•
(=>''7 '.''8>• (+8.??9
• "he 0ity utures rounded to +=. ence 0ity uturesprice should be =>+= *=>'' , +=.
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'' 7 3 +, *'. '.++:' 4 '.'?:' *8'589:6
• ( =>'' 7 +.''8> ( =>+8.??9 rounded oD to =>+=
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Valuation o )tock IndexFutures
• A stock index traces the changes in the $alue o ahypothetical portolio o stocks. "he $alue o autures contract on a stock# index may be obtainedby using the cost o carry model.
• For such contracts# the spot price is the Espot index$alue# the carry cost represents the interest on the
$alue o stock underlying index# while carry return isthe $alue o di$idends recei$able between the day
o $aluation and the deli$ery date.• Accordingly the indices are thought o as securities
that pay di$idends# and the utures contract $aluedaccordingly.
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)tock Index Futures 4 ase +
*example
• %hen the securities included in the index are notexpected to pay any di$idends during the lie o thecontract. ere we ha$e#
• F ( )' 7 ert
• %here F is the $alue utures contract# )' is the spot$alue index# r is the continuously compounded risk-reerate o return# and t is the time to maturity *in years.
•
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ase + contd.
• )pot )' ( 8'G' time to expiration @ ?9589:
• ontinuously compounded rate o return (ln*+.' ( '.'??
•Accordingly # F ( )' ert
• ( 8'G' 7 e*?9589: 7 '.'??
• ( 8'G' 7 e '.>'>+G+? 7 '.'??
• ( 8'G' 7 e '.'+9'8>??
• ( 8'G' 7 +.'+9+: ( 8+8G.G>
• "he $alue o contract ( 8+8G.G> 7 +'' (8#+8#GG>
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ase >
• %hen di$idend is expected to be paidby one or more o the securitiesincluded in index during the lie o
the contract. In the e$ent odi$idends expected to be paid onsome securities# the di$idend is
discounted amount is discounted topresent $alue terms and then therule o pricing securities with known
income is applied. "hus F ( *)' 4 Iert
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ase > contd.
• Assume that a market capitaliHation weighted indexcontains only three stocks A. B# as shown below. "hecurrent $alue o the index is +':9.
• alculate the price o utures contract with expirationin 9' days on this index i it is known that >: days
rom today# ompany A would pay a di$idend o Rs per share. "ake the risk ree rate o int. to be +:; pa.Assume the lot siHe to be >'' shares
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ase 8
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pen Interest
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pen Interest