THE BEHAVIOR OF OPTION S IMPLIED VOLATILITY INDEX: A CASE OF INDIA VIX

Verslas: Teorija ir prakika / Business: Theory and Pracice Issn 1648-0627 / eissn 1822-4202 hp://www.bp.vgu.l 2015 16(2): 149 158 doi:10.3846/bp.2015.463 THE BEHAVIOR OF OPTION S IMPLIED VOLATILITY INDEX: A CASE OF INDIA VIX Imlak SHAIKH 1, Puja PADHI 2 1 Deparmen of Managemen, Birla Insiue of Technology & Science, BITS Pilani, Pilani, 333031 Rajashan, India 2 Deparmen of Humaniies and Social Sciences, Indian Insiue of Technology Bombay, 400076 Mumbai, India E-mails: 1 imlak786@gmail.com (corresponding auhor); 2 pujapadhi@iib.ac.in Received 31 March 2014; acceped 05 May 2015 Absrac. The aim of his paper is o invesigae he behavior of implied volailiy in he form of day-of-he-week, year-of-hemonh and surround he expiraion of opions. The persisence of volailiy is modeled in ARCH/GARCH ype framework. The empirical resuls have shown significan effecs of he day-of-he-week, monh-of-he-year and day of opions expiraion. The posiive significan Monday effec explains ha India VIX rises significanly on he iniial days of he marke opening, and he significan negaive Wednesday effec shows ha expeced sock marke volailiy fall hrough Wednesday-Friday. Moreover, he sudy reveals he fac on opions expiraion, he evidence shows ha India VIX fall significanly on he day of expiraion of European call and pu opions. The March and December monhs have repored significan negaive impac on he volailiy index. Cerainly, his kind of resuls holds pracical implicaion for volailiy raders, and helps o he marke paricipan in hedging and pricing of opions. Keywords: implied volailiy, India VIX,, day-of-he-week, opions expiraion, monh-of-he-year, seasonal anomalies. JEL Classificaion: G11, G14. Inroducion Implied volailiy is he inversion of he Black-Scholes opion pricing model, and i is he funcion of opions raded price; ime-o-expiraion; risk-free-rae-of-ineres and dividend yield; srike price and spo price of underlying. Under he raional expecaion and marke efficiency, implied volailiy is he expecaion of he fuure sock marke volailiy. The marke paricipan rade ino opions o hedge he marke holdings and risk managemen, hence he expecaion of he invesors gauged ino he price of opions (call/pu) and he same raded price used o calculae he implied volailiy. Therefore, implied volailiy is he bes esimae of fuure realized reurn volailiy (Chrisensen, Prabhala 1998; Hansen 2001; Shaikh, Padhi 2013, 2014a, 2014b) for 30 days horizon (one monh opion). The informaion conen of implied volailiy as he marke s expeced volailiy has moivaed o consruc he volailiy index, which is ofen referred as he Invesor s-fear-gauge-index (Whaley 2000). The Chicago Board of Opions Exchange (CBOE) has sared calculaing implied volailiy index since 1993 known as VIX. The VIX is he premier baromeer of he invesor s senimen and he marke volailiy. The CBOE has calculaed more han 19 volailiy indices apar from VIX, which means he 30-day implied volailiy of differen securiies. The volailiy indices are he key measures of marke expecaion in near-erm calculaed based on he lised opion prices. From 2003, CBOE has sared calculaing VIX based on S&P 500 sock index, and also calculae volailiy of volailiy index (i.e. VVIX) based on he opions wrien on VIX index. The Naional Sock Exchange (NSE) of India limied has sared rading in opions from 2001 based on he S&P CNX Nify equiy index. India s firs volailiy index has been sared and calculaed since November 2007, and his volailiy index is available o he public on real ime basis. India VIX signifies he invesors senimen in near-erm for Copyrigh 2015 The Auhors. Published by VGTU Press. This is an open-access aricle disribued under he erms of he Creaive Commons Aribuion-NonCommercial 4.0 (CC BY-NC 4.0) license, which permis unresriced use, disribuion, and reproducion in any medium, provided he original auhor and source are credied. The maerial canno be used for commercial purposes. To link o his aricle: hp://dx.doi.org/10.3846/bp.2015.463

150 I. Shaikh, P. Padhi. The behavior of opion s implied volailiy index: a case of India VIX he nex 30 calendar days. India VIX (2007) uses he same mehodology as developed by CBOE for VIX (2003) mehodology. The marke paricipan, analys and academician have been inrigued by he volailiy index; he reason is ha sock indices and implied volailiy indices are negaively correlaed. The high level of implied volailiy index signifies owards oversold marke condiion. The correlaion beween sock index and volailiy index hovers in he rage of 0.70 o 0.90. Unlike he previous sudies on he seasonal anomalies in erm of sock reurns, exchange rae and fixed income securiies, he aim of our sudy is o analyze he behavior of implied volailiy in he emerging marke like India. The seasonaliy of India VIX (herein afer ) has been assessed like day-of-he-week, monh-of-he-year and opions expiraion effecs. There are quie good number of aemps (e.g. Dzikevičius, Sabužyė 2012; Marinkue-Kauliene 2013; Shaikh, Padhi 2013; Padhi, Shaikh 2014) ha deals wih he marke efficiency, sensiiviy of opions and forecasing, invesor senimen and informaion conen of opion prices. However, we do no find any sudy ha deals wih he opion volailiy and sylized naure of implied volailiy on Indian derivaives marke; hence, his is an aemp in his direcion o fill-up he gap. Moreover, recen sudies (e.g. Žilinskij, Rukauskas 2012; Lukaševičius e al. 2013; Evrim- Mandaci e al. 2013; Sádník 2013; Vilkancas 2014; Shaikh, Padhi 2014a, 2014b, 2014c) deal on he firm s performance and poenial reurn on invesmen; dynamics of sock price cycle; deerminans of sock marke dynamics in advanced and emerging economics; random walk and sock prices; porfolio opimizaion wih respec o omega funcion; volailiy index and forecasing performance of emerging marke s volailiy index. The sudies are in associaion wih he various issues on he sock marke developmen and porfolio opimizaion, our sudy idenifies he gap on he emerging marke volailiy index in erms of behavior of volailiy index as he expeced volailiy of he fuure sock marke realized volailiy. The formal sudies of seasonal anomalies are accessible in he works (e.g. Schwer 1989, 1990; French 1980; Gibbons, Hess 1981; Keim, Sambaugh 1984; Fleming e al. 1995). These sudies well documen he seasonaliy of sock index reurns and conclude he presence of seasonal anomalies. Some of he earlier sudies (e.g. Cross 1973; Jaffe, Weserfield 1985; Aggarwal, Rivoli 1989; Lakonishok, Levi 1982; Balaban e al. 2001) analyze he day-of-he-week effecs and heir empirical resuls has shown Monday and Friday effecs. Paricularly, hese sudies repor significan negaive reurns on Monday, and Friday reurns remain highes as compare o oher days. The monh of he year anomalies found in he works (e.g. Rozeff, Kinney 1976; Gulekin, M. N., Gulekin, N. B. 1983; Keim 1983; Lakonishok, Smid 1984; Jones e al. 1987; Ariel 1987; Tong 1992; Pandey 2002), he January effec happens due o several reasons indenified like, i occurs due o axmoivaed ransacion, marke paricipans inends o reduce heir ax expenses by closing heir bad posiions, reurns realized on small and large firms. Moreover, he lieraure evidences on he day-of-he-week and opions expiraion effecs are come up in he sudies (e.g. Fleming e al. 1995; Dowling, Muhuswamy 2005, Frijns e al. 2010). More recenly, Fleming e al. (1995) describes how implied volailiy index has been calculaed, moreover hey explain he behaviour of implied volailiy over seven years of period in he form of day-of-week and on he opions expiraion. Their sudy srongly suggess he presence of seasonaliy and ineremporal relaion beween implied volailiy and sock index reurns. In paricular, hey find an inverse and asymmeric relaion among fuure sock marke volailiy and sock reurns. Dowling and Muhuswamy (2005) examine he properies of Ausralian implied volailiy index (AVIX) in he form of seasonaliy and he informaion conen of AVIX as he predicor of fuure volailiy. They find srong seasonal anomalies and conemporaneous asymmeric relaion beween AVIX and sock reurns. Similarly, Frijns e al. (2010) revisis he sudy of Dowling and Muhuswamy (2005) and suppors he previous work for he more recen period from 2002 o 2006. A grea amoun of lieraure we have been explored in he previous paragraph bu very limied sudies are based on he seasonal anomalies of implied volailiy index, hence, his sudy is an aemp in his direcion. The aim of his paper is o explain he seasonal anomalies in he form of implied volailiy index (India VIX). The saisical properies have shown he presence of seasonal paern like day-of-he-week and opions expiraion effecs. Moreover, monh of he year effecs is also apparen. The empirical model has been framed in he form of simple OLS and ARCH/GARCH ype framework. The auocorrelaion and ARCH-es repors significan presence of auocorrelaion and heeroscedasiciy in he residuals, consequenly he regression models have been esimaed using AR-GARCH (1,1) specificaion. The empirical resuls show significan posiive Monday effec on he expeced marke volailiy, and significan negaive impac of he day of he opions expiraion. In addiions, here are some srong evidences on monh-of-he-year effec like March, May and December effecs. The res of he paper proceed as: Secion 1 deals wih he daa and mehodology and empirical model, Secion 2 repors he empirical resuls and las secion ends wih our conclusions. 1. Daa sources and empirical model Our daa sources consis of daily close of India VIX rerieved from he Naional Sock Exchange of India (NSE)

Business: Theory and Pracice, 2015, 16(2): 149 158 151 websie. The daa poins rages from November 1, 2007 o April 30, 2013, ha has resuled ino 1361 rading days. The reurns on he volailiy index has been obained as one day conemporaneous coninuously compounded logarihmic reurns R = ln ( ) ln ( 1 ). To isolae he effecs of day-of-he-week, expiraion of he opions and monh-of-he-year on expeced sock marke volailiy, a dummy ordinary leas squares (DOLS) by allowing an AR erm (i.e. AR-DOLS) has been srucured as follows. The regression model based on he day-of-he-week anomalies is expressed: R = 5 δidi + R 1 i= 1 γ + ε, (1) where: D i = 1, if Monday; = 0, oherwise i = 1: Monday, Tuesday, Wednesday, Thursday and Friday, and he behaviour of expeced sock marke volailiy surround he cycle of one monh opions expiraion is wrien, R = 2 ϕ jd j + R 1 j= 2 γ + ε, (2) where: D j = 1, he day of opion expiraion (i.e. las Thursday of he monh) = 0, oherwise j = 2, 1, 0, 1, 2. By combining he Eqs (1) and (2), R = 5 δidi + i= 1 2 ϕ jd j + γ R 1 + ε. (3) j= 2 Apar from he Eq. (3) we also develop he regression model ha accoun for he monh-of-he-year effecs on he implied volailiy, R = 12 πkdk + γ R 1 k= 1 + ε, (4) where: D k = 1, January; = 0, oherwise k = January, February,..., December. The Eqs (3) and (4) have been esimaed by aking ino accouns he problem of auocorrelaion and heeroscedasiciy. The Lagrange s Muliplier LM-es has shown significan presence of heeroscedasiciy, hence he esimaion framework is expressed in ARCH/GARCH. The AR-GARCH (1,1) model is srucured as, σ 2 = θ 0 + θε + θσ 2, (5) 1 2 2 1 where: θ 1 and θ 2 > 0 and θ 1 + θ2 1. The lieraure explains ha he assumpion of Gaussian (Normal) disribuion for he errors may no be appropriae for he GARCH model. Thus, for GARCH models Generalized Error Disribuion (GED) has been assumed. Where ε VIX / ω 1 ~ GED (0, σ 2, υ ). 1.1. Hypoheses of he models: (i) Day-of-he-week effecs: if day-of-he-week anomalies holds in he Indian capial marke han he slopes δi should be saisically differen from zero. Previous sudies on sock reurns anomalies found ou significan negaive Monday effec, hence in our model (he volailiy index) he slope of Monday should appear posiive and saisically significan. (ii) Opions-expiraion-effecs: Fleming e al. (1995) analyzes he behavior of expeced marke volailiy surround opions expiraion. I is expeced ha on he day of opions expiraion, marke posiions are cleared and ambiguiy regarding he marke also ge resolved, and invesors become cerain abou he marke condiion. Hence, he slope ϕ j on he day of opions expiraion should appear negaive and saisically significan. (iii) Monh-of-he-year effecs: if India VIX behaves sysemaically and hold an imporan paern based on he monhs, han he slopes π k should be differen from zero and remain significan. Generally speaking a he end of he year invesors clear heir marke posiions, hence i is expeced ha December and January monhs should have significan impac on he expeced sock marke volailiy. Moreover, he corporae resuls are due in he monh of July (Q1), Ocober (Q2), January (Q3) and April (Q4), hence he ambiguiy of corporae performance ge resolved in hese monhs, consequenly he slope for hese monhs should appear negaive as on hese monhs VIX reaches is normal level. 1.2. Saisical properies of India VIX In his secion some of he saisical properies of implied volailiy index have been presened based on he seasonaliy and opions expiraion cycle. Table 1 repors he summary saisics of daily closing of India VIX and is reurns. The summary saisics shows he mean, maximum, minimum and sandard deviaion of he India VIX. In addiions, he measures of auocorrelaion and auoregressive condiional heeroscedasiciy are calculaed up o hree lags. The analysis has been repored for full sample, calendar year wise and normal period. Now saring wih he Panel A, he average close of for he whole sample period found o be 27.74%, while for he normal period i is calculaed 21.11%. The average range of for he calendar years appears beween 21.82% (2010) o 39.34% (2008). The measure of cenral endency speaks ha implied volailiy was remain quie normal during he year 2010 13. Generally i is believed ha he reading of VIX beween 15 o 30% is good for he marke performance of he fuure realized volailiy. The average close of he

152 I. Shaikh, P. Padhi. The behavior of opion s implied volailiy index: a case of India VIX years 2008 09 violaes he normal range of VIX, i is due o he exreme naure of sock marke happened on he couner par of global financial crises ook place during 2008 09. The maximum and minimum values of o be observed 85.13% and 13.04% for he full sample, while for normal period i is 37.19% and 13.04%. The sandard deviaion of he enire sample (11.14) is more han he normal (4.70) period, and he range of volailiy of volailiy for he calendar years appears beween 4.20 (2012) o 11.43 (2008). The empirical resuls are repored for he enire sample and low volailiy (normal) period based on hese saisical properies. Panel B of he Table 1 shows he saisical measures of reurns (). The sock index and volailiy index are negaively correlaed, hence he average reurns on VIX expeced o be negaive. The means score of India VIX reurns for full and normal period appears respecively 0.0621% and 0 0.560%. The average reurn of he calendar years ranges beween 0.2510% (2009) o 0.2250% (2008). The volailiy of he reurns is found o be 7.39% for he enire daa poins and 5.16% for he low volailiy period. Once again, he volailiy of he volailiy index remains higher for he calendar years 2008 and 2009, which appears more han 10%. There are some evidences of auocorrelaion and heeroscedasiciy in he reurns of India VIX, hence in he empirical model an AR erm has been added o resolve he auocorrelaion problem, and he resuled residuals are modelled in ARCH/ GARCH framework o conrol he heeroscedasiciy. Table 2 summarizes he behavior of India VIX based on he day-of-he-week and opions expiraion. The average close of he India VIX on Monday (28.18%) is remain higher as compare o oher days, and he corresponding reurn on Monday also observed o be posiive (2.06%), ha implies implied volailiy becomes more volaile on he marke opening (see Fig. 1). The sandard deviaion of he close and reurns appears respecively 11.76 and 8.48, which is higher han he oher day s volailiy. The descripive saisic on he opions expiraion and surround he expiraion cycle (i.e. Thursday, he las week of he respecive monhs) he average close and reurns o be recorded respecively 27.47% and 2.76%, his numbers explains ha India VIX on he day of opions expiraion remains more normal and falls significanly. The paerns surround he opions expiraion show ha VIX increases prior o he expiraion and keeps on falling afer he scheduled expiraion. The volailiy of he volailiy also confirms hese paerns. Table 3 explains he changes in he India VIX based on he monh-of-he-year (also see Fig. 1). The Panel A and B shows he descripive saisics for VIX close and corresponding reurns. The average highes VIX close calculaed for Table 1. Summary saisics on India VIX Panel A VIX Close Saisics Full sample 2008 2009 20010 2011 2012 Normal period Mean 27.7433 39.3363 38.1386 21.8155 23.8358 19.7230 21.1084 Maximum 85.1300 85.1300 83.7100 34.3700 37.1900 28.9200 37.1900 Minimum 13.0400 23.2500 22.6900 15.2200 16.7300 13.0400 13.0400 S.D. 11.1430 11.4284 9.4200 3.8141 4.3453 4.1978 4.7003 Observaions 1361 246 243 252 247 251 832 Panel B VIX reurn Saisics Full sample 2008 2009 20010 2011 2012 Normal period Mean ( 100) 0.0621 0.2250 0.2510 0.1410 0.2021 0.2401 0.0560 S.D. 0.0739 0.1020 0.1026 0.0538 0.0588 0.0446 0.0516 r 1 0.230 a 0.245 a 0.377 a 0.092 0.008 0.121 c 0.061 c r2 0.000 a 0.056 a 0.007 a 0.084 0.042 0.033 0.054 c r 3 0.062 a 0.061 a 0.042 a 0.023 0.206 b 0.010 0.092 a ARCH(1) 240.07 a 32.51 a 44.57 a 0.00 20.02 a 0.02 30.51 a ARCH(2) 246.00 a 40.88 a 45.09 a 1.66 20.71 a 6.57 b 39.72 a ARCH(3) 247.48 a 41.93 a 44.88 a 1.81 22.36 a 6.71 c 41.14 a Observaions 1360 245 242 251 246 250 831 Noe: Table 1 shows he descripive saisics for daily close of India VIX and VIX reurns. The sample period consiss of 11/07/2007 o 04/30/2013. The auocorrelaion coefficien r is calculaed upo lag hree and he ARCH-LM es is also repored upo hree lags. Significan a a 1%, b 5%, c 10%.

Business: Theory and Pracice, 2015, 16(2): 149 158 153 Table 2. Summary saisics based on seasonaliy and opions expiraion Panel A Day-of-he-week VIX close Saisics Mon Tues Wed Thu Fri Mean 28.18 27.89 28.09 26.99 27.51 SD 11.76 11.36 11.04 10.33 11.21 Observaions 273 275 272 266 275 Panel B Day-of-he-week VIX reurn Saisics Mon Tues Wed Thu Fri Mean (x 100) 0.64 0.73 0.38 0.63 0.64 SD (x 100) 7.59 7.43 6.15 6.74 7.59 Observaions 273 275 272 266 275 Panel C VIX close surround opions expiraion Days surround expiraion Saisic 2 1 0 +1 +2 Mean 28.61 28.29 27.47 26.71 26.97 SD 11.91 11.39 10.97 10.06 10.67 Panel D VIX reurn surround opions expiraion Days surround expiraion Saisic 2 1 0 +1 +2 Mean (x 100) 1.14 1.39 2.76 2.14 0.57 SD (x 100) 9.19 8.66 7.46 6.75 7.37 Observaions 132 66 66 66 132 Table 3. Summary saisics based on monh-of-he-year Panel A Monh-of-he-year VIX close Saisics Jan Feb Mar Apr May Jun Jul Aug Sep Oc Nov Dec Mean 26.91 29.79 25.90 25.50 29.94 28.08 27.04 27.13 26.13 28.25 31.02 27.27 Maximum 54.41 50.65 44.44 57.88 83.71 62.05 61.73 63.58 39.56 70.27 85.13 55.26 Minimum 13.23 13.76 13.07 13.88 16.82 16.73 16.01 15.64 14.76 13.04 13.66 13.63 SD 11.16 10.24 8.23 10.86 12.06 9.53 10.40 10.39 7.32 13.08 16.08 10.64 Panel B Monh-of-he-year VIX reurn Saisics Jan Feb Mar Apr May Jun Jul Aug Sep Oc Nov Dec Mean (x 100) 0.67 0.09 0.46 0.44 0.36 0.20 0.06 0.05 0.21 0.10 0.04 0.71 Maximum 0.25 0.21 0.27 0.27 0.52 0.40 0.46 0.50 0.20 0.39 0.20 0.11 Minimum 0.29 0.22 0.27 0.23 0.65 0.23 0.47 0.29 0.11 0.19 0.28 0.17 SD (x 100) 6.25 6.05 6.58 7.00 11.23 7.75 8.82 9.86 5.64 7.03 6.38 4.80 Observaions 127 120 122 115 105 108 111 105 103 101 120 124

154 I. Shaikh, P. Padhi. The behavior of opion s implied volailiy index: a case of India VIX he monh of May and November are respecively 29.94% and 31.02%, and he average corresponding reurns found o be respecively 0.36% and 0.04%. This signifies ha for he whole sample he May and November monhs appears o be more volaile for he invesors. The SD s of he respecive monhs also appear o be high as compare o oher monhs. More paricularly, he monhs July (Q1), Ocober (Q2), January (Q3) and April (Q4) are he monhs in which he quarerly corporae resuls are scheduled o be announced, we can observe ha he average reurn on VIX recorded negaive for he April and July. This signifies ha VIX index is an efficien invesor s fear gauge index ha reflecs he corporae announcemens. On he oher hand, we record posiive reurns on he India VIX for oher monhs, plausible reason could be, more uncerainy abou he fuure corporae resuls and oher domesic economic facors. 2. Empirical resuls and discussion This secion presens he empirical resuls obained on he behavior of India VIX in he form of day-of-he-week, opions expiraion and monh-of-he-year effecs. The empirical resuls are presened using Eqs (3) and (4) based on AR DOLS and AR GARCH framework. The resuls are organized for enire daa poins and normal/low volaile period. Table 4 repors he AR DOLS/AR GARCH esimaes for he seasonal anomalies of India VIX, in which we es he day-of-he-week and opions expiraion effecs. The resuls are presened in four columns, he column (1) and (2) show he oupu on AR DOLS and AR GARCH for he full sample and column (3) and (4) for low volaile normal period. The column (1) shows significan posiive Monday effec and negaive opions expiraion effec. The slope of Monday effec appears 0.0235 (2.35%) and remains saisically significan a 1% level of significance. We do no find significan changes on India VIX on oher rading days. When we fi AR GARCH (1,1) he slope of Monday calculaed posiive 2.44%, his signifies ha on he marke opening he increases by 2.44%, hence invesors can plan heir profiable sraegy hrough volailiy rading. The pracical implicaion of his phenomenon explains ha (i) a rise in he VIX level implies he fear among he invesors on Monday, hence he opions seller can make profi by selling he opions a high rae of premium (ii) he marke uncerainy experienced Fig. 1. Seasonaliy of India VIX Noe: Fig. 1 speaks abou he seasonaliy of India VIX based on he day-of-he-week and monhof-he-year. The figure shows he plo of average weekly and monhly close of India VIX and corresponding VIX reurns.

Business: Theory and Pracice, 2015, 16(2): 149 158 155 by he invesors in holidays (i.e. SAT SUN) ge refleced on he Monday, and due o marke uncerainy invesors bid higher premium for he call/pu opions, ulimaely i resuls ino rises of volailiy of Black Scholes model. The AR GARCH (1,1) for Tuesday shows significan negaive impac on India VIX, he esimaed slope ( 0.129) explain ha afer Monday, once he marke coninuous is business VIX keeps on falling as he marke uncerainy resolved, and keeps on falling hrough Tuesday Wednesday Friday, bu no significanly. A his poin we can conclude ha India VIX hold day-of-he-week effecs paern unlike previous sudies have shown Monday significan negaive effec on sock indices. More paricularly, he markes expeced volailiy rises significanly on he marke opening and falls significanly on he oher days. The similar kinds of resuls are also obained for he normal period as shown in columns (3) and (4). Table 4 also repors he behaviour of expeced sock marke volailiy surround he expiraion of one monh European opions, which are cash, seled. Generally i is believed ha marke paricipan buys opions o hedge heir marke holding, marke players buy one monh opions o proec heir porfolio in near erm. The European opions can be exercised only on he day of scheduled expiraion; hence, invesor exercises heir righ o buy/sell of he underlying if he rade is profiable. The esimae of he slope ϕ 0 = 0.032, which is negaive and saisically significan a 1% level. The resul signifies ha on he day of opions expiraion India VIX falls significanly by 3.2%. This happen due o posiions cleared by he invesors and hey ake new marke posiions on he nex rading day. The slope of AR GARCH (1,1) also appears saisically significan, and he resuls on he normal period are also idenical wih he full sample. We do no find any significan movemen in he India VIX before and afer, from he day of opions expiraion. The AR GARCH parameers appears highly saically significan ha implies ha volailiy persis in he reurns of expeced sock marke volailiy index. The LB Q(12) saisic speaks ha resuls are no suffering from auocorrelaion. Finally, a his sage we can conclude ha India VIX holds some seasonal anomalies like day-of-he-week and opions expiraion effecs. This kind of predicive elemens can helpful o he volailiy raders for he risk managemen and profiable rade from he rading of opions. Table 4. OLS/GARCH esimaion of day-of-he-week and opions expiraion Full sample AR DOLS Full sample AR GARCH (1,1) Normal period AR DOLS Normal period AR GARCH (1,1) Variables (1) (2) (3) (4) Esimae p value Esimae p value Esimae p value Esimae p value 0.0235 0.0000 0.0244 0.0000 0.0230 0.0000 0.0256 0.0000 δ 2 0.0051 0.2910 0.0129 0.0000 0.0105 0.0131 0.0152 0.0000 δ 0.0052 0.2847 0.0040 0.1722 0.0029 0.5029 0.0026 0.5023 3 δ4 0.0044 0.3889 0.0026 0.3822 0.0007 0.8801 0.0010 0.7816 δ 5 0.0012 0.8014 0.0039 0.1898 0.0012 0.7838 0.0006 0.8743 ϕ 2 0.0076 0.4363 0.0048 0.4322 0.0065 0.4550 0.0101 0.1273 ϕ 1 0.0011 0.9405 0.0037 0.6802 0.0176 0.1587 0.0143 0.1394 ϕ 0 0.0320 0.0020 0.0264 0.0001 0.0276 0.0026 0.0228 0.0041 ϕ +1 0.0106 0.4954 0.0020 0.8304 0.0141 0.2665 0.0057 0.5846 ϕ +2 0.0105 0.2859 0.0141 0.0284 0.0249 0.0049 0.0198 0.0063 γ 0.2411 0.0000 0.0644 0.0168 0.0525 0.1331 0.0410 0.2370 θ1 0.2841 0.0000 0.0851 0.0011 θ2 0.5038 0.0000 0.8659 0.0000 Adj. R 2 0.08 0.05 0.05 0.04 LB Q(12) 17.41(0.096) 16.68(0.121) LB Q 2 (12) 7.76(0.745) 8.16(0.699) Noe: Table 4 repors he esimaion of Eq. (3). R = δid + i 5 i= a 2 ϕ jd + R j 1 j= 2 γ + ε. Where D i = 1, if Monday, oherwise zero; i = 1, Monday, Tuesday, Wednesday, Thursday and Friday. Where D = 1, he day of opion expiraion, oherwise zero; j = 2, j 1, 0, 1, 2. The value wih bold leer signifies saisically significan a 1%, 5% and 10% level of significance. The LB Q(12) and LB Q 2 (12) explain ha residual are free from auocorrelaion. Where ε VIX / ω 1 ~ GED (0, σ 2, υ).

156 I. Shaikh, P. Padhi. The behavior of opion s implied volailiy index: a case of India VIX Table 5 shows he resuls on monh-of-he-year anomalies, he evidences show significan March, May, June and December effecs. The column (1) repors he AR DOLS resuls in which only December monhs appears wih negaive significan slope. The column (2) reveals he slope of March 0.0085 (0.85%) and for he December i is 0.0087 (0.87%), boh he slopes are saisically significan a 5% level. While he slope of May appear wih posiive value 0.0092(0.92%), and significan a 5% level. These are he prima facie evidences of seasonal anomalies in he form of monh-of-heyear effecs on he expeced sock marke volailiy. One can explain ha India VIX rises significanly in he monh of May and fall significanly during March and December. Generally, he marke paricipans are uncerain abou he corporae earning declared quarerly (i.e. during July (Q1), Ocober (Q2), January (Q3) and April (Q4)). Hence, he slope of he monhs (July, Ocober, January and April) should appear negaive and for he res of he monhs i should be posiive. The slopes wih negaive sign are April, July and Ocober (for normal period) bu no saisically significan, his indicaes corporae scheduled announcemens deermine he expeced level of implied volailiy. In paricular, he slope wih negaive sign are (March, April, June, Sepember, Ocober, November, and December) bu only March and December appear saisically significan, his implies before declaraion of corporae earnings, resuls for he quarer 3 and 4 maer for he invesmen decisions. The marke paricipans ake ino accoun he Q3 and Q4 resuls in heir asses valuaion ha is refleced in he expeced marke volailiy. The res of he monhs (January, February, May, July and Augus) appears wih posiive slopes, only May shows significan posiive impac on, he plausible reason could be invesors remain more uncerain abou heir invesmen during he May monh, hence hey buy more and more hedge funds (opions) o proec heir porfolio, consequenly VIX level increases. We do no find any significan resuls for he low volailiy period only excep o he Ocober monh. Finally, he empirical resuls have suppored he presence of seasonal anomalies in he expeced sock marke volailiy. Table 5. AR DOLS/AR GARCH esimaion based on monh-of-he-year Full sample AR DOLS Full sample AR GARCH (1,1) Normal period AR DOLS Normal period AR GARCH (1,1) Variables (1) (2) (3) (4) Esimae p value Esimae p value Esimae p value Esimae p value π1 0.0071 0.1742 0.0017 0.6368 0.0027 0.6014 0.0004 0.9284 π 2 0.0007 0.8955 0.0029 0.4536 0.0024 0.6545 0.0047 0.2769 π 0.0052 0.3281 0.0085 0.0265 0.0056 0.2838 0.0055 0.2417 3 π 4 0.0036 0.5099 0.0039 0.3259 0.0040 0.4602 0.0051 0.2854 π5 0.0038 0.5097 0.0092 0.0279 0.0071 0.2371 0.0053 0.3161 π 6 0.0025 0.6594 0.0063 0.1032 0.0065 0.2780 0.0068 0.2224 π 7 0.0006 0.9188 0.0029 0.4523 0.0035 0.5529 0.0034 0.4909 π 8 0.0008 0.8921 0.0006 0.8861 0.0045 0.4534 0.0012 0.8301 π9 0.0022 0.7045 0.0022 0.6161 0.0061 0.3176 0.0034 0.5613 π10 0.0010 0.8606 0.0053 0.1996 0.0088 0.1531 0.0093 0.1024 π 11 0.0003 0.9556 0.0041 0.2859 0.0034 0.5822 0.0043 0.3911 π 12 0.0073 0.1086 0.0087 0.0178 0.0035 0.5594 0.0047 0.3970 γ 0.2341 0.0000 0.0994 0.0002 0.0737 0.0349 0.0788 0.0257 θ1 0.2508 0.0000 0.0747 0.0035 θ2 0.5169 0.0000 0.8598 0.0000 Adj. R 2 0.05 0.03 0.05 0.07 LB Q(12) 19.97(0.050) 24.61(0.013) LB Q 2 (12) 8.09(0.705) 6.84(0.812) Noe: Table 5 repor he esimaion of Eq. (4): R = 12 πkd + γ R k + 1 ε, where: D k = 1, January, oherwise zero; k = January, February,..., December. k= 1 The value wih bold leer signifies saisically significan a 1%, 5% and 10% level of significance. The LB Q(12) and LB Q 2 (12) explain ha residual are free from auocorrelaion. Where: ε VIX / ω 1 ~ GED (0, σ 2, υ).

Business: Theory and Pracice, 2015, 16(2): 149 158 157 Unlike he previous sudies, volailiy index also holds he seasonal componen in he form of day-of-he-week, opions expiraion and monh-of-he-year effecs. Our empirical evidences have shown significan impac of seasonal anomalies on he India VIX. This kind of predicive paern can help o he volailiy raders, policy makers and financial insiuions for poenial invesmen and financing decisions. Conclusions This sudy demonsraes he seasonal anomalies of he emerging marke s volailiy index in he form of day-ofhe-week, opions expiraion and monh-of-he-year effecs based on India VIX. To he bes of our knowledge, his is he firs aemp in he emerging markes like India ha analyzes he behavior of volailiy index based on seasonaliy. The resuls have been presened based on simple dummy OLS and condiional volailiy GARCH framework. The imporan finding of he sudy has shown significan posiive Monday effec on he expeced sock marke volailiy. The average VIX close of he Monday is recorded 28.18% wih posiive reurn 2.06%. The slope of he Monday appears posiive 2.44%, which signifies on he iniial marke opening VIX rises significanly by 2.44%, and i fall significanly on Wednesday. Unlike he previous sudies, India VIX also shows he posiive Monday effecs. Moreover, our findings repors significan negaive impac of he day of opions expiraion, he India VIX falls by 2.64% on he Thursday (he las week of he monh). Mos ineresing evidence on he monh-of-he-year effec reveals ha March and December have significan negaive impac on he India VIX, while he monh May repors posiive impac. There are some evidences of he effecs of quarerly announcemen of corporae earnings on he India VIX. The pracical implicaions of he empirical evidence are definiely helpful o he volailiy raders who rade in he opions. The seasonal anomalies of he India VIX provide an insigh for he pricing of fuure opions. 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