06. Index Futures Pricing

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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

06. Index Futures Pricing

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