Asymmetric Stochastic Volatility in Nordic Stock Markets

Transcription

1 Proceedings 5-7 January, 017; Rome, Ialy Asymmeric Sochasic Volailiy in Nordic Sock Markes Aycan Hepsağ 1 Absrac The goal of his paper is o invesigae he asymmeric impac of innovaions on volailiy and he relaionship beween he sock reurn and volailiy dynamics in he case of Nordic sock markes using he framework of asymmeric sochasic volailiy models. The empirical findings provide srong evidence of asymmery, significan and high volailiy persisence in he sock markes of he Nordic region. The mos ineresing and differen resuls obained from he presen paper are ha here are boh of a low variabiliy of volailiy and a high volailiy persisence in he sock markes of Denmark, Finland, Norway and Sweden. Addiionally, he sock markes of he Denmark, Finland, Norway and Sweden, which have leverage effec, have lower variabiliy of volailiy and in hese markes he fuure volailiy is relaively cerain. Keywords: Asymmeric Sochasic Volailiy, MCMC, Nordic Sock Markes JEL Codes: C11, G10 1 Deparmen of Economics, Faculy of Economics, Isanbul Universiy, Isanbul, hepsag@isanbul.edu.r 1

2 Asymmeric Sochasic Volailiy in Nordic Hepsağ 1. Inroducion The volailiy of asse reurns is sill one of he major issues of financial economerics. The undersanding of volailiy in sock markes maers because volailiy has an imporan role in opion pricing, porfolio managemen and asse allocaion. I is well known ha sock marke volailiy, defined as he condiional variance or sandard deviaion of sock reurns, changes over ime. The relaionship beween a sock marke index (or a sock price) and is volailiy has been sudied widely in marke economies and also i is well documened ha a negaive shock increases he sock marke volailiy more han he posiive shock a he same magniude and his circumsance is described as asymmery. As menioned in Cappiello e al. (006), asymmeric volailiy could be handled in wo ways: leverage effec and volailiy feedback effec. The leverage effec is described as he noion ha a fall in sock price causes an increase in he deb-equiy raio (financial leverage) of he firm and he risk (volailiy) of he firm increases righ afer (Selçuk, 005). On he oher hand, volailiy feedback effec is specified as he noion ha once volailiy is priced, an expeced increase in volailiy enhances he required reurn on equiy, leading o an urgen sock price downfall. The main difference beween leverage effec and volailiy feedback effec is he direcion of causaliy beween sock reurns and volailiy. In he leverage effec, he direcion of causaliy is running from he sock reurns o volailiy whils he volailiy feedback effec implies ha he causaliy running from he volailiy o sock reurns. The main goal of he presen paper is o invesigae he asymmeric impac of innovaions on volailiy and he relaionship beween he sock reurn and volailiy dynamics in he case of Nordic markes, which have been researched far less han he oher markes, using univariae asymmeric sochasic volailiy approach. Alhough sock reurn and is volailiy in advanced markes have been well sudied, here exis relaively few conribuions o reurn and volailiy dynamics in Nordic region. The volailiy in he Nordic sock markes ends o be relaively higher in comparison wih advanced sock markes. Also, he rading volume and he number of raded firms of he Nordic sock markes are narrow bu are growing a a greaer rae han advanced markes. The presen paper differs from he exan lieraure in he following way: o he bes of our knowledge, i is he firs sudy ha examines he sock reurns and volailiy dynamics and asymmeric innovaions o volailiy in he sock markes from he Nordic region using he framework of he asymmeric sochasic volailiy models. The remainder of he paper is organized as follows: in secion we discuss he lieraure review and in secion 3 we presen he economeric mehodology. Secion 4 conains he daa descripion and empirical resuls of he sudy. The 5 h and las secion includes conclusions.. Lieraure Review As menioned above, here exis fewer empirical sudies on he Nordic region and he empirical findings on asymmeric volailiy are confliced. Booh e al. (1997) invesed he volailiy in he sock markes of Nordic region, i.e. Denmark, Finland, Norway and Sweden using EGARCH model and hey reached he findings on he persisency of volailiy and also findings on asymmeric impac of innovaion on volailiy for he Nordic sock markes. Kulp-Tag (007a) also explored he volailiy in he sock markes of Nordic region, i.e. Denmark, Finland, Norway and Sweden using EGARCH model and repored ha negaive

3 Proceedings 5-7 January, 017; Rome, Ialy innovaions have a higher impac on volailiy han posiive innovaions, so he asymmeric volailiy exiss in Nordic sock markes. Kulp-Tag (007b) examined he volailiy in he sock markes of Nordic region, i.e. Denmark, Finland, Norway and Sweden using GARCH model and is exensions and found ou weak evidence of asymmeric volailiy in Nordic sock markes. Urooj e al. (009) used ARCH and GARCH models in heir empirical sudy and found ou he persisency of volailiy and volailiy clusering in he sock marke of Finland. 3. Economeric Mehodology A general represenaion of a volailiy model for a saionary series of reurns r akes he form: r y y (1) where is i.i.d. random variable wih zero mean and uni variance and deerminisic of sochasic random process which depends on he pas values of reurns. is eiher a denoes eiher a consan or an auoregressive variable wih a parameer close o zero and y denoes a sochasic process i.e. demeaned reurns. The main issue is relaed o which process follows; if is expressed as a deerminisic funcion of lagged (squared) reurns, we are wihin he ARCH models (Engle, 198; Bollerslev, 1986), which have achieved widespread populariy in applied empirical research (Pellegrini and Rodriguez, 007). On he oher hand, when is expressed as a sochasic funcion of an unobserved laen variable, we inroduce he sochasic volailiy model proposed by Taylor (1986). Sochasic volailiy models are aracive because hey are close o he models ofen used in Financial Theory o represen he behaviour of financial prices and heir saisical properies are easy o derive using well-known resuls on log-normal disribuions (Broo and Luiz, 004). The main relaive advanages of sochasic volailiy models are discussed by Carnero e al. (004) and also Das e al. (011) emphasise ha sochasic volailiy models have he capabiliy o provide one-sep-ahead predicion and o beer harmonise wih excess kurosis and leverage effecs compared o GARCH models. The sochasic volailiy model is represened as he following form; y exp h / h h 1 where h is laen sochasic volailiy which equals o ln. is i.i.d. random variable wih zero mean and uni variance and also is i.i.d. random variable wih zero mean and variance, independen of. indicaes he volailiy (variabiliy) of volailiy and measures he uncerainy abou fuure volailiy. The parameer is described as a measure of he persisence of shocks o he volailiy. There is such a rade-off relaionship beween and ; namely when approximaes o one, ends o approximae o zero. () 3

4 Asymmeric Sochasic Volailiy in Nordic Hepsağ As menioned Ghysels e. al. (1996), i can be noiced ha if and are allowed o be correlaed wih each oher, he model can pick up he kind of asymmeric behaviour. Indeed a negaive correlaion beween and induces a leverage effec. Harvey and Shephard (1996), propose a specificaion which considers conemporaneous dependence and allows he correlaion beween and as corr,. In oher respecs, Jacquier e. al. (004) propose a specificaion which considers ineremporal dependence and allows he correlaion beween and 1 as corr, 1. Asai and McAleer (005) presen a specificaion ha capures asymmery in dynamic leverage model hrough he direc negaive correlaion beween reurns and volailiy innovaions as he following form: y exp h / h 1 E h ~N0,1 ~N0, (3) We could describe his ype of asymmery, namely when 0, as he Dynamic Leverage Sochasic Volailiy model. When 0, here exiss no dynamic leverage beween he innovaions o reurns and volailiy (Asai and McAleer, 005). 4. Daa and Empirical Resuls The daa se involves daily closing price indices of four Nordic counries for he period from January, 009 o Sepember 30, 016 (pos-008 Global financial crisis period) and consiss of sock indices of Denmark (KFX Index), Finland (HEX Index), Norway (OBX Index) and Sweden (OMX Index). The source of daa is he Bloomberg Daabase. Finally, we calculae he ln P P 100 sock reurns from he sock marke indices of he seleced counries using he formula where P denoes he value of he sock price indices of each counry a ime. The descripive saisics for he sock reurns of each sock marke indices are repored in Table 1. 1 Table 1: Descripive Saisics of he Sock Reurns Denmark Finland Norway Sweden Mean Median Maximum Minimum Sd. Dev Skewness Kurosis Jarque-Bera Probabiliy Observaions

5 Proceedings 5-7 January, 017; Rome, Ialy All of he sock reurn series have small mean and he sandard deviaions of he sock reurns are greaer han he means of sock reurns, indicaing ha he sock marke of Nordic counries follow a random walk process. Addiionally, he sock reurn series have negaive skewness and he excess kurosis for each is significanly posiive, indicaing ha hey have heavy ails relaive o he normal disribuion, which is also ypical in hese financial daa (Ding and Vo, 01). The sochasic volailiy models can be esimaed using differen echniques. The mos popular approaches are he quasi-maximum likelihood mehod as proposed by Harvey and Shephard (1996) and he Markov Chain Mone Carlo (MCMC) mehod which was inroduced by Jacquier e. al. (1994). In his sudy, we employ he MCMC approach for esimaing Dynamic Leverage model and we use he code provided by Yasuhiro Omori (1) uilized for he WinBUGS sofware. ~Inverse-Normal -10,1, In MCMC esimaion sraegy, we deermine he prior values as ~Inverse-Uniform -1,1, ~Inverse-Gamma.5,0.05 and ~Inverse-Bea 0,1.5 following Yasuhiro Omori and MCMC sampler is also iniialized by seing he values 9, 100, 0.95 and 0.4 following also Yasuhiro Omori. We obain he poserior means of he coefficiens ignoring he firs ieraions and uilizing he following ieraions in all cases. The poserior means of parameer esimaes wih 95% poserior credibiliy inervals are presened in Table. The esimaion resuls shown in Table indicae ha he volailiy persisence coefficiens are in beween (Denmark) and (Norway) and he empirical findings imply ha here exiss a remarkable volailiy persisence and srong evidence of volailiy clusering in he Nordic sock markes. Table : The Esimaion Resuls of he Poserior Means of Parameers ˆ ˆ ˆ ˆ Denmark Finland Norway Sweden * 0.939* * 0.63* (0.097) (0.013) (0.059) (0.031) [ ] [ ] [ ] [ ] * 0.978* * 0.164* (0.134) (0.006) (0.065) (0.01) [ ] [ ] [ ] [ ] -8.75* 0.987* * 0.169* (0.194) (0.004) (0.050) (0.016) [ ] [ ] [ ] [ ] * 0.973* * 0.05* (0.130) (0.006) (0.046) (0.03) [ ] [ ] [ ] [ ] Noes: The poserior sandard deviaions and 95% poserior credibiliy inervals are presened in he parenheses and brackes, respecively. * denoes saisical significance a he 5% level. The poserior means of he coefficien ˆ, indicaing he correlaion beween innovaions o reurns and volailiy, are negaive and saisically significan a he 5% level for all of Nordic 5

6 Asymmeric Sochasic Volailiy in Nordic Hepsağ sock markes. The smalles value is for Denmark and he highes value is for Norway. I can be concluded ha here is a high leverage effec in he sock markes of Denmark, Finland, Norway and Sweden so a negaive shock increases he sock marke volailiy more han he posiive shock a he same magniude in hese markes. In oher respecs, he poserior means of he volailiy of volailiy coefficien, indicaing he ˆ measure of uncerainy abou he fuure volailiy are wihin he range of (Finland) and 0.63 (Denmark). I can be concluded ha he Nordic sock markes exhibi a low variabiliy of volailiy and also he fuure volailiy is relaively cerain in hese sock markes. 5. Conclusions The presen paper is a firs aemp o find ou sock marke volailiy dynamics in he Nordic economies using he framework of asymmeric sochasic volailiy models. The daa se involves daily closing price indices of four Nordic counries and consiss of sock indices of Denmark (KFX Index), Finland (HEX Index), Norway (OBX Index) and Sweden (OMX Index). The empirical findings provide srong evidence of asymmery for all of he Nordic sock markes. The esimaion resuls display ha here is a high leverage effec in he sock markes of Denmark, Finland, Norway and Sweden so a negaive shock increases sock marke volailiy more han a posiive shock a he same magniude in hese markes. Also i is shown ha he Nordic sock markes have significan and high volailiy persisence. I can be implied ha he volailiy clusering occurs in he sock markes of Denmark, Finland, Norway and Sweden. Moreover, he empirical resuls demonsrae ha here exiss a low variabiliy of he volailiy in sock markes of he Nordic region which are Denmark, Finland, Norway and Sweden. The mos ineresing and unique resuls obained from he presen paper are ha here is boh a low variabiliy of volailiy and a high volailiy persisence in he sock markes of Denmark, Finland, Norway and Sweden. Addiionally, we can conclude ha he sock markes of Denmark, Finland, Norway and Sweden, which have leverage effec, have lower variabiliy of volailiy and in hese markes he fuure volailiy is relaively cerain. The resuls presened in his paper could be a guide for he invesors who are planning o inves in sock markes from he Nordic region. Noes (1) Code used in MCMC esimaions of he parameers can be downloaded from Professor Yasuhiro Omori s web sie hp:// References Asai, M., & McAleer, M. (005). Dynamic Asymmeric Leverage in Sochasic Volailiy Models. Economeric Reviews, 4(3), Bollerslev, T. (1986). Generalized Auoregressive Condiional Heeroskedasiciy. Journal of Economerics, 31(3), Booh, G. G., Marikainen, T., & Tse, Y. (1997). Price and volailiy Spillovers in Scandinavian Sock Markes. Journal of Banking & Finance, 1(6),

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