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tone of the al instrumen ts in econo s have conti ives, altern ductible equ

ys have gon now area o last 30 year ts serve the and risk m pants. Pricin

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most accur Scholes mod uses ideas f involves cer nt volatility modern finan

ent place sp bel prize for the receipien

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dge portfoli ways be equ rmined by t the portfol io and the ac

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he most dyn e free enter nts have bec

mic conditi inued to pro native risk

ity.

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and put opt e financial m

rate level del is consid from the Bro rtain inheren during the t nce theory B pecially afte r economics nt of the pri

odel

this model a xpiry. In thi

mprising a l io will be co ual to the opt the Black-S lio mix has ct of mainta

LES FORM

namic area i rprise syste come comp ions. In tod oduce a mul

transfer p

mple busine s controlled ves have be portant econ

t tools by mportant in o tions prices market. The or to the dered as a v ownian mot nt assumptio tenure of th Black - Sch er 1997 whe s. Sadly, Fis

ize (Hull &

are current s s model pri long positio onstituted in

tion’s price Scholes form

to be const aining the p

MULA FOR

in the mode em. Due to plex and it i

day’s highl ltitude of ne products, ex

ess graduate by mathem ecome incre nomic funct facilitating options cont s. Many mo

certainity o level of m very elegant tion and oth ons such as he option, in holes – Mert en Robert M scher Black

Basu 2010

stock price, icing of an on in stock a n such a wa e at that time mula.As the tantly adjus portfolio in b

R OPTION

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ern corporat high volat s undergoin ly volatile ew products xchange tra

es were ma maticians and

easignly im tions of pric

the tradin tract. Option odels have b of these mod minimum de t piece of re her theories

log-normal nterest rate, ton differen Merton and k died in 199

).

exercise pri option invo and a short p ay that at an e. The propo e formula c sted. So the

balance is c

N PRICING

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e arena and tility and u ng constant and dynam s including m

aded funds

anaging the d computer mportant in f ce discovery

g of risks ns traders us been develo dels to predi eviation is esearch into s based on ‘

l distribution exercise pr ntial equatio Myron Sch 95, otherwis

ice, expecte olves constru position in a ny given poi ortion of sto onsists of c

portfolio is alled as hed

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ch Design research pap – Scholes - M ed price of o re it with the Scholes-Me

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subject. Re with 29/9/2 nt industries

of Analysis s based upo ive segment A has been c.

heses ere is no sig by taking hi ere is no im options price ack- Schole

rice.

ture Review er of studie and Scholes ithin the B

feasibility data from NS

re the impac Merton mod

significanc e.

per, real tim Merton mod option. We e calculated rton model

Methods an ased on rea egment. Ot al time data 2011. To m s has been

on applicati t. For the t used. Othe

gnificant dif istorical vol mpact of len

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es can be t s (1973) stu lack-Schole

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we are starti ations and c urity. MacB

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and

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Mervill (CEV) m Gonede In the m promine the Nob one of t Bhattac ideal co applicat Radu, T STOCK type: ∂V constan dividen Heston, Black-S differen provide elasticit solution arbitrag satisfied lookbac Ross. Scott M investig evaluate

1 MacBe models.

2

Blattb statistica

3

Bhatta Journal

4

Turcan p795-79

5

Heston Mar200 6 McKen model:e Journal,

le (1980)1 t model, whi es (1974)2 s modern finan

ent place sp bel prize for the receipien charya, M. (

onditions, e tions in the Turcan(2010 KS OPTION V/∂t + 1/2σ² nt and conti nd are depen , Steven L Scholes-Me ntial equatio e new solut

ty of varian ns reflect a ges. We pro d, put-call p ck calls hav

McKenzie, gation of th

es the prob

eth, J. D., an Journal of fi berg, R. C., a

al models for

acharya, M. of financial

n. (2010) An 99,

n, Steven L.; 7, Vol. 20 Iss nzie, S.; Gera

vidence from , 1(4), 2007.

ested the B ch assumes suggest vola

nce theory B pecially afte r economics nt of the pri 1980)3 in h xamined th 21st centur 0)4,in their NS” mentio ²S²²V/²S² + inue dividen ndent on tim L.; Loewen rton option on (PDE). B

ions for the nce (CEV) asset pricin ovide condi parity might

e infinite va

Dionigi Ge he Black-Sc bability of

nd Merville, L finance, 35(2) nd Gonedes, r stock prices

(1980). Emp and quantita

nals of the U

Loewenstein sue 2, p359-3 ace, D.; and m the Austral

lack – Scho volatility c atility of the Black - Sch er 1997 whe s. Sadly, Fis

ize (Hull & his paper Em he "Black-S

ry economy paper “BL oned that Pa

rS ∂V/∂S - r nds or in ev me.

nstein, Mar n valuation But this met

e Cox-Inger model, an ng bubbles,

itions to rul t not hold, A alue. We cla

erace, Zaff choles mod

an exchang

L. J. (1980). ), 285-301.

J. (1974). A s. Journal of

pirical proper ative analysis

University of

n, Mark; Wil 390, 32p d Subedar, Z.,

lian Stock Ex

oles model changes whe e underlying holes – Mert en Robert M scher Black

Basu 2010 mpirical prop

choles" me y.

LACK-SCH artial differ rV=0 is use valuate opt

rk; Willard n method i thod can ge rsoll-Ross ( nd the Hest dominated le out bubb

American c arify a long

far Subedar del: Eviden ge traded E

Tests of the B

A comparison f business, 4

rties of the B s, 15(5), 108

f Oradea, Eco

llard, Gregor

, (2007)An e xchange, Aus

against the en the stock g stock is st

ton differen Merton and k died in 199

).

perties of th ethod for pr

OLES MOD rential equa ed in evaluat ions in whi

d, Gregory involves de enerate mul

(CIR) term ton stochas d investmen bles on und calls have n standing co

r, (2007)6 nce from th

European ca

Black-Schole

n of the stabl 7(2), 244- 28

Black Scholes 81-1105.

onomic Scien

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mpirical inve stralasian Ac

constant el k prices chan

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Myron Sch 95, otherwis

he Black Sch icing, its fu

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in their pa he Australia all option b

es and Cox c

le and studen 80.

s formula un

nce Series, 2

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estigation of ccounting Bu

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f Financial St

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constant Multiple feasible) y are not licy, and soll, and

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models with allow for g the model

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tian. (2002) g & Finance,

2006), Option 31 Issue 1/2

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of-sample p y a GARCH

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produce rel itioner Bla but also redu on of GARC The Practitio urity groups titled Estim

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Empirical an index option

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nalysis of GA ns of India., D

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approac options option t

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Jul-2010 omputed atility by

(10)

Table 1 DATA Underlyin Exercise P Considera Expiry Da Historical Risk Free Dividend Time(Yea d1 N(d1) d2 N(d2) Expected Actual Pri Difference % Differe

Source: c

Table N 7 days. which i free rate in case option p price is case of

. Difference

ng Price Price ation Date ate l Volatility

Rate yield ars)

Price ice e in value ence

computed on t

No. 1 shows Expected p is based on e of return, T

of short per price. The d absent due INFY Call

e between a JP Assoc 67.00 70.00 9/22/201 9/29/201 43.56% 8.30% 0.86% 0.02 -0.67230 0.2507 -0.7326 0.2319 0.5871 0.9 0.3129 34.76667

the basis of re

difference rice has bee

5 factor viz Time to exp riod (7 days difference is to zero valu option i.e. R

an expected ciate RIL

786 780 11 9/2 11 9/2 23. 8.3 0.7 0.0 07 0.3 0.6 0.2 0.6 14. 18. 4.4 7 23.

ealtime data ob

between an en computed

z. Spot pric piry of the op s) there is si s m,aximum ue of N(d1) Rs. 1.9780

d and actual L

6.35 0.00 22/2011 29/2011

.71% 30% 76% 02 3073922 6207 2746 6082 .4184 .9 4816

.71217

btained from N

n expected a d by using U ce of stock,

ption, Annu gnificant di m in case of H

and N(d2), (27.6780-25

price of a c SBI

1,937.55 2,300.00 9/22/2011 9/29/2011 31.45% 8.30% 1.08% 0.02 -3.883767 0.0001 -3.9273 0.0000 0.0010 0.75 0.7490 99.86667

NSE Derivati

and actual pr Using the Bl Exercise pr ual volatility ifference be Hindalco ca while the co 5.7) 7.15%

call option e HINDALC 139.40 180.00 9/22/2011 9/29/2011 35.50% 8.30% 0.72% 0.02 -5.145161 0.0000 -5.1943 0.0000 0.0000 0.1 0.1000 100

ve segment.

rice of a cal lack – Scho rice of the o y of the stoc etween expe all option pr omperative

only .

expiring in 7 CO INFY 2,352 2,400 9/22/ 9/29/ 23.34 8.30% 1.85% 0.02 -0.35 0.360 -0.40 0.342 27.67 25.7 1.97 7.146

ll option exp oles – Merto

option, Ann ck. Table sh ected and ac rice where e difference i

7 days Y

2.60 0.00 /2011 /2011 4% % %

56009 09 052

27 780

80 647012

(11)

Table 2 days DATA Underlyin Exercise Consider Expiry D Historica Risk Free Dividend Time(Ye d1 Nd1 d2 Nd2 Expected Actual Pr Differenc % Differ

Source:

Table 2 of all se incresed differen highest with .24 SBI cal

2. Price diffe

ng Price Price ration Date Date

al Volatility e Rate d yield ears)

d Price rice ce in value

ence

: computed

2 indicates th elected und d because o nce between

in case of R 447 as a perc l option pri

ference betw

JP A 68.3 70.0 9/14 9/29 43.5 8.30 0.86 0.04 -0.1 0.42 -0.2 0.38 1.78 2.05 0.26 13.1

on the basis

hat increase erlaying sto f time value n expected RIL call opt

centage diff ce with 99.7

ween an exp

Associate 35 00 4/2011 9/2011 56% 0% 6% 4

9134995 241

797 899 807 5 693

3659

s of realtim

e in the time ock. Due to e of option a price and tion price w ference in In

77%.

pected and a

RIL 825.40 780.00 9/14/2011 9/29/2011 23.71% 8.30% 0.76% 0.04 1.2655302 0.8972 1.2175 0.8883 49.7800 56.15 6.3700 11.34461

me data obta

e to expiry b increase in and relative actual pric with Rs. 6.37

nfosys Call

actual price

SBI 1,826.75 2,300.00 9/14/201 9/29/201 31.45% 8.30% 1.08% 0.04 -3.53491 0.0002 -3.5987 0.0002 0.0058 2.55 2.5442 99.77255

ained from N

brings positi n time to exp

difference h ce. The diff

7 While low option is low

of a call op

HIN 5 145 0 180 11 9/14 11 9/29 35.5 8.30 0.72 0.04 11 -2.9 0.00 -2.9 0.00 0.00 0.25 0.24 5 97.8

NSE Deriva

ive impact o piry call op has been mi ference in t west in HIND

west with 6

ption expirin

NDALCO I

.10 2

.00 2

4/2011 9 9/2011 9

50% 2

0% 8

2%

4 0

915668

-018 0

9876

-014 0

053 4

5 5

447 3

88 6

ative segmen

on call optio ption price h inimized in the value h DALCO cal .44% and hi

ng in 15

INFY 2,351.65 2,400.00 9/14/2011 9/29/2011 23.34% 8.30% 1.85% 0.04 -0.209978 0.4168 -0.2819 0.3890 49.1178 52.5 3.3822 6.44228

nt.

on prices has been terms of has been

(12)

Table 3 30 days DATA Underlyin Exercise Consider Expiry D Historica Risk Free Dividend Time (Ye d1 Nd1 d2 Nd2 Expected Actual Pr Differenc % Differ

Source:

Table 4 43 days DATA Underlyin Exercise Consider Expiry D Historica Risk Free Dividend Time(Ye d1 Nd1 d2 Nd2 Expected Actual Pr Differenc % Differ

. The price s

ng Price Price ration Date Date

al Volatility e Rate d yield ears)

d Price rice ce in value

ence

: computed

4. The price s

ng Price Price ration Date Date

al Volatility e Rate d yield ears)

d Price rice ce in value

ence

difference b

JP Asso 58.30 70.00 8/29/20 9/29/20 43.56% 8.30% 0.86% 0.08 -1.3274 0.0922 -1.4544 0.0729 0.3018 0.45 0.1482 32.9333

on the basis

difference b

JP Asso 57.15 70.00 8/16/20 9/29/20 43.56% 8.30% 0.86% 0.12 -1.2060 0.1139 -1.3573 0.0873 0.4493 0.7 0.2507 35.8142

between an

ociate RI 75 78 11 8/ 11 9/

% 23

8. 0. 0. 45587 -0 0.

4 -0

0. 12 16 3. 33 21

s of realtim

between an

ociate RI 75 78 11 8/ 11 9/

% 23

8. 0. 0. 0949 -0 0. -0 0. 18 22 3. 29 16

expected a

IL 55.05 80.00 /29/2011 /29/2011 3.71%

30% 76% 08 0.343263

3657 0.4124

3400 2.5778 6

4222 1.38875

me data obta

expected a

IL 59.15 80.00 /16/2011 /29/2011 3.71%

30% 76% 12 0.177559

4295 0.2599

3975 8.8363 2.6

7637 6.65354

nd actual pr

SBI 1,938.60 2,300.00 8/29/2011 9/29/2011 31.45% 8.30% 1.08% 0.08 -1.752344 0.0399 -1.8440 0.0326 2.7623 6.5 3.7377 57.50308

ained from N

nd actual pr

SBI 2,196.95 2,300.00 8/16/2011 9/29/2011 31.45% 8.30% 1.08% 0.12 -0.285489 0.3876 -0.3947 0.3465 61.4032 55.05 6.3532 11.54078

rice of a cal

HINDALC 144.10 180.00 8/29/2011 9/29/2011 35.50% 8.30% 0.72% 0.08 -2.036193 0.0209 -2.1397 0.0162 0.1109 0.5 0.3891 77.82

NSE Deriva

rice of a cal

HINDALC 144.35 180.00 8/16/2011 9/29/2011 35.50% 8.30% 0.72% 0.12 -1.654948 0.0490 -1.7782 0.0377 0.3465 0.7 0.3535 50.5

ll option exp

CO INF 2,29 2,40 8/29 9/29 23.3 8.30 1.85 0.08 -0.3 0.37 -0.4 0.33 57.8 47.1 10.7 22.7

ative segmen

ll option exp

CO INF 2,39 2,40 8/16 9/29 23.3 8.30 1.85 0.12 0.12 0.54 -0.0 0.49 126. 81.2 45.0 55.4

piring in

Y 96.25 00.00 9/2011 9/2011 34% 0% 5% 8

22466 735

259 351 8701 15 7201 73616119

nt.

piring in

Y 99.30 00.00 6/2011 9/2011 34% 0% 5% 2 223442 487

009 996

(13)

Source:

Observ In the c achieve Associa differen followe expiry o Rs.0.14 option w associat Table 5 days.

DATA Underlyi Exercise Consider Expiry D Historica Risk Fre Dividend Time(Ye d1 Nd1 d2 Nd2 Expected Actual P Differenc % Differ

Source:

: computed

vations case of call ed in Hinda ates with Rs nce in price ed by JaiPra of 30 days, 482 and fol with time to tes which is . The price

ing Price Price ration Date Date

al Volatility e Rate d yield ears)

d Price Price

ce in value rence

: computed

on the basis

l option wi alco Indust s.0.3129. In e was achi akash Asso the least di lowed by H o expiry of 4 s Rs.0.2507

difference b

JP Assoc 67.00 70.00 9/22/201 9/29/201 43.56% 8.30% 0.86% 0.02 -0.67230 0.2507 -0.7326 0.2319 3.4868 3.9 0.4132 10.5948

on the basis

s of realtim

ith time to tries limited n the case of ieved in Hi ociates with

fference in Hindalco In

43 days, the and follow between an

ciate RIL 786 780 11 9/2 11 9/2 23.7 8.30 0.7 0.02 07 0.30 0.62 0.27 0.60 6.94 14.4 7.50 7 51.9

s of realtim

me data obta

expiry of 7 d which is f call option indalco Ind h Rs.0.2693

price was a ndustries lim

e least diffe wed by Hind expected an

L S

6.35 1

0.00 2

2/2011 9 9/2011 9

71% 3

0% 8

6% 1

2 0

073922

-207 0

746

-082 0

424 1

45 1

076 4

95571 2

me data obta

ained from N

7 days, the Rs.0.1000 n with time dustries lim . In the cas achieved in

mited with erence in pri dalco Industr

nd actual pri

SBI 1,937.55 2,100.00 9/22/2011 9/29/2011 31.45% 8.30% 1.08% 0.02 -1.795032 0.0363 -1.8386 0.0330 160.7120 165 4.2880 2.598788

ained from N

NSE Deriva

least diffe and follow to expiry o mited which se of call o JaiPrakash Rs.0.3891. ice was ach ries limited ice of a put o

HINDALCO 139.40 150.00 9/22/2011 9/29/2011 35.50% 8.30% 0.72% 0.02 -1.436585 0.0754 -1.4857 0.0687 10.6079 11.5 0.8921 7.757391

NSE Deriva

ative segmen

erence in pr wed by Jai of 15 days, t h is Rs.0.24 option with associates w .In the case hieved in Jai d with Rs.0.3

option expi

O INFY 2,352.6 2,400.0 9/22/20 9/29/20 23.34% 8.30% 1.85% 0.02 -0.3560 0.3609 -0.4052 0.3427 72.095 78.5 6.4047 8.1588

ative segmen nt.

rice was iPrakash the least 447 and

time to which is e of call iPrakash 3535 ring in 7

60 00 011 011 %

009 9

2 7 53

7 853503

(14)

Table 6 15 days DATA Underlying Exercise P Considerat Expiry Da Historical Risk Free Dividend y Time (Yea d1 Nd1 d2 Nd2 Expected P Actual Pric Difference % Differen

Source:

Table 7 30 days DATA Underlying Exercise P Considerat Expiry Dat Historical Risk Free R Dividend y Time (Yea d1 Nd1 d2 Nd2 Expected P Actual Pric Difference % Differen

6. The price s

g Price Price

tion Date ate

Volatility Rate yield ars)

Price ce e in value

nce

: computed

7. The price s

g Price Price

tion Date te Volatility Rate yield ars)

Price ce e in value

nce

difference b

JP Assoc 68.35 70.00 9/14/201 9/29/201 43.56% 8.30% 0.86% 0.04 -0.191349 0.4241 -0.2797 0.3899 3.2165 3.85 0.6335 16.45455

on the basis

difference b

JP Assoc 58.30 70.00 8/29/201 9/29/201 43.56% 8.30% 0.86% 0.08 -1.32745 0.0922 -1.4544 0.0729 11.5526 14.35 2.7974 19.49408

between an

iate RIL 825 780 1 9/14 1 9/29 23.7 8.30 0.76 0.04 995 1.26 0.89 1.21 0.88 1.98 9.75 7.76 5 79.6

s of realtim

between an

iate RIL 755 780 1 8/29 1 9/29 23.7 8.30 0.76 0.08 587 -0.3 0.36 -0.4 0.34 32.5 38.7 6.2 8 16.0

n expected a

L S

5.40 1

0.00 2

4/2011 9 9/2011 9

71% 3

0% 8

6% 1

4 0

655302

-972 0

175

-883 0

818 2

5 2

682 0

67385 0

me data obta

n expected a

L S

5.05 1

0.00 2

9/2011 8 9/2011 9

71% 3

0% 8

6% 1

8 0

343263

-657 0

4124

-400 0

5359 1

75 1

141 8

03639 4

and actual p

SBI 1,826.75 2,100.00 9/14/2011 9/29/2011 31.45% 8.30% 1.08% 0.04 -2.108033 0.0175 -2.1718 0.0149 267.6310 267 0.6310 0.23633

ained from N

and actual p

SBI 1,938.60 2,100.00 8/29/2011 9/29/2011 31.45% 8.30% 1.08% 0.08

0.759796 0.2237

0.8515 0.1973 170.3353 178.4 8.0647 4.520572

rice of a pu

HINDALCO 145.10 150.00 9/14/2011 9/29/2011 35.50% 8.30% 0.72% 0.04 -0.382229 0.3511 -0.4542 0.3248 6.8076 7.85 1.0424 13.27898

NSE Deriva

rice of a pu

HINDALCO 144.10 150.00 8/29/2011 9/29/2011 35.50% 8.30% 0.72% 0.08 -0.273911 0.3921 -0.3774 0.3529 8.8275 11.15 2.3225 20.8296

ut option exp

O INFY VALU 2,351 2,400 9/14/2 9/29/2 23.34 8.30% 1.85% 0.04 -0.209 0.416 -0.28 0.389 91.08 103.3 113.4

ative segmen

ut option exp

O INFY 2,296 2,400 8/29/2 9/29/2 23.34 8.30% 1.85% 0.08 -0.322 0.373 -0.425 0.335 148.3 140 8.366 5.975

piring in

Y UE

.65 0.00 2011 2011 4% % %

9978 68

19 90

26 5 4684341

nt.

piring in

Y 6.25 0.00 2011 2011 4% % %

2466 5 59

1 663

(15)

Source:

Table 8 43 days DATA Underlyin Exercise Consider Expiry D Historica Risk Free Dividend Time (Ye d1 Nd1 d2 Nd2 Expected Actual Pr Differenc % Differ

Source:

Observ In the ca in JaiPr Rs.0.89 was ach with Rs price w JaiPrak the leas followe cases Ja providin It is als and hin than the

: computed

8. The price s.

ng Price Price ration Date Date

al Volatility e Rate d yield ears)

d Price rice ce in value

ence

: computed

vations ase of put op rakash assoc 921. In the c

hieved in St s.0.6335 In was achieve kash Associa st differenc ed by Hinda

aiPrakash A ng least diff so observed ndalco Indus e historical

on the basis

difference b

JP Asso 57.15 70.00 8/16/20 9/29/20 43.56% 8.30% 0.86% 0.12 -1.2060 0.1152 -1.3505 0.0884 12.5859 11.15 0.2439 2.18744

on the basis

ption with t ciates which case of put o

ate Bank of the case of ed in Hind ates with Rs

e in price w alco Industr Associates an

fference from d that JaiPra

stries limited annual vola

s of realtim

between an

ociate R 75 78 011 8/ 011 9/

% 23

8. 0. 0. 0949 -0 0.

5 -0

0.

9 32

38 5. 44 14

s of realtim

ime to expir h is Rs.0.41 option with t f India whic

put option w alco Indust s.2.7974. In was achieve ries limited

nd Hindalco m the actual akash associ d has got a h atility of oth

me data obta

n expected a

RIL 59.15 80.00 /16/2011 /29/2011 3.71% .30% .76% .12 0.177559

.4295 0.2599

.3975 2.6161 8 .3839 4.16816

me data obta

ry of 7 days 132 and foll time to exp ch is Rs.0.63

with time to tries limite n the case of ed in JaiPra

with Rs.2.8 o Industries

l price. iates has go historical an her three com

ained from N

and actual p

SBI 2,196.95 2,100.00 8/16/2011 9/29/2011 31.45% 8.30% 1.08% 0.12 0.5476283 0.7080 0.4384 0.6695 46.5982 55 8.4018 15.276

ained from N

s, the least d lowed by Hi

iry of 15 da 310 and foll o expiry of d which is f put option akash assoc 8651. So it limited has

ot a historic nnual volati mpanies.

NSE Deriva

rice of a pu

HINDAL 144.35 150.00 8/16/201 9/29/201 35.50% 8.30% 0.72% 0.12 -0.17573 0.4302 -0.2990 0.3825 9.5349 12.4 2.8651 23.10565

NSE Deriva

ifference in indalco Indu ays, the least

lowed by Ja 30 days, the s Rs.2.3225 with time to ciates which can be seen occupied th

cal annual v ility of 35.5

ative segmen

ut option exp

LCO IN 2,3 2,4 1 8/1 1 9/2 23 8.3 1.8 0.1 8 0.1 0.5 -0. 0.4 10 79 29 5 37

ative segmen

n price was a dustries limi

t difference aiPrakash as e least diffe 5 and follo o expiry of

h is Rs.0.2 n that most he first two

volatility of % which ar

nt.

piring in

NFY 399.30 400.00 16/2011 29/2011

.34% 30% 85% 12 1223442 5487

0009 4996

8.4941

.4941 .3343038

nt.

achieved ited with e in price ssociates erence in owed by

43 days, 438 and tly in all ranks in

(16)

It can al all com prices m volatilit and actu Market State B limited Rs.24,7 It can b JaiPrak compan predicti

Table 9 Days to e

7 days 15 days 30 days 43 days

Observ From th values. decreas Black-S days to options average percent Black-S analysis

lso be seen mpanies in ca

mostly when ty, the Black ual value of

capitalizati Bank of Ind is Rs.2,68 725.59 crore be seen tha kash associa nies. So Bl ion for the c

9. Table sho expiry Ca ave 1.5 2.5 3.6 11.

vations he above an

In the Table sing as the Scholes-Me expiry incre

are mostly e percentag

age differen Scholes-Me

s of differen

that Infosys ase of histo n compared

k-Scholes-M f call and pu

ion of Infos dia is Rs. 1 8,533.75 cro

es and Mark at the avera ates is nea lack-Schole companies w

wing the av all option

erage differen 5243

56208 68346 .16276

nalysis it is f e 9, it can b

number of rton model eases. It can y lower than

e differenc nces compa

rton model nce in follow

s Limited w rical annual to other com Merton mod ut options o

sys Limited ,11,013.7 c ores, Marke ket capitaliz

age market arly 8.7 tim

es-Merton m with lower m

verage differ

nce in price

found that t e found that

days to ex in computa n also be fou n the avera e is not sim ared to put

for a call op wing section

which has hi l volatility a mpanies. Th del can prov of that stock

d is Rs. 1,4 crores, Mar et capitaliz zation of Jai t capitalizat mes lower

model seem market capi

rence in opt

% Avg dif 53.21 45.72 42.48 34.00

the expected t the percen xpiry increa ation of call und that the age differen milar in all option pric ption is high n makes ou

istorical vol and it has s he companie vide least di k.

46,532.7 cro rket capital zation of H iPrakash ass tion of Hin than the m ms to prov

italization.

tion prices o Put opt ff. average

3.90112 4.4685 5.553 9.2777

d values var ntage averag ses. This sh l option pric e average dif nce in rupee l four cases e. This show her than tha ur inference

atility of 23 hown the hi es which ha ifference be

ores , Mark ization of R Hindalco Ind

sociates is R ndalco Indu market capi vide least d

of five stock tion

e difference in 2

6

ry significan ge difference hows that t ces increase fference in r e prices for s as call op ws that the at of the put

more valid.

3.34% is the highest diffe ave higher h etween the e

ket capitaliz Reliance In dustries Lim Rs.15586.76 ustries Limi

italization o difference

k options

n price % 1 4 1 1

ntly from th e in prices k the accurac es as the nu rupee prices r put option

ption shows prediction t option. Re

.

e least of erence in historical expected

zation of ndustries mited is 6 crores. ited and of other in price

% Avg diff. 16.21 44.62 13.37 18.41

he actual keeps on y of the umber of s for call ns, while

(17)

Regress Model 1

a Predic

Mod 1

a Predic b Depen

Model

1

a Depen

Model 1

a Predic

Model 1

a Predic b Depen

sion Analys R .9

ctors: (Cons

del Regressi Residua Total

ctors: (Cons ndent Varia

(Constant) Days

ndent Varia

(i

R .939(a)

ctors: (Cons

Regression Residual Total

ctors: (Cons ndent Varia

sis: Regress

R R

905(a) .8

stant), Days

Sum Squa ion 47.0 al 10.3 57.4

stant), Days able: ECPRI

Unstanda

B -1.151 .248

able: ECPRI

ii) Regressi

R Square .881

stant), Days

Sum of 15.455 2.079 17.534

stant), Days able: EPPRI

ion Value o Square A

19 .

s

ANO

m of ares df 059 1 393 2 452 3

s

ICEDIF

Coeffic

ardized Coeffi

Std. Err 2.263 .082

ICEDIF

on Value o

Adjusted R .822

s

ANO

Squares d

2 3

s

ICEDIF

of Differenc Adjusted R Sq

729

OVA(b)

Mean 47.05 5.196

cients(a)

ficients S C

ror B

.

of Differenc

Square

OVA(b)

df 1 2 3

ce in Call Op quare St

2.

n Square F

9 9.

6

Standardized Coefficients

Beta

905

ce in Put O

Std. Error of 1.01955

Mean Squa 15.455 1.039

ption prices td. Error of the

27955

Si 056 .0

t

B -.508 3.009

ption price

f the Estimate

are F 14.8

s

e Estimate

ig. 095(a)

Sig.

Std. Err .662 .095

es:

e

Si 868 .0

ror

(18)

Model

1

a Depen

Mod 1

a Predic

Model 1

a Predic Regress depende indepen expiry. option p model. differen Similar Square to expir to expir Greek u B-S-M says tha increase So far a freedom call opt the case

(Constant) Days

ndent Varia

Model Sum

del R .973(a)

ctors: (Cons

Model Sum

R .323(a)

ctors: (Cons sion analysi

ent variable ndent variab

On the basi prices have Here R valu nce that say

relationship value .881 w ry. Based on ry is more st under the B model, thou at it is not e in time to anova is con m of denom

tion price an es.

Unstandar

B 2.428 .142

able: EPPRI

mmary: Re

R Squa .946

stant), Days

mmary: Re

R Squa .104

stant), Days is is a metho e, in this s ble while ca is of outcom e positive re

ue is .905 a ys that if tim

p has been o which indic n the regress

trong than t B-S-M mode

ugh when it necessary t expiry will ncern the tab minator for 5

nd 14.868 fo

C

rdized Coeffic

Std. Error 1.012 .037

ICEDIF

gression Va

are

s

egression V

are Adjus -.344

s

od to deal w study days all and put o

me of regres elationship

nd R Squar me to expir observed in cate close re sion value w the call opti el. Our stud

comes to pe that always

increase pu ble value fo 5 % level of for put optio

oefficients(

cients Sta Co

Bet

.93

alue of % D

Adjusted R .920

Value of %

sted R Square 4

with the relat to expiry option prices

ssion analys as it has b re .819 in ca ry decreases case of put elation ship we can say t on price. Th dy based on

ercentage d s reduction ut option pric

or 1 degree f significanc on price, the

(a)

andardized efficients

ta

9

Difference

Square

Difference

e Std.

16.7

tionship betw i.e. 7, 15, s are depend sis we can s been one of ase of Europ s call prem

option beha between the that put opti

his relations n regression difference in in time wil ce as the Ad of freedom ce is 18.5 a erefore null

t

B 2.399 3.856

in Call Op

Std. Erro 2.25733

in Put Opt

Error of the E 76026

ween indep 30 and 43 dent over th say that tim f the basic p

pean Call O ium decrea aviour with e put option ion price rel ship is also n analysis pr n the put opt

ll reduce pu djusted R Sq for numera and compute hypothesis

Sig.

Std. .139 .061

ption prices

or of the Estim

tion prices:

Estimate

pendent vari are consid he change in me to expiry

principle of Option price ases and vic h R value .93 n premium a lationship w explain by t rove the va tion prices a ut option p quare value ator and 2 d ed value is is accepted

Error 9 1

:

mate

:

able and dered as n time to

and call f B-S-M average ce versa. 39 and R and days with time theta (θ) alidity of analaysis rice and is -.344. degree of

(19)

Pair 1

Pair 1

Pair 1

C PP

CPD: C PPD: Pu Table v indicate accepte Hypoth H1: The Model Accept H2: Th actual o corelati H3: Bla option p

Recom

Me CPD 43. PPD 23.

CPD & PP

Paire

Mean CPD -

PD 20.7

Call price Av ut price Av value at 5% es that B-S-ed.

hesis can be ere is no sig by taking h ed.

ere is no im options pric ion between ack Schole M

price. Accep

mendation Traders nee price of put compared t

ean N 8525 4 1525 4

N PD 4

ed Differences

n Std. Deviation

15.77646

verage % D erage % Di % significanc

-M model is

concluded gnificant dif historical vo

mpact of len ce. Rejecte n time to exp

Merton mod pted

ns for the A ed to be cau t option as t to call optio

Paired

Std 7.9 14.

Paired Sa

Correlat .102

Paire

s

Std. Er Mean

7.88823

Difference w fference wi ce level for s identical f

in the follow fference bet

olatrility an

ngth of tim d/ Not Acc piry and pri del gives id

Application utious while

the averge v on.

Samples S

d. Deviation 95835

.45960

amples Cor

tion

ed Samples

rror

95% Co Differen

Upper

-4.4038

with Actual P ith Actual P r 3DF is 3.1

for both cal

wing manne tween the ex nd actual pr

me to expiry cepted bec ice.

dentical resu

of Model: e using Blac

variation in

tatistics

Std 3.9 7.2

rrelations

S .8

s Test

onfidence Inte nce

Low

7 45.80

Price Price

182 while c ll and put op

er:

xpected opti rice determ

y on the diff ause for bo

ult for both

k-Schole-M the prices a

d. Error Mean 97917 22980

Sig. 898

t rval of the

er

0387 2

computed t ption pricin

ions price c ined by ma

fference betw oth call and

call option

Merton mode are higher in n

t

df Si (2

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2.624 3 .0

value is 2. ng hencefor

computed by arket forces

tween expec d put there

price as we

el for predic n case of pu

ig. 2-tailed)

tio Std. Erro r Mea n

079

624 that rth H3 is

y B-S-M s. Result

cted and is stong

ell as put

(20)

Conclu On the b prices o stock o results volatilit increase Black-S options From th options Black-S model w is driven investor Indian s

Refern Black, efficien Black, F

politica

Blattber as sta http://dx Burasch markets Chen, R Empiric http://dx Copelan New Yo

Traders sho nearer as th in number o are less wil actual value Traders sho seem to pro

usion basis of the of stock opti options. The of Black-S ty and the m es as the n Scholes-Me

.

he research trading Scholes-Me would lead t

n by large n rs. Therefor stock option

ces

F., & Scho ncy. Journal

F., & Schol

al economy,

rg, R. C., & atistical m

x.doi.org/10 hi, A., & Ja s. Review of

R., & Palm cal Eviden

x.doi.org/10 nd, T., Wes ork: Pearson

ould avoid u he relative /

of days to e ll lead to hig

es of call an ould use Bla ovide better

real time da ions have be e difference choles-Mer market capit number of rton model

h it is found in NSE I rton model the possibil number of m

re there is n n products.

oles, M. (1

l of finance,

les, M. (197

81(4),

637-& Gonedes, models for

0.1086/2956 ackwerth, J.

f financial s

mon, O. (20 nce. Review

0.1007/s111 ston, J., & S

n Addison W

using Black percentage expiry. Usin gh percentag nd put optio ack-Scholes

results.

ata collected een compute e between t rton model alization of days to ex

provides b

d that the fe India mark seems to va lity of price macro econo need to brin

1972). The

, 27(3), 399

73). The pr -659. http:// J. (1974). A

stock p 634 . (2001). Th

studies, 14(2

005). A No

w of Quan

156-005-633 Shastri, K. (2

Wesley.

k-Scholes-M difference ng Black-Sc age differenc ons

s-Merton mo

d from the d ed and com the expecte have certai f the stock. I xpiry decrea

better result

feasibility o ket is ver ary highly fr differencia omic factors ng more ref

valuation 9-417. http:/

ricing of op /dx.doi.org/ A comparis prices. Jou

he price of 2), 495-527 on-Paramet

ntitative Fi

33-2 2005). Fina

Merton mode in prices inc holes-Merto ce in prices

odel when d

derivative se mpared with t ed and actu

in relations It is also fou ases and it ts for call o

of Black-Sch ry low. A rom the actu ation in Indi

s as well as form in this

of option //dx.doi.org/ ptions and c /10.1086/26 son of the s

urnal of

a smile: He . http://dx.d tric Options

nance and

ancial theory

el when day creases high on model w between th

days to expir

egment of N the actual ca al values w hip with th und that the also has b options whe

holes-Merto As the pri

ual values. A an derivativ the emotion model to m

contracts in /10.2307/29 corporate lia 60062

table and st

business,

edging and doi.org/10.1 s Pricing M

d Accountin

ry and corpo

ys to expiry hly with the when days to

he expected

ry are more

NSE, the call all and put p were found he historica

difference i been observ en compare

on model f ices predic At present u ve market as ns of the tra make it feas

n a test of 978484 abilities. Jo

tudent distr

47(2), 2

spanning in 1093/rfs/14. Model: The

ng, 24(1),1

orate policy

are e decrese

o expiry and

e, as they

l and put prices of and the l annual in prices ved that

d to put

for stock cted by

sing this s market ders and sible for

f market

urnal of

ributions 244-280.

n option 2.495 eory and

115-134.

(21)

Das, S.

Journal

http://dx Draper, Duffie, jump-di http://dx Dumas, tests. Jo

Finnerty

of finan

Galai, D

of busin

Geske, 63-81. h Geske, and “B http://dx Hull, J.

Journal

Johnson

financia

Macbet option http://dx MacBet valuatio http://dx Naik, V with http://dx Peiro, A

econom

www.ns

R., & Sund

l of

x.doi.org/10 , N., & Smit D., Pan, J., iffusions. x.doi.org/10 , B., Flemin

ournal of fin

y, J. E. (197

nce and qua

D. (1977). T

ness, 50(2),

R. (1979). http://dx.do R., R, Roll. Biases” in t x.doi.org/10

, & White,

l of finance

n, H., & Sh

al and quan

th, J. D., & pricing x.doi.org/10 th, J. D., &

on m

x.doi.org/10 V., & Lee M

discontinu x.doi.org/10 A. (1994). T

mics, 4(6), 43

seindia.com

daram, R. K

financial

0.2307/2676 th, H. (1981 , & Singleto

0.1111/1468 ng, J., and

nance, 53(6

78). The Ch

antitative an

Tests of mar 167-197. h The valuati oi.org/10.10

., & Shastri the Black-S 0.1111/j.154 A. (1987).

42(2), 281–

hanno, D. (1

ntitative ana

Merville, L g mode 0.1111/j.154 &Merville, models.

0.1111/j.154 M. (1990). G uous retu

0.1093/rfs/3 The distribu 31-439. http m

K. (1999). O

and

6279 1). Applied R

on, K. J. (20

Econome

8-0262.001 Whaley, R ), 2059-210 hicago Boar

nalysis, 13(1

rket efficien ttp://dx.doi. ion of comp 16/0304-40 , K. (1984). Scholes mo 40-6261.19

The Pricin –300. http:// 987). Optio

alysis, 22(2)

L. J. (1979).

el. Jour

40-6261.19 L. J. (1980

Journal

40-6261.19 General equ urn. Revi

3.4.493 ution of sto

p://dx.doi.or

Of Smiles an

quantitati

Regression

000). Trans

trica,

64 R. E. (1998

06. http://dx rd Options 1), 29-38. ncy of the C

.org/10.108 pound optio 05X(79)900

. Over-the-c odel: A no 83.tb02295 ng of Optio /dx.doi.org/ on pricing w ), 143-151.

An empiric

rnal of

79.tb00063 0). Tests of

of

80.tb02157 uilibrium: P

iew of

ck returns: rg/10.1080/

nd Smirks:

ive ana

Analysis (2

sform analy

68

). Implied x.doi.org/10 Exchange a

Chicago Boa 86/295929

ons. Journa

22-9 counter opti ote. Journa

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f financ

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finance

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07/2330709 Black-Scho 5), 117

nd Cox cal

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he market p

, 3, 4

e. Applied f

spective. 211-239.

Wiley. or affine 43-1376.

mpirical 83

Journal

Journal

ics 7(1),

rotection 71-1277.

latilities. 68.x

ournal of

9 oles Call 73-1186.

ll option 285-301.

portfolio 493-521.

Figure

Table 1. Differencee between aan expected d and actual price of a ccall option eexpiring in 77 days
Table 22. Price diffe
Table 330 days. The price s difference bbetween an  expected and actual prrice of a calll option exppiring in
Table 5days. . The price difference bbetween an expected annd actual priice of a put ooption expiring in 7
+5

References

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