Global Financial Crisis Volatility Impact and ...

Global Financial Crisis Volatility Impact and Contagion Effect…

Estocástica:

FINANZAS Y RIESGO

Global Financial Crisis Volatility Impact and Contagion Effect on NAFTA Equity Markets Impacto de la volatilidad y efecto de contagio de la crisis global financiera en los mercados bursátiles del TLCAN Miriam Sosa* Edgar Ortiz** Fecha de recepción: 3 de agosto de 2016, Fecha de aceptación 16 de diciembre de 2016

RESUMEN Ž‘„Œ‡–‹˜‘†‡‡•–ƒ‹˜‡•–‹‰ƒ…‹×‡•ƒƒŽ‹œƒ”‡Ž‹’ƒ…–‘†‡Žƒ…”‹•‹•ϐ‹ƒ…‹‡”ƒ‰Ž‘„ƒŽ ‡ Žƒ †‹ž‹…ƒ †‡ Žƒ ˜‘Žƒ–‹Ž‹†ƒ† †‡ Ž‘• ‡”…ƒ†‘• ƒ……‹‘ƒ”‹‘• †‡Ž „Ž‘“—‡ ǡ —•ƒ†‘…‘””‡Žƒ…‹×‡†‹†ƒƒ–”ƒ˜±•†‡˜‡–ƒƒ•×˜‹Ž‡•›‘†‡Ž‘• •‹±–”‹…‘•ȋ ͳǡͳȌ›ƒ•‹±–”‹…‘•ȋͳǡͳȌǤƒ•˜ƒ”‹ƒ„Ž‡•ϐ‹ƒ…‹‡”ƒ•‡’Ž‡ƒ†ƒ• •‘Ž‘•”‡†‹‹‡–‘•†‡Ž‘•’”‡…‹‘•†‡…‹‡””‡†‹ƒ”‹‘•†‡Ž‘•À†‹…‡•„—”•ž–‹Ž‡•ǣƬ ͷͲͲȋ•–ƒ†‘•‹†‘•Ȍǡ ȋ±š‹…‘Ȍ›Ƭ‘’‘•‹–‡ȋƒƒ†žȌ‡†×Žƒ”‡•†‡ •–ƒ†‘•‹†‘•ǡ†—”ƒ–‡‡Ž’‡”‹‘†‘†‡Ž’”‹‡”‘†‡‡‡”‘†‡ʹͲͲ͵ƒŽʹ͹†‡ˆ‡„”‡”‘ †‡ʹͲͳͷǤƒ‡˜‹†‡…‹ƒ…‘ϐ‹”ƒŽƒ‡š‹•–‡…‹ƒ†‡˜‘Žƒ–‹Ž‹†ƒ†ƒ•‹±–”‹…ƒ‡Žƒ••‡”‹‡• †—”ƒ–‡–‘†‘‡Ž’‡”‹‘†‘†‡‡•–—†‹‘ǡƒ•À…‘‘‹…”‡‡–‘‡Žƒ˜‘Žƒ–‹Ž‹†ƒ†ƒ’ƒ”–‹” †‡Žƒ…”‹•‹•„—”•ž–‹Ž’”‡•‡–ƒ†ƒ‡ʹͲͲ͹Ǥ Žƒ•‹ϐ‹…ƒ…‹× ǣ Ͳͳǡ ͳͷǡ ͸ͷǡͷͺ Palabras clave: ˜‘Žƒ–‹Ž‹†ƒ†ƒ•‹±–”‹…ƒǡ ǡǡǡ…”‹•‹•ϐ‹ƒ…‹‡”ƒǤ

ABSTRACT The aim of this paper is to analyze the contagion effect and the impact of the ‰Ž‘„ƒŽϔ‹ƒ…‹ƒŽ…”‹•‹•‹ „Ž‘…•–‘…ƒ”‡–•´ volatility, using rolling window correlation and a GARCH approach. Once the contagion effect is established through an increasing correlation during the crisis period, volatility changes and leverage effects are tested with symmetric and asymmetric GARCH models with a dummy variable in the variance equation. Canada, the United States and Mexico´s equity * **

Facultad de Economía, Universidad Nacional Autónoma de México, Ciudad de México, México, [email protected]. Programa de Posgrado en Ciencias Políticas y Sociales, Universidad Nacional Autónoma de México, Ciudad de México, México, [email protected].

Volumen 7, número 1, enero-junio 2017, pp. 67-88 ISSN 2007-5383 versión digital, ISSN 2007-5375 versión impresa ISSN 2007-5383 versión digital, ISSN 2007-5375 versión impresa

67

Estocástica:

Miriam Sosa y Edgar Ortiz

FINANZAS Y RIESGO

markets stock indexes daily yields, in US dollars, from January 2003 through February ͸Ͷͷͻ ™‡”‡ •–—†‹‡†Ǥ ‡•—Ž–• …‘ϔ‹”‡† –Š‡ ’”‡•‡…‡ ‘ˆ ƒ•›‡–”‹… ˜‘Žƒ–‹Ž‹–› †—”‹‰ the whole period and an increasing volatility since the Global Financial Crisis.

Žƒ••‹ϔ‹…ƒ–‹‘ǣ G01, G15, F65, C58 Key wordsǣ ǡ ǡǡϔ‹ƒ…‹ƒŽ…”‹•‹•ǡŽ‡˜‡”ƒ‰‡‡ˆˆ‡…–Ǥ

Introduction

T

Š‡ ‰Ž‘„ƒŽ ϐ‹ƒ…‹ƒŽ …”‹•‹• ȋ Ȍ Šƒ• „‡‡ ‘‡ ‘ˆ –Š‡ ‘•– •‹‰‹ϐ‹…ƒ– ‰Ž‘„ƒŽ‡˜‡–•‹Š‹•–‘”›…‘…‡”‹‰‡…‘‘‹…•ƒ†ϐ‹ƒ…‡ǡ†—‡–‘–Š‡ ˆƒ•– –”ƒ•‹••‹‘ ‘ˆ ‹–• ’”‘ˆ‘—† ‹’ƒ…– ƒ”‘—† –Š‡ ™‘”Ž†Ǥ Š‡ ϐ‹ƒ…‹ƒŽ …”‹•‹• ϐ‹”•– •‹‰• „‡‰ƒ –‘„‡‡˜‹†‡––Š”‘—‰Š–Š‡•—„’”‹‡…”‹•‹•‹ ʹͲͲ͹ ƒ†Žƒ•–‡†—–‹Ž–Š‡‡†‘ˆʹͲͳʹǤ‡…‘†Ǧ”‘—†‡ˆˆ‡…–•ƒ’’‡ƒ”‡†—–‹ŽʹͲͳͷǡ ™‹–Š–Š‡—”‘’‡ƒ•‘˜‡”‡‹‰†‡„–…”‹•‹•ȋ‹œ‡ƒet alǤǡʹͲͳʹƒ†‡•–‘•ǡ ʹͲͳͷȌǤ Š‡•‡ †‹•‡“—‹Ž‹„”‹ƒ ™‡”‡ ‡˜‹†‡– „› ‡“—‹–› ƒ”‡–• —•–‡ƒ†‹‡•• ƒ”‘—† –Š‡ ™‘”Ž†ǡ …Šƒ”ƒ…–‡”‹œ‡† „› Š‹‰Š‡” •–‘… •Šƒ”‡• ƒ† •–‘… ’”‹…‡ ‹†‡š‡•˜‘Žƒ–‹Ž‹–›ƒ†Ž‘™‡”ǡƒ†‡˜‡‡‰ƒ–‹˜‡ǡ›‹‡Ž†•Ǥ Š‡ ‘”–Š ‡”‹…ƒ ”‡‡ ”ƒ†‡ ‰”‡‡‡– ȋ Ȍǡ ‹–‡‰”ƒ–‡† „› ‡š‹…‘ǡ ƒƒ†ƒ ƒ† –Š‡ ‹–‡† –ƒ–‡•ǡ ȋǤǤȌǡ ”‡Žƒ–‡• –‘ ‘‡ ‘ˆ –Š‡ ‰‡‘‰”ƒ’Š‹…ƒŽ œ‘‡• —†‡”‰‘‹‰ ‹’‘”–ƒ– …Šƒ‰‡• †—‡ –‘ –Š‡ Ǥ Š‡ ’”‹ƒ”› ”‘Ž‡ ’Žƒ›‡† „› –Š‡ ǤǤ ‹ –Š‡ …”‹•‹• ƒ† ‹–• •–”‘‰ ”‡Žƒ–‹‘• ™‹–Š ‡š‹…‘ ƒ† ƒƒ†ƒ „ƒ•‡† ‘ –”ƒ†‡ǡ ˆ‘”‡‹‰ †‹”‡…– ‹˜‡•–‡– ƒ†ǡ ƒ„‘˜‡ ƒŽŽǡˆ‘”‡‹‰’‘”–ˆ‘Ž‹‘‹˜‡•–‡–•ƒ›‡š’Žƒ‹–Š‡‹’Ž‹…ƒ–‹‘•‘ˆ–Š‡‰Ž‘„ƒŽ ϐ‹ƒ…‹ƒŽ…”‹•‹•‹–Š‡”‡‰‹‘Ǥ ‘ƒŽƒ”‰‡‡š–‡–ǡ’”‘ˆ‘—†ƒ†’‡”•‹•–‡–‰Ž‘„ƒŽϐ‹ƒ…‹ƒŽ‹„ƒŽƒ…‡• ™‡”‡ …ƒ—•‡† „› ‹–‡‰”ƒ–‹‘Ǥ  ’ƒ”–‹…—Žƒ”ǡ …‘—–”‹‡• ™‹–Š Š‹‰Š‡” Ž‡˜‡Ž ‘ˆ ‹–‡‰”ƒ–‹‘ǡƒ•–Š‘•‡„‡Ž‘‰‹‰–‘–Š‡ „Ž‘…ǡŠƒ˜‡Š‹‰Š‡””‹•‡š’‘•—”‡ –‘ ‰Ž‘„ƒŽ –—”‘‹ŽǤ Š‡”‡ˆ‘”‡ǡ –‘ ƒƒŽ›œ‡ –Š‡ ”‡Žƒ–‹‘ ƒ‘‰ –Š‡   •–‘…ƒ”‡–•‹•ƒ‡›ˆƒ…–‘”‹‘”†‡”–‘‡•–ƒ„Ž‹•Š–Š‡…‘–ƒ‰‹‘‡ˆˆ‡…–„› ‡šƒ‹‹‰‹…”‡ƒ•‹‰…‘””‡Žƒ–‹‘†—”‹‰–Š‡…”‹•‹•Ǥ…‡…”‹•‹•–”ƒ•‹••‹‘ ‡ˆˆ‡…–•ƒ”‡†‡–‡”‹‡†ǡ–Š‡’”‡•‡…‡‘ˆŠ‹‰Š‡”˜‘Žƒ–‹Ž‹–›ƒ†Š‹‰Š‡”Ž‡˜‡”ƒ‰‡ ‡ˆˆ‡…–ǡ•‹…‡–Š‡ ǡ…ƒ„‡–‡•–‡†ˆ‘”„›‘†‡Ž‹‰ •–‘…ƒ”‡–ǯ• ˜‘Žƒ–‹Ž‹–›–Š”‘—‰Šƒ ƒ’’”‘ƒ…ŠǤ

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Volumen 7, número 1, enero - junio 2017, pp. 67-88

Global Financial Crisis Volatility Impact and Contagion Effect…

Estocástica:

FINANZAS Y RIESGO

– ‹• ‘ˆ —––‡”‘•– ‹’‘”–ƒ…‡ –‘ •–—†› ‡“—‹–› ƒ”‡–• ˜‘Žƒ–‹Ž‹–› ƒ† –Š‡‹” ”‡Žƒ–‹‘•Š‹’• ‹ ƒ ‹–‡”…‘‡…–‡† ƒ† †‡‡’Ž› ‹–‡‰”ƒ–‡† ϐ‹ƒ…‹ƒŽ „ƒ…†”‘’ǡƒ•‹•–Š‡ „Ž‘……ƒ•‡ǡ•‹…‡–Š‡•‡ƒ”‡–•Šƒ˜‡‡š’‡”‹‡…‡† ƒƒ……‡Ž‡”ƒ–‡†‰”‘™–ŠǤŠ‡‹””ƒ’‹†”‹•‡ƒ††‡˜‡Ž‘’‡–Šƒ•ƒŽŽ‘™‡†–Š‡•‡ •–‘… ƒ”‡–• –‘ ‘’‡”ƒ–‡ ƒ• ƒ Ž‹ „‡–™‡‡ †‹ˆˆ‡”‡– ‡…‘‘‹… ƒ† •‘…‹ƒŽ ƒ‰‡–• ȋ•ƒ˜‡”•ǡ ’‡•‹‘ ˆ—†•ǡ ’—„Ž‹… ƒ† ’”‹˜ƒ–‡ ‹˜‡•–‘”• ƒ† ‹••—‡”•Ȍǡ „‡…‘‹‰ ƒ ‹’‘”–ƒ– ‹˜‡•–‡– …Šƒ‡ŽǤ  –Š‹• •‡•‡ǡ ƒ ‡ˆϐ‹…‹‡– ’‡”ˆ‘”ƒ…‡ ‘ˆ •–‘… ƒ”‡–•ǡ ƒ• ƒ ‹˜‡•–‡– …Šƒ‡Žǡ ƒ› ‡Šƒ…‡ ‡…‘‘‹… ƒ…–‹˜‹–› ƒ† ”‡‹ˆ‘”…‡ ‡…‘‘‹… ‰”‘™–Š ƒ† …‘’‡–‹–‹˜‡‡•• ‘ˆ –Š‡ „Ž‘…‡…‘‘‹‡•Ǥ  –Š‡ ‘–Š‡” Šƒ†ǡ –Š‹• ’ƒ’‡” •Š‘™• ‹’‘”–ƒ– ‹’Ž‹…ƒ–‹‘• ˆ‘” ƒ••‡– ƒŽŽ‘…ƒ–‹‘ǡˆ‘”’‘”–ˆ‘Ž‹‘†‹˜‡”•‹ϐ‹…ƒ–‹‘ƒ†ǡƒ„‘˜‡ƒŽŽǡˆ‘”–Š‡…‘•–”—…–‹‘ ‘ˆ–”‹Žƒ–‡”ƒŽ’‘”–ˆ‘Ž‹‘•…‘•‹†‡”‹‰–Šƒ–Š‹‰Š‡”…‘””‡Žƒ–‹‘Ž‡˜‡Ž•ƒ†•‹‹Žƒ” ”‡•’‘•‡• –‘ ‡š–‡”ƒŽ ϐ‹ƒ…‹ƒŽ •Š‘…• ‹Š‹„‹– –Š‡ –”ƒ†‹–‹‘ƒŽ ’‘”–ˆ‘Ž‹‘ †‹˜‡”•‹ϐ‹…ƒ–‹‘–‡…Š‹“—‡•Ǥ ‹ƒŽŽ›ǡ–‘‡šƒ‹‡–Š‡˜‘Žƒ–‹Ž‹–›„‡Šƒ˜‹‘”‘ˆ–Š‡  •–‘…ƒ”‡–••Š‘—Ž†•Š‡†•‘‡Ž‹‰Š–ƒ„‘—––Š‡‹–‡‰”ƒ–‹‘’”‘…‡•• „‡–™‡‡–Š‡•‡ƒ”‡–•Ǥ1 Š‹•’ƒ’‡”‹•‘”‰ƒ‹œ‡†ƒ•ˆ‘ŽŽ‘™•Ǥ‡…–‹‘ͳ’”‡•‡–•ƒ”‡˜‹‡™‘ˆ–Š‡ Ž‹–‡”ƒ–—”‡Ǥ‡…–‹‘ʹ—ˆ‘Ž†•–Š‡†ƒ–ƒƒ†‡–Š‘†‘Ž‘‰›—•‡†–‘ ‡•–‹ƒ–‡ –Š‡…‘–ƒ‰‹‘‡ˆˆ‡…–ƒ†–Š‡…”‹•‹•‡ˆˆ‡…–••–‘…ƒ”‡–˜‘Žƒ–‹Ž‹–›ǤŠ‡ˆ‘ŽŽ‘™‹‰•‡…–‹‘†‹•…—••‡•–Š‡‡’‹”‹…ƒŽ‡˜‹†‡…‡Ǥ ‹ƒŽŽ›ǡ…‘…Ž—•‹‘•ƒ”‡ ’”‡•‡–‡†Ǥ

1. Evidence from previous studies ‹ƒ…‹ƒŽ ‹–‡‰”ƒ–‹‘ Šƒ• ‹…”‡ƒ•‡† ‹˜‡•–‡– ‘’–‹‘• ’”‘‘–‹‰ Š‹‰Š‡” Ž‡˜‡Ž• ‘ˆ ϐ‹ƒ…‹ƒŽ ƒ••‡–• †‡ƒ†Ǥ ‘™‡˜‡”ǡ ‹– Šƒ• ƒŽ•‘ Ž‡†  –‘ –Š‡ ‹•–ƒ–ƒ‡‘—•–”ƒ•‹••‹‘‘ˆϐ‹ƒ…‹ƒŽ†‹•‡“—‹Ž‹„”‹ƒƒ‘‰ƒ”‡–•–Šƒ–ǡ ƒ’’ƒ”‡–Ž›ǡƒ”‡‘–…Ž‘•‡Ž›”‡Žƒ–‡†ǤŠ‡‰”‘™–Š‘ˆ‹–‡”…‘‡…–‹‘•ƒ‘‰ •–‘… ƒ”‡–• ƒ† –Š‡‹” ”‡Žƒ–‹‘• ™‹–Š †‹ˆˆ‡”‡– ‡…‘‘‹… ƒ‰‡–• Šƒ˜‡ „‘‘•–‡† –Š‡ ‡š–‡”ƒŽ •Š‘…• ‹’ƒ…– ‘ ‡…‘‘‹… ƒ…–‹˜‹–›ǡ Ž‡ƒ†‹‰ –‘ –Š‡ ‡‘”‘—•†‡˜ƒ•–ƒ–‹‘”‡•—Ž–‹‰ˆ”‘–Š‡”‡…‡–‰Ž‘„ƒŽϐ‹ƒ…‹ƒŽ…”‹•‹•ƒ† ‹–•‡ˆˆ‡…–•Ǥ ‹˜‡–Š‡‹’‘”–ƒ…‡‘ˆ–Š‹•’Š‡‘‡‘ǡ‡š–‡•‹˜‡Ž‹–‡”ƒ–—”‡

1

If the price of a security, commodity or asset is different in two different markets, then an arbitrageur will purchase the asset in the cheaper market and sell it the most expensive. Otherwise, the markets are integrated.

ISSN 2007-5383 versión digital,

ISSN 2007-5375 versión impresa

69

Estocástica:

Miriam Sosa y Edgar Ortiz

FINANZAS Y RIESGO

Šƒ•„‡‡”‡…‡–Ž›’—„Ž‹•Š‡†ƒ„‘—––”ƒ•‹••‹‘‡ˆˆ‡…–•ƒ†–Š‡‹”‹’ƒ…–•‘ –Š‡„‡Šƒ˜‹‘”‘ˆ‡“—‹–›ƒ”‡–•Ǥ  ‹•‘‡‘ˆ–Š‡™‘”Ž†ǯ•Žƒ”‰‡•–ˆ”‡‡–”ƒ†‡œ‘‡•Ǥ‡…‡–Ž›–Š‡—„‡” ƒ† †‡’–Š ‘ˆ •–—†‹‡• †‡ƒŽ‹‰ ™‹–Š  Ʋ• •–‘… ƒ”‡–• Šƒ• ‹…”‡ƒ•‡†Ǥ ‘‰ –Š‡•‡ ’—„Ž‹…ƒ–‹‘• •–ƒ†• ‘—– –Š‡ ƒ”–‹…Ž‡ ™”‹––‡ „› ‡›‡• ƒ† ”–‹œ ȋʹͲͳ͵ȌǢ –Š‡› ƒƒŽ›œ‡ ”‡‰‹‘ƒŽ †‹˜‡”•‹ϐ‹…ƒ–‹‘ –Š”‘—‰Š –Š‡ Ǧ ‡–Š‘†‘Ž‘‰›ǡ ™Š‹…Š ’”‡•—’’‘•‡• ‰”‡ƒ–‡” …‘•‡”˜ƒ–‹• ƒ† ’”‡…‹•‹‘ ‘ ‡•–‹ƒ–‹‰ ’‘–‡–‹ƒŽ Ž‘••‡• ‘ˆ ‹˜‡•–‡– ’‘”–ˆ‘Ž‹‘•Ǥ Š‡‹” ”‡•—Ž–• •Š‘™ –Šƒ–ǡ†‡•’‹–‡–Š‡‹–‡””‡Žƒ–‹‘ƒ‘‰ •–‘…ƒ”‡–•ǡ–Š‡”‡•–‹ŽŽƒ”‡ ‘’’‘”–—‹–‹‡•–‘…‘•–”—…–’”‘ϐ‹–ƒ„Ž‡–”‹Ǧƒ–‹‘ƒŽ’‘”–ˆ‘Ž‹‘•Ǥ ‘‰ –Š‡ •–—†‹‡• ƒ„‘—– …‘–ƒ‰‹‘ ‡ˆˆ‡…–ǡ Š‹––‡†‹ ȋʹͲͳͷȌ ƒƒŽ›œ‡• –Š‡ …‘–ƒ‰‹‘ˆ”‘–Š‡–‘ †‹ƒǤ’‹”‹…ƒŽϐ‹†‹‰••Š‘™–Šƒ––Š‡”‡ Šƒ•„‡‡ƒ•‹‰‹ϐ‹…ƒ–‹…”‡ƒ•‡‹–Š‡…‘””‡Žƒ–‹‘…‘‡ˆϐ‹…‹‡–‡ƒ„‡–™‡‡ –Š‘•‡ƒ”‡–•†—”‹‰–Š‡…”‹•‹•’‡”‹‘†•…‘’ƒ”‡†–‘–Š‡’”‡Ǧ…”‹•‹•’‡”‹‘†ǡ ™Š‹…Š‡•–ƒ„Ž‹•Š‡•–Š‡‡š‹•–‡…‡‘ˆ…‘–ƒ‰‹‘„‡–™‡‡–Š‡ǤǤǡƒ† †‹ƒ ƒ”‡–•Ǥ ‹ƬȋʹͲͳ͸ȌǡƒƒŽ›œ‡–Š‡ …‘–ƒ‰‹‘‡ˆˆ‡…–•„‡–™‡‡–Š‡  Ʋ• ƒ† –Š‡ Ǥ Ǥ •–‘… ƒ”‡–•Ǥ Š‡‹” ‡’‹”‹…ƒŽ ”‡•—Ž–• •Š‘™ –Šƒ– –Š‡”‡ƒ”‡•‹‰‹ϐ‹…ƒ–…‘–ƒ‰‹‘‡ˆˆ‡…–•ˆ”‘–Š‡ǤǤ–‘–Š‡ Ʋ•‡“—‹–› ƒ”‡–•Ǥ–Š‡””‡…‡–•–—†‹‡•‹…Ž—†‡–Š‘•‡„› ƒ™ƒ†‹et alǤǢ‘—Š‹…Š‹ƒ† Š‡ˆˆ‘— ȋʹͲͳͷȌǢ ƒ”–‹ ƒ† ‰—›‡ ȋʹͲͳͷȌǢ ”ƒ‰‹†‹• et alǤ ȋʹͲͳͷȌǢ ƒ† ‘ŽŽƒŠet alǤȋʹͲͳ͸ȌǤ ‡Žƒ–‡† –‘ –Š‡  ‹’ƒ…– ‘ ˜‘Žƒ–‹Ž‹–› ’‡”ˆ‘”ƒ…‡ǡ ƒŽ•‹‡ ƒ† ”‘”ƒȋʹͲͳ͸Ȍ‡šƒ‹‡–Š‡˜‘Žƒ–‹Ž‹–›‘ˆ–Š‡ Ʋ•ƒ†–Š‡ǤǤƒ”‡–•ǤŠ‡› ’”‡•‡–‡˜‹†‡…‡ƒ„‘—–ƒ—‹ˆ‘”‹…”‡ƒ•‡‹–Š‡ƒ„•‘Ž—–‡˜‘Žƒ–‹Ž‹–›†—”‹‰ –Š‡ …”‹•‹• ’‡”‹‘† …‘’ƒ”‡† –‘ –Š‡ ’”‡Ǧ…”‹•‹• ’‡”‹‘† ˆ‘” ƒŽŽ –Š‡ …‘—–”‹‡• —†‡” •–—†›Ǥ ‹‹ƒ‘—‹ et alǤ ȋʹͲͳͷȌ •–—†› –Š‡ ’‡”ˆ‘”ƒ…‡ ‘ˆ •Žƒ‹… ƒ† …‘˜‡–‹‘ƒŽ‹†‡š‡•‘ˆ–Š‡ —Žˆ‘‘’‡”ƒ–‹‘‘—…‹Žȋ Ȍ…‘—–”‹‡•‹–Š‡ ™ƒ‡‘ˆ–Š‡ ǤŠ‡‹””‡•—Ž–••Š‘™–Šƒ––Š‡ Šƒ†ƒ‹’ƒ…–‘–Š‡‡ƒ ”‡–—”•‘ˆƒŠ”ƒ‹ǡŽ‡ƒ˜‹‰–Š‡‘–Š‡”‹†‡š‡•—ƒˆˆ‡…–‡†Ǥ‡…‡–Ž‹–‡”ƒ–—”‡ Šƒ•„‡‡ƒŽ•‘’”‡•‡–‡†„›ǣ—Ž•Š”‡•Š–Šƒƒ†‹––ƒŽȋʹͲͳͷȌǢ‹ŠƒȋʹͲͳͷȌǢ ‘Šƒƒ†‹ƒ†ƒȋʹͲͳͷȌǢ›”‹‘’‘—Ž‘•ǡ et alǤȋʹͲͳͷȌǢ†”‹‘•‘’‘—Ž‘•et alǤȋʹͲͳ͸ȌǢƒ—Žƒ†‹ƒ–ƒȋʹͲͳ͸ȌǤ –Š‹•’ƒ’‡”ǡ–™‘•–—†‹‡•™‡”‡”‡‰ƒ”†‡†ƒ•ƒ•–ƒ”–‹‰’‘‹–Ǥ ‹”•–ǡ–Š‡ ‘‡’”‡•‡–‡†„›‘Šƒƒ†‹ƒ†ƒȋʹͲͳͷȌ™ƒ•…‘•‹†‡”‡†ǤŠ‡›—•‡† ƒ …‘’Ž‡‡–ƒ”› ‡–Š‘†‘Ž‘‰› –Šƒ– ‹–‡‰”ƒ–‡• …‘””‡Žƒ–‹‘ ƒƒŽ›•‹• ƒ† ƒ

ƒ’’”‘ƒ…Šǡ‹‘”†‡”–‘ƒƒŽ›œ‡…‘–ƒ‰‹‘ƒ†‹–•‡ˆˆ‡…–•‘–Š‡ǤǤǡ ‘‰‘‰ƒ†Š‹ƒ•–‘…ƒ”‡–•Ǥ‡…‘†Ž›ǡ–Š‡•–—†›†‡˜‡Ž‘’‡†„› ‘•Š‹ ȋʹͲͳʹȌ™ƒ•”‡˜‹‡™‡†Ǥ‡ƒ’’Ž‹‡••›‡–”‹…ƒ†ƒ•›‡–”‹… ‘†‡Ž•

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Volumen 7, número 1, enero - junio 2017, pp. 67-88

Global Financial Crisis Volatility Impact and Contagion Effect…

Estocástica:

FINANZAS Y RIESGO

™‹–Š ƒ †—› ˜ƒ”‹ƒ„Ž‡ ‹ –Š‡ ˜ƒ”‹ƒ…‡ ‡“—ƒ–‹‘ –‘ –‡•– –Š‡ ’”‡•‡…‡ ‘ˆ ‹…”‡ƒ•‹‰˜‘Žƒ–‹Ž‹–›ƒ†Ž‡˜‡”ƒ‰‡‡ˆˆ‡…–•‹…‡–Š‡ ‘–Š‡•–‘…ƒ”‡–• ‘ˆ †‹ƒǡ‘”‡ƒǡƒŽƒ›•‹ƒǡ‘‰‘‰ƒ† †‘‡•‹ƒǤ

2. Data and methodology 2.1 Data Š‡ƒ‹Ž›…Ž‘•‹‰’”‹…‡‘ˆ‡š‹…‘ȋ Ȍǡƒƒ†ƒȋȌƒ†–Š‡ǤǤȋƬͷͲͲȌ •–‘…‹†‡š‡•ǡ‹†‘ŽŽƒ”•ǡ™‡”‡—•‡†–‘–‡•–…‘–ƒ‰‹‘‡ˆˆ‡…–ƒ†…Šƒ‰‡• ‹–Š‡˜‘Žƒ–‹Ž‹–›„‡Šƒ˜‹‘”ǤŠ‡–‹‡’‡”‹‘†ƒƒŽ›œ‡†‹…Ž—†‡•ˆ”‘ ƒ—ƒ”› ͳǡ ʹͲͲ͵ –‘ ‡„”—ƒ”› ʹ͹ǡ ʹͲͳͷǤ Š‡ ’”‡Ǧ…”‹•‹•’‡”‹‘†…‘•‹†‡”‡†…‘’”‹•‡•

ƒ—ƒ”› ʹͲͲ͵ –‘ —‰—•– ͺǡ ʹͲͲ͹ ƒ† –Š‡ …”‹•‹• ’‡”‹‘† —‰—•– ͻǡ ʹͲͲ͹ –‘ ‡„”—ƒ”›ʹͲͳͷǡƒ……‘”†‹‰–‘–Š‡’‡”‹‘†•‹†‡–‹ϐ‹‡†„›ƒ›Ž‘”ƒ†‹ŽŽ‹ƒ• ȋʹͲͲͻȌƒ† ‘•Š‹ȋʹͲͳʹȌǤ

2.2 Methodology Š‡ ƒƒŽ›•‹• ‘ˆ ‡’‹”‹…ƒŽ …‘–ƒ‰‹‘ ƒ‹• –‘ †‡–‡”‹‡ ™Š‡–Š‡” ‘” ‘– …Šƒ‡Ž•ƒ†‹–‡•‹–‹‡•‘ˆ•Š‘…’”‘’ƒ‰ƒ–‹‘ƒ…”‘••…‘—–”‹‡•…Šƒ‰‡†—”‹‰ …‡”–ƒ‹ …”‹•‡• ’‡”‹‘†•Ǥ ƒ”–‹…—Žƒ”Ž›ǡ –Š‡ …‘–ƒ‰‹‘ ‡ˆˆ‡…– ‹• ƒ ’Š‡‘‡‘ …Šƒ”ƒ…–‡”‹œ‡†„›ƒ•‹‰‹ϐ‹…ƒ–‹…”‡ƒ•‡‹…‘””‡Žƒ–‹‘Ž‡˜‡Ž•ƒ‘‰†‹ˆˆ‡”‡– ƒ”‡–•ƒ•ƒ…‘•‡“—‡…‡‘ˆƒ”‡Ž‡˜ƒ–•Š‘…ˆ”‘‘–Š‡”ƒ”‡–•ȋƒ†‡”Ƭ Ž‡‹‡‹‡”ǡʹͲͲ͵ȌǤ‘•‹†‡”‹‰–Š‹•†‡ϐ‹‹–‹‘ƒ•ƒ•–ƒ”–‹‰’‘‹–ǡ–Š‹••–—†› ƒ’’Ž‹‡• ƒ ”‘ŽŽ‹‰ ™‹†‘™ …‘””‡Žƒ–‹‘ ‡–Š‘†‘Ž‘‰› –‘ –‡•– …Šƒ‰‡• ‹ –Š‡ •›•–‡‹… ˜ƒ”‹ƒ–‹‘ ‘ˆ ‘‡ ˜ƒ”‹ƒ„Ž‡ ‹ ”‡Žƒ–‹‘ –‘ ƒ‘–Š‡”Ǥ Š‡ …‘””‡Žƒ–‹‘ ‹†‡š‡•–‹ƒ–‹‘‹•‡ƒ•—”‡†ˆ‘”͸Ͳ†ƒ›•”‘ŽŽ‹‰™‹†‘™…‘””‡Žƒ–‹‘ǤŠ‡ ‡•–‹ƒ–‹‘…Šƒ‰‡•‡˜‡”›†ƒ›ǡ‹‘”†‡”–‘‘„•‡”˜‡†ƒ‹Ž›…Šƒ‰‡•‹–Š‡…‘Ǧ ‘˜‡‡–•„‡–™‡‡–™‘˜ƒ”‹ƒ„Ž‡•Ǥ ‹‰—”‡ͳ‡š‡’Ž‹ϐ‹‡•Š‘™…‘””‡Žƒ–‹‘‹•‡•–‹ƒ–‡†‡˜‡”›͸Ͳ†ƒ›•ǡˆ”‘ †ƒ–ƒͳ–‘†ƒ–ƒ͸ͳǡˆ”‘†ƒ–ƒʹ–‘†ƒ–ƒ͸ʹǡƒ†•‘‘Ǥ –Š‹••‡•‡ǡ–Š‡”‘ŽŽ‹‰ ™‹†‘™…‘””‡Žƒ–‹‘ƒŽŽ‘™•–‘‡•–‹ƒ–‡ʹ͵ͻͷ†ƒ‹Ž›…‘‡ˆϐ‹…‹‡–•ˆ‘”‡ƒ…Š–‹‡ ˜ƒ”›‹‰…‘””‡Žƒ–‹‘„‹Žƒ–‡”ƒŽ”‡Žƒ–‹‘ǡƒ••Š‘™‹–Š‡‰”ƒ’Š‹…”‡’”‡•‡–ƒ–‹‘ ˆ‘” –Š‡ ’‡”‹‘† —†‡” ƒƒŽ›•‡•Ǥ ‹‰‹ϐ‹…ƒ– ‹…”‡ƒ•‹‰ …‘””‡Žƒ–‹‘ ’”‘˜‹†‡• ‡˜‹†‡…‡ƒ„‘—–…‘–ƒ‰‹‘‡ˆˆ‡…–‹ …‘—–”‹‡••–‘…ƒ”‡–•Ǥ ‘ŽŽ‹‰™‹†‘™…‘””‡Žƒ–‹‘•Š‘™•…‘–ƒ‰‹‘‡ˆˆ‡…–•ǡ„—–‹–†‘‡•‘–‰‹˜‡ ‹ˆ‘”ƒ–‹‘ƒ„‘—––Š‡…”‹•‹•‡ˆˆ‡…–•‘˜‘Žƒ–‹Ž‹–›„‡Šƒ˜‹‘”Ǥ‘‘˜‡”…‘‡–Š‹• Ž‹‹–ƒ–‹‘ǡ–Š‹•’ƒ’‡”’”‘’‘•‡•ƒ…‘’Ž‡‡–ƒ”›‡–Š‘†‘Ž‘‰›–Šƒ–‹…Ž—†‡•

ISSN 2007-5383 versión digital,

ISSN 2007-5375 versión impresa

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Estocástica:

Miriam Sosa y Edgar Ortiz

FINANZAS Y RIESGO

Figure 1. Methodology to measure the rolling window correlation graphic representation.

Source: Prepared by author

ƒ ƒ’’”‘ƒ…Šǡ—•‹‰•›‡–”‹…ƒ†ƒ•›‡–”‹…‘†‡Ž•™‹–Šƒ†—› ˜ƒ”‹ƒ„Ž‡‹–Š‡˜ƒ”‹ƒ…‡‡“—ƒ–‹‘ǡ’”‘˜‹‰™Š‡–Š‡”‘”‘––Š‡˜‘Žƒ–‹Ž‹–›ƒ† Ž‡˜‡”ƒ‰‡‡ˆˆ‡…–‹…”‡ƒ•‡†•‹…‡–Š‡ Ǥ

2.3 GARCH model  ȋ—–‘”‡‰”‡••‹˜‡ ‘†‹–‹‘ƒŽ ‡–‡”‘•…‡†ƒ•–‹…‹–›Ȍǡ  ‘†‡Ž• ƒ†ƒŽŽ–Š‡‹”‡š–‡•‹‘•Šƒ˜‡„‡‡‹†‡–‹ϐ‹‡†‹–Š‡‡’‹”‹…ƒŽŽ‹–‡”ƒ–—”‡ƒ• ‡ˆˆ‡…–‹˜‡ ‹ ‘†‡Ž‹‰ –Š‡ ˜‘Žƒ–‹Ž‹–› ‘ˆ ϐ‹ƒ…‹ƒŽ •‡”‹‡•Ǥ Š‹• ‹• „‡…ƒ—•‡ –Š‡

‘†‡Ž•…ƒ’–—”‡•‘‡ˆ‡ƒ–—”‡•‘ˆ–Š‡ƒ••‡–•”‡–—”•˜‘Žƒ–‹Ž‹–›ϐŽ‘™•Ǥ ‘‰–Š‡•–›Ž‹œ‡†ˆƒ…–‘”•–Š‡›…ƒ’–—”‡ƒ”‡ǣ–Š‹…–ƒ‹Ž•ǡ˜‘Žƒ–‹Ž‹–›…Ž—•–‡”‹‰ǡ Ž‡˜‡”ƒ‰‡ ‡ˆˆ‡…–•ǡ …——Žƒ–‹˜‡ ‹ˆ‘”ƒ–‹‘ ‹ ‘Ǧ–”ƒ†‹‰ ’‡”‹‘†•ǡ •–”‘‰ ‹˜‡”•‡”‡Žƒ–‹‘„‡–™‡‡˜‘Žƒ–‹Ž‹–›ƒ†•‡”‹ƒŽ…‘””‡Žƒ–‹‘ƒ†…‘Ǧ‘˜‡‡–• ‹˜‘Žƒ–‹Ž‹–‹‡•ȋ‘ŽŽ‡”•Ž‡˜et alǤǡͳͻͻͶȌǤ ƒ•‡† ‘ –Š‡ ‡ˆˆ‡…–‹˜‡‡•• ƒ† ‰‘‘† ϐ‹– ‘ˆ –Š‡  ƒ’’”‘ƒ…Š ‘ ‘†‡Ž‹‰ ƒ••‡– ’”‹…‡• ˜‘Žƒ–‹Ž‹–›ǡ –Š‹• ’ƒ’‡” —•‡† –Š‡•‡ ‘†‡Ž• ‹ ‘”†‡” –‘ ’”‘˜‡ –Šƒ– –Š‡  ‹’ƒ…–‡† –Š‡ †›ƒ‹… ‘ˆ –Š‡   …‘—–”‹‡• •–‘… ƒ”‡–•ǡ „› ‹…”‡ƒ•‹‰ –Š‡‹” ˜‘Žƒ–‹Ž‹–› ƒ† –Š‡‹” ˜‘Žƒ–‹Ž‹–› ƒ•›‡–”›Ǥ

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Volumen 7, número 1, enero - junio 2017, pp. 67-88

Global Financial Crisis Volatility Impact and Contagion Effect…

Estocástica:

FINANZAS Y RIESGO

‘–Š‡” ƒ†˜ƒ–ƒ‰‡ ‘ˆ –Š‡  ‘†‡Ž• ‹• –Š‡‹” ’ƒ”•‹‘›Ǥ Š‹• ƒŽŽ‘™• ‡•–‹ƒ–‹‰ƒ†‹–‡”’”‡–‹‰–Š‡”‡•—Ž–•‹ƒ•‹’Ž‡™ƒ›Ǥ ƒ‹Ž›”‡–—”•ƒ”‡‹†‡–‹ϐ‹‡†ƒ•–Š‡…Ž‘•‹‰‹†‡š˜ƒŽ—‡ƒ–—”ƒŽŽ‘‰ƒ”‹–Š †‹ˆˆ‡”‡…‡ˆ‘”–™‘…‘•‡…—–‹˜‡–”ƒ†‹‰†ƒ›•Ǣ

ܴ௧ ൌ Ž‘‰ሺ‫ܥܲܫ‬ሻሺ‫ݐ‬ሻ െ Ž‘‰ሺ‫ܥܲܫ‬ሻሺ‫ ݐ‬െ ͳሻ

(1)

‹–”‘‘––‡•–•™‡”‡ƒ’’Ž‹‡†–‘†‡–‡”‹‡–Šƒ–ƒ‹†‹˜‹†—ƒŽϐ‹ƒ…‹ƒŽ •‡”‹‡•‹••–ƒ–‹‘ƒ”›ǤŠ‡”‡ˆ‘”‡ǡ—‰‡–‡†‹…‡› —ŽŽ‡”ƒ†Š‹ŽŽ‹’•‡””‘ ‡•–• ™‡”‡ —•‡† Ǥ Š‡ —ŽŽ Š›’‘–Š‡•‹• ‹• ‫ܪ‬଴ ǣ ߜ ൌ Ͳ y ‫ܪ‬ଵ ǣ ߜ ൏ ͳǤ Š‡ —ŽŽ Š›’‘–Š‡•‹•ƒ……‡’–ƒ…‡‡ƒ•–Šƒ––Š‡•‡”‹‡•Šƒ•ƒ—‹–”‘‘–Ǥ‘Ǧ•–ƒ–‹‘ƒ”› •‡”‹‡•…ƒ„‡–”ƒ•ˆ‘”‡†–Š”‘—‰Š–Š‡†‹ˆˆ‡”‡–‹ƒ–‹‘‘ˆ–Š‡•‡Ž˜‡•ǡǡ  ƒ† ‘†‡Ž•ƒ”‡…‘‘Ž›—•‡†‹–Š‹•’”‘…‡••Ǥ

‘†‡Ž‹‰ȋ‘ŽŽ‡”•Ž‡˜ǡͳͻͺ͸Ƭƒ›Ž‘”ǡͳͻͺ͸Ȍƒ••—‡•…‘†‹–‹‘ƒŽ Š‡–‡”‘•…‡†ƒ•–‹…‹–› ™‹–Š Š‘‘•…‡†ƒ•–‹… —…‘†‹–‹‘ƒŽ ‡””‘” ˜ƒ”‹ƒ…‡Ǥ ƒ”‹ƒ…‡ ‹• ƒ ˆ—…–‹‘ ‘ˆ –Š‡ ”‡ƒŽ‹œƒ–‹‘• ‘ˆ ’”‡˜‹‘—• ‡””‘” –‡”• ƒ† –Š‡ •“—ƒ”‡† ‘ˆ ’”‡˜‹‘—• †‹•–—”„ƒ…‡• ȋƒ•ƒ• Ƭ ‡’‡†ƒǡ ʹͲͲͺȌǤ Š—•ǡ –Š‡ …‘†‹–‹‘ƒŽ˜ƒ”‹ƒ…‡‘ˆ ȋ’ǡ“Ȍ‹••’‡…‹ϐ‹‡†ƒ•ˆ‘ŽŽ‘™•ǣ

݄௧ ൌ ߙ଴ ൅ σ௤௝ୀଵ ߙ௝ ߝ௧ି௝ ଶ ൅ σ௣௜ୀଵ ߚ௜ ݄௧ି௜

(2)

‹–Š ߙ଴ ൐ Ͳǡ ߙଵ ǡ ߙଶ ǡ ǥ ߙ௤ ൒ Ͳ and ߚଵ ǡ ߚଶ ǡ ߚଷ ǡ ǥ ߚ௤ ൒ Ͳ  –‘ ‡•—”‡ –Šƒ– –Š‡…‘†‹–‹‘ƒŽ˜ƒ”‹ƒ…‡‹•’‘•‹–‹˜‡ǡ ݄௧ ”‡’”‡•‡–•–Š‡…‘†‹–‹‘ƒŽ˜ƒ”‹ƒ…‡ ‡•–‹ƒ–‡†…‘•‹†‡”‹‰”‡Ž‡˜ƒ–’ƒ•–‹ˆ‘”ƒ–‹‘Ǣ ߚ௜ ƒ”‡–Š‡Žƒ‰‰‡†  …‘‡ˆϐ‹…‹‡–•ǡ ™Š‹…Š ‹†‹…ƒ–‡ –Šƒ– …Šƒ‰‡• ‹ –Š‡ …‘†‹–‹‘ƒŽ ˜ƒ”‹ƒ…‡ †‹•ƒ’’‡ƒ” •Ž‘™Ž›ǡ ‹ ‘–Š‡” ™‘”†•ǡ –Š‡› •Š‘™ ˜‘Žƒ–‹Ž‹–› ’‡”•‹•–‡…‡Ǣ ߙ௝ is –Š‡ ‡””‘” …‘‡ˆϐ‹…‹‡–ǡ ‹ˆ ‹– –ƒ‡• ƒ Š‹‰Š ˜ƒŽ—‡ǡ ‹– ‡ƒ• –Šƒ– –Š‡”‡ ‹• ƒ Š‹‰Š •‡•‹„‹Ž‹–› –‘ ˜‘Žƒ–‹Ž‹–› †‡”‹˜‡† ˆ”‘ ƒ”‡– ‘˜‡‡–•Ǥ ˆ ሺߙ ൅ ߚሻ value ‹•‡ƒ”„—–Ž‘™‡”–Šƒ–Š‡—‹–ǡ‹–‡ƒ•–Šƒ–ƒ•Š‘…‹–‹‡t™‹ŽŽ’‡”•‹•– ‹ˆ—–—”‡’‡”‹‘†•Ǣƒ˜ƒŽ—‡‡ƒ”‘‡ǡ‹’Ž‹‡•–Šƒ––Š‡•‡”‹‡•Šƒ•Ž‘‰‡‘”› ȋ ‘•Š‹ǡʹͲͳʹȌǤŠ‹• ‘†‡Ž‹•ƒŽ•‘‘™ƒ•ƒ•›‡–”‹…‘†‡Žǡ•‹…‡ ‹–…‘•‹†‡”•–Šƒ–‡‰ƒ–‹˜‡ƒ†’‘•‹–‹˜‡˜ƒ”‹ƒ–‹‘•Šƒ˜‡–Š‡•ƒ‡‹’ƒ…–‹ ˜‘Žƒ–‹Ž‹–›Ǥ …”‡ƒ•‹‰ ˜‘Žƒ–‹Ž‹–› ƒ• ƒ ”‡•—Ž– ‘ˆ …‘–ƒ‰‹‘ ‡ˆˆ‡…– ‹• †‡–‡”‹‡† „› ‹–”‘†—…‹‰ƒ†—›˜ƒ”‹ƒ„Ž‡‹–Š‡˜ƒ”‹ƒ…‡‡“—ƒ–‹‘ƒ•ˆ‘ŽŽ‘™•ǣ

݄௧ ൌ ߙ଴ ൅ σ௤௝ୀଵ ߙ௝ ߝ௧ି௝ ଶ ൅ σ௣௜ୀଵ ߚ௜ ݄௧ି௜ ൅ ߜ௞ ‫ܦ‬ ISSN 2007-5383 versión digital,

ISSN 2007-5375 versión impresa

(3)

73

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 ”‡’”‡•‡–• –Š‡ †—› ˜ƒ”‹ƒ„Ž‡ ™Š‹…Š –ƒ‡• ˜ƒŽ—‡ Ͳ „‡ˆ‘”‡ —‰—•– ͺǡ ʹͲͲ͹ ƒ† ‘‡ ƒˆ–‡”™ƒ”†•Ǥ ˆ –Š‡ †—› ˜ƒ”‹ƒ„Ž‡ …‘‡ˆϐ‹…‹‡– ‹• ’‘•‹–‹˜‡ ƒ†•–ƒ–‹•–‹…ƒŽŽ›•‹‰‹ϐ‹…ƒ–ǡƒ‹…”‡ƒ•‡†˜‘Žƒ–‹Ž‹–›™ƒ•…ƒ—•‡†„›–Š‡ Ǥ Š‡ǡ–Š‡‘†‡Ž™ƒ•–‡•–‡†ˆ‘”‡ˆˆ‡…–—•‹‰ƒǦ–‡•–Ǥ ˆ–Š‡ …‘‡ˆϐ‹…‹‡–‹•‘–•–ƒ–‹•–‹…ƒŽŽ›•‹‰‹ϐ‹…ƒ–ǡ–Š‡‘†‡Ž™‹ŽŽ„‡ƒ†‡“—ƒ–‡Ǥ

2.4 TARCH model Š‡”‡ ‹• ƒ ™‹†‡ ”ƒ‰‡ ‘ˆ ƒ•›‡–”‹…  ‘†‡Ž•ǣ   †‡ ‡Ž•‘ ȋͳͻͻͳȌǡ

Ǧ ȋ Ž‘•–‡et alǤǡͳͻͻ͵ȌǡǦ ȋƒ‘‹ƒǡͳͻͻͶȌǡ ȋ‹‰et alǤǡͳͻͻ͵ȌǡǦ ȋƒ‡›ƒ”‘Ž›‹ǡop citǤȌ‘”Ǧ ȋ•‹ǡ ʹͲͲͶȌƒ”‡•‘‡‘ˆ–Š‡Ǥ Š‡‘†‡Ž•’”‘’‘•‡†‹–Š‹•’ƒ’‡”Šƒ˜‡–Š‡ˆ‘ŽŽ‘™‹‰‰‡‡”ƒŽ‹œ‡†•’‡…‹ϐ‹…ƒ–‹‘‘ˆ–Š‡˜ƒ”‹ƒ…‡‡“—ƒ–‹‘:

ߪ ଶ ൌ ߙ ൅ σ௤௝ୀଵ ߚ௝ ߪ௧ି௝ ଶ ൅ σ௣௜ୀଵ ߙ௜ ߝ௧ି௜ ଶ ൅ σ௥௛ୀଵ ߛ௛ ߝ௧ି௛ ଶ ݀௧ି௛

(4)

‹ˆ ݀௧ ൌ ͳ if ߝ௧ ൏0 –Š‹•‘†‡Ž‹ˆ ߝ௧ି௜ ൐ Ͳ –Š‡’‘••‹–‹˜‡”‡•‹†—ƒŽ˜ƒŽ—‡•ƒ”‡‹–‡”’”‡–‡† ƒ•’‘•‹–‹˜‡•Š‘…•Ǥ ˆ ߝ௧ି௜ ൏ Ͳ ǡ‡‰ƒ–‹˜‡”‡•‹†—ƒŽ˜ƒŽ—‡•”‡’”‡•‡–‡‰ƒ–‹˜‡ •Š‘…•Ǥ‘•‹–‹˜‡‡™•Šƒ•ƒߙଵ ‹’ƒ…–ƒ†‡‰ƒ–‹˜‡‡™•Šƒ•ƒߙଵ ൅ߛଵ ‡ˆˆ‡…–Ǥ Š‡–Š‡” ߛଵ ൐ Ͳǡ‡‰ƒ–‹˜‡‡™•‹…”‡ƒ•‡•˜‘Žƒ–‹Ž‹–›ǡ–Š‹•‡ˆˆ‡…–‹•‘™ƒ• ƒ•›‡–”‹…˜‘Žƒ–‹Ž‹–›‘”Ž‡˜‡”ƒ‰‡‡ˆˆ‡…–ǡ‹‘–Š‡”™‘”†•‹ˆ ߛଵ ് Ͳǡ –Š‡‹’ƒ…– ‘ˆ‰‘‘†ƒ†„ƒ†‡™•‹•ƒ•›‡–”‹…ȋ ‘•Š‹ǡʹͲͳʹȌǤŠ‡ƒ‹‘„Œ‡–‹˜‡‘ˆ–Š‹• ’ƒ’‡”‹•–‘’”‘˜‡ƒ•‹‡–”‹‡•‹–‡”•‘ˆ’‘••‹–‹˜‡ƒ†‡‰ƒ–‹˜‡•Š‘…•Ǥ

ߪ ଶ ൌ ߙ ൅ σ௤௝ୀଵ ߚ௝ ߪ௧ି௝ ଶ ൅ σ௣௜ୀଵ ߙ௜ ߝ௧ି௜ ଶ ൅

(5)

σ௥௛ୀଵ ߛ௛ ߝ௧ି௛ ଶ ݀௧ି௛ ൅ ߜ௞ ‫ݑܦ‬ ‡”‡—–ƒ‡•ƒ˜ƒŽ—‡‘ˆͲ„‡ˆ‘”‡—‰—•–ͻǡʹͲͲ͹ƒ†‘‡ƒˆ–‡”™ƒ”†•Ǥ ˆ –Š‡†—›˜ƒ”‹ƒ„Ž‡…‘‡ˆϐ‹…‹‡–ǡ—‹•’‘••‹–‹˜‡ƒ†•–ƒ–‹•–‹…ƒŽŽ›•‹‰‹ϐ‹…ƒ–ǡ ‹–‹†‹…ƒ–‡•ƒ‹…”‡ƒ•‡‹ƒ‰‹–—†‘ˆŽ‡˜‡”ƒ‰‡‡ˆˆ‡…–Ǥ

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3. Empirical analysis ‹‰—”‡ ʹ ’”‡•‡–• –Š‡ ƒƒ†ƒǡ –Š‡ ǤǤ ƒ† ‡š‹…‘ Ž‡˜‡Ž ‹†‡š ˜ƒŽ—‡• ƒ† •–‘… ‹†‡š ”‡–—”•ǡ „‡ˆ‘”‡ ƒ† †—”‹‰ –Š‡ ϐ‹ƒ…‹ƒŽ …”‹•‹•Ǥ Š‡ ‹…”‡ƒ•‡ ‹ ƒŽŽ Ž‡˜‡Ž ‹†‡š ˜ƒŽ—‡•ǡ †—”‹‰ –Š‡ –Š‹”† “—ƒ”–‡” ‘ˆ ʹͲͲ͹ǡ ‹• ‡š’Žƒ‹‡† „› ƒ •’‡…—Žƒ–‹˜‡ „—„„Ž‡ ’‡ƒǤ Š‹• ’‡ƒ ™ƒ• ˆ‘ŽŽ‘™‡† „› ƒ „‹‰ ˆƒŽŽ ‹ ƒŽŽ –Š‡ •–‘…ƒ”‡–•”‡•—Ž–‹‰ˆ”‘–Š‡ ‡ˆˆ‡…–•Ǥ–Š‡‘–Š‡”Šƒ†ǡ”‡–—”•ǡ ƒ’’ƒ”‡–Ž›ǡ ’”‡•‡– Š‹‰Š‡” …Šƒ‰‡• ȋ‹…”‡ƒ•‹‰ ˜‘Žƒ–‹Ž‹–›Ȍ ƒ† ˜‘Žƒ–‹Ž‹–› …Ž—•–‡”•†—”‹‰–Š‡…”‹•‹•’‡”‹‘†…‘’ƒ”‡†–‘–Š‡’”‡Ǧ…”‹•‹•’‡”‹‘†Ǥ˜‡”ƒŽŽǡ ƒŽŽ•‡”‹‡•‡’–ƒ•–”‘‰”‡Žƒ–‹‘•Š‹’†—‡–‘‰‡‡”ƒŽ‹•–ƒ„‹Ž‹–›ƒ†ˆƒŽŽ•‹ƒŽŽ

Figure 2. Mexico, Canada and the U. S. Level Value and Stock Price Index Returns (January, 2003-February, 2015)

Source: Prepared by author using Bloomberg and Economatica data. ISSN 2007-5383 versión digital,

ISSN 2007-5375 versión impresa

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–Š‡•–‘…ƒ”‡–•ǤŠ‡•‡ˆƒ…–•ƒ”‡ƒƒŽ›œ‡†–Š”‘—‰Š–Š‡‹’Ž‡‡–ƒ–‹‘‘ˆ –Š‡‡–Š‘†‘Ž‘‰›‹–Š‡ˆ‘ŽŽ‘™‹‰•‡…–‹‘Ǥ ƒ„Ž‡ͳ•Š‘™•–Š‡†ƒ–‡‘ˆ–Š‡ƒš‹—’‘•‹–‹˜‡ƒ†‡‰ƒ–‹˜‡˜ƒ”‹ƒ–‹‘• ƒ† –Š‡ Š‹‰Š‡•– ƒ† Ž‘™‡•– Ž‡˜‡Ž• ˆ‘” ‡ƒ…Š ‹†‡šǤ ƒš‹— ˜ƒ”‹ƒ–‹‘• ȋ’‘•‹–‹˜‡ ƒ† ‡‰ƒ–‹˜‡Ȍ ‘……—””‡† ™Š‡ –Š‡ …”‹•‹• –—”‡† ‹–‘ ƒ ‰Ž‘„ƒŽ ϐ‹ƒ…‹ƒŽ …”‹•‹•ǡ ƒˆ–‡” –Š‡ ˆƒ‹Ž—”‡ ‘ˆ ‡Šƒ ”‘–Š‡”• ‹ •‡’–‡„‡” ʹͲͲͺǤ Š‡Žƒ…‘ˆ…‘‹…‹†‡…‡„‡–™‡‡–Š‡†ƒ–‡‘ˆ–Š‡Š‹‰Š‡•–ƒ†–Š‡Ž‘™‡•–Ž‡˜‡Ž •—‰‰‡•–•–Šƒ––Š‡•‡ˆƒ…–•ƒ›„‡”‡Žƒ–‡†–‘Ž‘…ƒŽ…‘†‹–‹‘•Ǥ Table 1. Stock Price Index Maximum Positive and Negative Variation and Highest and Lowest level index values Level

Index

Maximum variation

High Level/Change IPC

TSE

Positive

Negative

3680.127

722.170

0.162

-0.115

Date

11/04/2013

24/11/2003

29/10/2008

06/10/2008

Level/Change

15323.764

5849.301

0.095

-0.105

Date

31/10/2007

18/05/2004

29/10/2008

01/12/2008

2115.480

676.530

0.104

-0.095

24/02/2015

09/03/2009

14/10/2008

15/10/2008

Level/Change S&P 500

Low

Date

Source: Prepared by author using Bloomberg and Economatica data.

3.1 Rolling window correlation analysis ‹‰—”‡ ͵ •Š‘™• …Šƒ‰‡• ‹ –Š‡ …‘””‡Žƒ–‹‘ ‹†‡š ƒ‘‰   …‘—–”‹‡• ‡“—‹–› ƒ”‡–•Ǥ Š‡ ‡š‹…ƒ ƒ† –Š‡ ǤǤ •–‘… ƒ”‡–• Š‡Ž† –Š‡ Š‹‰Š‡•– …‘””‡Žƒ–‹‘ Ž‡˜‡Ž• †—”‹‰ –Š‡ ™Š‘Ž‡ ’‡”‹‘†Ǥ Š‡ •‡…‘† ‘•– ‹’‘”–ƒ– ”‡Žƒ–‹‘•Š‹’ ‹• „‡–™‡‡ –Š‡ ƒƒ†‹ƒ ƒ† –Š‡ ǤǤ ƒ”‡–•Ǥ Š‡ Ž‘™‡•– …‘””‡Žƒ–‹‘•Ž‡˜‡Ž•™‡”‡–Š‘•‡’”‡•‡–‡†„›–Š‡‡š‹…ƒƒ†–Š‡ƒƒ†‹ƒ ‡“—‹–›ƒ”‡–•ǤŠ‹•Žƒ•–”‡•—Ž–ƒ›„‡…ƒ—•‡†„›–Š‡‰‡‘‰”ƒ’Š‹…ƒŽŽ‘…ƒ–‹‘

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‘ˆ„‘–Š–Š‡‡š‹…ƒƒ†ƒƒ†‹ƒƒ”‡–•‡š––‘–Š‡ǤǤ‡…‘‘›ƒ†‘– „›ƒ…Ž‘•‡”‡Žƒ–‹‘•Š‹’„‡–™‡‡–Š‡ǡƒ•™‡ŽŽƒ•ǡ„›–Š‡ˆƒ…––Šƒ––Š‡ǤǤ‹• –Š‡Žƒ”‰‡•–’‘”–ˆ‘Ž‹‘ˆ‘”‡‹‰‹˜‡•–‡–•‘—”…‡ƒ†”‡…‹’‹‡–…‘—–”›Ǥ Figure 3. Rolling window correlation results

Source: Prepared by author based on results obtained.

™‘Ž‹‡•…ƒ„‡‘„•‡”˜‡†‹ ‹‰—”‡͵ǡ–Š‡ϐ‹”•–‘‡ǡˆ”‘–Š‡„‘––‘—’ǡ …‘””‡•’‘†•–‘–Š‡…‘””‡Žƒ–‹‘…‘‡ˆϐ‹…‹‡–ƒ˜‡”ƒ‰‡„‡ˆ‘”‡–Š‡…”‹•‹•ǡ™Š‹…Š ‹• ͲǤͷ͵Ǣ ™Š‹Ž‡ –Š‡ †‹•…‘–‹—‘—• Ž‹‡ ƒ„‘˜‡ ‹– ”‡’”‡•‡–• –Š‡ …‘””‡Žƒ–‹‘ …‘‡ˆϐ‹…‹‡– ƒˆ–‡” –Š‡ …”‹•‹•ǡ ™Š‹…Š Šƒ• ƒ ˜ƒŽ—‡ ‘ˆ ͲǤ͸ͺǤ – ‹• ‹’‘”–ƒ– –‘ ‡–‹‘–Šƒ–ǡ–Š‡…‘””‡Žƒ–‹‘ƒ˜‡”ƒ‰‡ǡƒ•ƒ‹‡†‹ƒ–‡‡ˆˆ‡…–‘ˆ–Š‡…”‹•‹• ȋ—‰—•–ʹͲͲ͹Ǧ‡…‡„‡”ʹͲͳʹȌ‹•ƒ„‘˜‡ͲǤ͹Ǥ –Š‹••‡•‡ǡ”‡Žƒ–‡†Ž‹–‡”ƒ–—”‡ Šƒ• ‹†‡–‹ϐ‹‡† –Šƒ– ƒ …‘””‡Žƒ–‹‘ Ž‡˜‡Ž Š‹‰Š‡” –Šƒ ͲǤ͹ ”‡’”‡•‡–• •–”‘‰ …‘””‡Žƒ–‹‘Ǥ ‡…‡ǡ ‹‰—”‡ ͵ ’”‘˜‹†‡• ‡˜‹†‡…‡ ƒ„‘—– …‘–ƒ‰‹‘ ‡ˆˆ‡…– ‘  •–‘…ƒ”‡–•†—”‹‰–Š‡ Ǥ

ISSN 2007-5383 versión digital,

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3.2 GARCH model results ‡•…”‹’–‹˜‡ •–ƒ–‹•–‹…• ‘ˆ   …‘—–”‹‡• ‡“—‹–› ƒ”‡–• ‹†‡š‡• ƒ”‡ ’”‡•‡–‡†‹ƒ„Ž‡•ʹƒ†͵Ǥ–ƒ†ƒ”††‡˜‹ƒ–‹‘ǡ‡ƒǡ—”–‘•‹•ǡ•‡™‡••ǡ

ƒ”“—‡‡”ƒƒ†Ǧ–‡•–•ƒ”‡‹…Ž—†‡†Ǥƒ„Ž‡ʹ…‘–ƒ‹•–Š‡’”‡Ǧ…”‹•‹• ’‡”‹‘†”‡•—Ž–•ƒ†–ƒ„Ž‡͵•Š‘™•–Š‡†‡•…”‹’–‹˜‡•–ƒ–‹•–‹…•‘—–…‘‡‘ˆ–Š‡ …”‹•‹•’‡”‹‘†‹‘”†‡”–‘…‘’ƒ”‡–Š‡ϐ‹ƒ…‹ƒŽ•‡”‹‡•’‡”ˆ‘”ƒ…‡„‡–™‡‡ –™‘’‡”‹‘†•Ǥ Table 2. Descriptive Statistics before Crisis Period- January 1, 2001 to August 8, 2007 &RXQWU\

6'

0HDQ

.XUWRVLV

6NHZQHVV -DUTXH%HUD$5&+ F-statistics Probability

86

0.0084

0.0005

4.3735

-0.0342

73.99635*

5.81 (2)*

0.00

&DQDGi

0.0098

0.0012

4.2862

-0.3532

84.2478*

3.48 (3)**

0.02

México

0.0145

0.0016

5.9237

-0.2688

345.745*

9.78 (1)*

0.00

Reported values are statistically representative at *1%,** 5% and ***10% significance levels. Note: the statistic test ARCH LM corresponds to the Lagrange multiplier used to detect the ARCH effect; the null hypothesis represents the absence of heteroscedasticity, distribution of that parameter is ߣʹ ሺ݇ሻ.

Table 3. Descriptive Statistics Crisis Period- August 8, 2007 to February 27, 2015 &RXQWU\

6'

0HDQ

86

0.015

0.0002380

10.371

-0.454

3483.70*

172.03*

0.00

&DQDGD

0.016 -0.0000319

9.703

-0.484

2897.44*

191.95*

0.00

Mexico

0.020

11.086

0.256

4146.74*

103.35*

0.00

0.0000574

.XUWRVLV 6NHZQHVV -DUTXH%HUD$5&+ F-statistics Probability

Reported values are statistically representative at * 1%,** 5% and ***10% significance levels. Note: As in Table 2, the statistic test ARCH LM corresponds to the Lagrange multiplier used to detect the ARCH effect; the null hypothesis represents the absence of heteroscedasticity, distribution of that parameter is ߣʹ ሺ݇ሻ.

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Volumen 7, número 1, enero - junio 2017, pp. 67-88

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Global Financial Crisis Volatility Impact and Contagion Effect…

FINANZAS Y RIESGO

– …ƒ „‡ ‘„•‡”˜‡† –Šƒ–  ˜‘Žƒ–‹Ž‹–›ǡ ‡ƒ•—”‡† „› –Š‡ ‹…”‡ƒ•‡ ‹ –Š‡ •–ƒ†ƒ”††‡˜‹ƒ–‹‘ǡ‹•—…ŠŠ‹‰Š‡”ƒˆ–‡”–Š‡…”‹•‹•ˆ‘”ƒŽŽ–Š‡ƒ”‡–•ǤŠ‡ ”‡–—”•†‹•–”‹„—–‹‘‹•‡‰ƒ–‹˜‡Ž›•‡™‡††—”‹‰–Š‡’”‡Ǧ…”‹•‹•’‡”‹‘†‹ ƒŽŽ…ƒ•‡•ƒ†‡‰ƒ–‹˜‡Ž›„‹ƒ•‡†‹–Š‡…”‹•‹•’‡”‹‘†ǡ‡š…‡’–ˆ‘”–Š‡‡š‹…ƒ ƒ”‡––Šƒ–‹•’‘•‹–‹˜‡Ž›„‹ƒ•‡†ǡ‹†‹…ƒ–‹‰–Š‡’”‡•‡…‡‘ˆƒ•›‡–”›ǤŠ‡ ˜ƒŽ—‡• … ‘…‡”‹‰ —”–‘•‹• •—‰‰‡•– –Šƒ–ǡ –Š‡ †‹•–”‹„—–‹‘ ‹• Ž‡’–‘—”–‹… ™‹–ŠƒŠ‹‰Š…‘…‡–”ƒ–‹‘‘–Š‡…‡–”ƒŽ˜ƒŽ—‡•ƒ†–Š‡’”‡•‡…‡‘ˆŠ‡ƒ˜› –ƒ‹Ž•Ǥ††‹–‹‘ƒŽŽ›ǡ”‡•—Ž–•‹†‹…ƒ–‡–Š‡’”‡•‡…‡‘ˆ‡ˆˆ‡…– ˆ‘”‡ƒ…Šƒ†‡˜‡”›‘‡‘ˆ–Š‡•‡”‹‡•—†‡”•–—†›Ǥ‹…‡–Š‡ ‘†‡Ž ‹• •—‹–ƒ„Ž‡ ˆ‘” ‘†‡Ž‹‰ Ž‡’–‘—”–‹… •‡”‹‡•ǡ ‹– ‹• ‡š’‡…–‡† –‘ …‘””‡…–Ž› ƒƒŽ›œ‡‡“—‹–›ƒ”‡–•‹†‡š‡•„‡Šƒ˜‹‘”Ǥ ‹ƒŽŽ›ǡ˜ƒŽ—‡•‘ˆ–Š‡ ȋͳǡͳȌ •Š‘™‹ƒ„Ž‡•ʹƒ†͵‹’Ž›–Š‡’”‡•‡…‡‘ˆ…Ž—•–‡”•‘ˆ˜‘Žƒ–‹Ž‹–›ǡ™Š‡”‡ Žƒ”‰‡…Šƒ‰‡•‹˜‘Žƒ–‹Ž‹–›–‡†–‘„‡ˆ‘ŽŽ‘™‡†„›Žƒ”‰‡…Šƒ‰‡•ƒ†•ƒŽŽ …Šƒ‰‡•–‡†–‘„‡ˆ‘ŽŽ‘™‡†„›•ƒŽŽ…Šƒ‰‡•ȋ‰Ž‡ƒ†‘ŽŽ‡”•Ž‡˜ǡͳͻͺ͸ȌǤ ‘•‡“—‡–Ž›ǡ–Š‡’”‘„ƒ„‹Ž‹–‹‡•‘ˆ ƒ”“—‡Ǧ‡”ƒ–‡•–‹‰”‡’‘”–‡†‹ƒ„Ž‡•ʹ ƒ†͵ǡƒŽŽ‘™–Š‡”‡Œ‡…–‹‘‘ˆ–Š‡‘”ƒŽ†‹•–”‹„—–‹‘Š›’‘–Š‡•‹•ƒ––Š‡ͳΨ •‹‰‹ϐ‹…ƒ…‡Ž‡˜‡ŽǤ Š‡ …‘†‹–‹‘ ‘ˆ •–ƒ–‹‘ƒ”‹–› ™ƒ• –‡•–‡† ƒ’’Ž›‹‰ –Š‡ Š‹ŽŽ‹’• ‡””‘ ƒ†–Š‡—‰‡–‡†‹…‡› —ŽŽ‡”–‡•–•Ǥ‡•—Ž–•”‡’‘”–‡†‹ƒ„Ž‡Ͷ•—‰‰‡•– Table 4. Unit Root Testing of Daily Returns of Stock markets ADF 

3UHFULVLV

86.

&DQDGD

Mexico

Phillips- Perron &ULVLV

3UHFULVLV

&ULVLV

Levels

FD

Levels

FD

Levels

FD

Levels

FD

-32.46

-16.59

-43.26

-21.41

-32.72

-307.81

-43.26

-376.45

(0.00)*

(0.00)

(0.00)

(0.00)

(0.00)

(0.00)

(0.00)

(0.00)

-29.98

-14.69

-35.25

-17.16

-29.99

-322.64

-35.21

-369.68

(0.00)

(0.00)

(0.00)

(0.00)

(0.00)

(0.00)

(0.00)

(0.00)

-29.48

-18.26

-35.19

-18.75

-29.34

-313.92

-38.02

-332.14

(0.00)

(0.00)

(0.00)

(0.00)

(0.00)

(0.00)

(0.00)

(0.00)

Critical MacKinnon criteria at a significance level of 1% is -3.44. Null hypothesis, series has unit root *Values within parentheses indicate probabilities

ISSN 2007-5383 versión digital,

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Estocástica:

Miriam Sosa y Edgar Ortiz

FINANZAS Y RIESGO

–Šƒ––Š‡—ŽŽŠ›’‘–Š‡•‹•ƒ„‘—––Š‡’”‡•‡…‡‘ˆƒ—‹–”‘‘–‹•”‡Œ‡…–‡†Ǣ˜ƒŽ—‡• ‘ˆ •–‘… ‹†‡š‡• ƒ”‡ ‰”‡ƒ–‡” –Šƒ –Š‡ …”‹–‹…ƒŽ ƒ…‹‘ ˜ƒŽ—‡ ƒ– ƒ ͳΨ •‹‰‹ϐ‹…ƒ…‡Ž‡˜‡ŽǤŠ‡”‡ˆ‘”‡ǡ‹–‹•…‘ϐ‹”‡†–Šƒ––Š‡•‡”‹‡•ƒ”‡•–ƒ–‹‘ƒ”› „‘–Šˆ‘”Ž‡˜‡Ž•ȋŽ‘‰•Ȍƒ†ˆ‘”–Š‡ϐ‹”•–†‹ˆˆ‡”‡…‡•Ǥ ‘…‘ϐ‹”–Šƒ––Š‡•‡”‹‡•ƒ”‡•–ƒ–‹‘ƒ”›ǡƒ”‡‰”‡••‹‘‡“—ƒ–‹‘ˆ‘”–Š‡ ƒ˜‡”ƒ‰‡›‹‡Ž†ˆ‘”‡ƒ…Š‘ˆ–Š‡•–‘…‡š…Šƒ‰‡•‹•’‡”ˆ‘”‡†„›ƒ’’Ž›‹‰–Š‡ ”‡—•…ŠǦ ‘†ˆ”‡› –‡•–Ǥ Š‡ —ŽŽ Š›’‘–Š‡•‹• ”‡“—‹”‡• –Šƒ– –Š‡ ”‡•‹†—ƒŽ• ƒ”‡ ‘–•‡”‹ƒŽŽ›…‘””‡Žƒ–‡†ǤŠ‡‡˜‹†‡…‹ƒ•—‰‰‡•–•–Šƒ––Š‡’”‘„ƒ„‹Ž‹–›˜ƒŽ—‡‹• ‰”‡ƒ–‡”–ŠƒͲǤͲͷǡ”‡Œ‡…–‹‰–Š‡‡š‹•–‡…‡‘ˆƒ—–‘…‘””‡Žƒ–‹‘Ǥ

3.3 Application of the GARCH (1,1) model ‘” ’ƒ”ƒ‡–‡” ‡•–‹ƒ–‹‘ –Š‡ ƒ”“—ƒ”†– ‘’–‹‹œƒ–‹‘ Ž‘‰ƒ”‹–Š ™ƒ• ‡’Ž‘›‡†ǡ ‹ …‘Œ—…–‹‘ ™‹–Š –Š‡ ƒš‹— Ž‹‡Ž‹Š‘‘† ‡–Š‘†Ǥ ‡”‹˜‡† ˆ”‘ ƒš‹— Ž‹‡Ž‹Š‘‘† ƒƒŽ›•‹• ƒ  ȋͳǡͳȌ ‘†‡Ž ™ƒ• …Š‘•‡ǡ •‹…‡ –Š‡‘–Š‡”‘†‡Ž•’”‡•‡–‡†‡‰ƒ–‹˜‡…‘‡ˆϐ‹…‹‡–•Ƚ1›Ⱦ1 ˆ‘”ƒŽŽ‹βͲǡ‘”–Š‡› ™‡”‡‘–•‹‰‹ϐ‹…ƒ–ƒ–Ž‡ƒ•–ƒ–ƒͻͲΨ…‘ϐ‹†‡…‡Ž‡˜‡ŽǤ ‡•—Ž–•‘ˆ–Š‡ ȋͳǡͳȌ†—›˜ƒ”‹ƒ„Ž‡ˆ‘”–Š‡ϐ‹ƒ…‹ƒŽ•‡”‹‡•ǡƒ”‡”‡’‘”–‡†‹ƒ„Ž‡ͷǤŠ‡ ‘†‡Ž‹•–‡•–‡†—•‹‰–Š‡Ǧ •–ƒ–‹•–‹…ǡ”‡˜‡ƒŽ‹‰–Š‡’”‡•‡…‡‘ˆƒ‡ˆˆ‡…–ƒˆ–‡”ƒ’’Ž›‹‰–Š‡‘†‡Ž•ǡ ”‡•—Ž–•ˆ”‘–Š‹•–‡•–ƒ”‡•–ƒ–‹•–‹…ƒŽŽ›•‹‰‹ϐ‹…ƒ–ǡ–Š‡‹”’”‘„ƒ„‹Ž‹–›‹•Š‹‰Š‡” –ŠƒͲǤͲͷǤ —”–Š‡”‘”‡ǡƒ„Ž‡ͷ•Š‘™•–Šƒ–ƒŽŽ’ƒ”ƒ‡–‡”•‡•–‹ƒ–‡†„›–Š‡  ȋͳǡͳȌ ‘†‡Ž ƒ”‡ ’‘•‹–‹˜‡ ƒ† •–ƒ–‹•–‹…ƒŽŽ› •‹‰‹ϐ‹…ƒ–ǡ ™‹–Š ƒ ’”‘„ƒ„‹Ž‹–› ‘ˆ Ž‡••–ŠƒͲǤͲͷǤ ƒ††‹–‹‘ǡ–Š‡˜ƒŽ—‡‘ˆ–Š‡’ƒ”ƒ‡–‡”‡•–‹ƒ–‡‹•Š‹‰Š‡”‹ ƒŽŽ…ƒ•‡•–Šƒ–Š‡˜ƒŽ—‡‘ˆȽ1ǡƒ•™‡ŽŽƒ•ǡ–Š‡•—Ƚ1ΪȾ1 ‹••ƒŽŽ‡”ƒ†˜‡”› …Ž‘•‡–‘‘‡ǡ•—…Š…‘†‹–‹‘‹•—”‡•–Šƒ––Š‡’”‘…‡••‹••–ƒ–‹‘ƒ”›ǡ‹Ǥ‡Ǥ –Š‡˜ƒ”‹ƒ…‡†‘‡•‘–‹…”‡ƒ•‡‹†‡ϐ‹‹–‡Ž›ǤŠ‡ˆƒ…––Šƒ––Š‡Žƒ‰…‘‡ˆϐ‹…‹‡–‘ˆ –Š‡…‘†‹–‹‘ƒŽ˜ƒ”‹ƒ…‡™ƒ•Žƒ”‰‡”–Šƒ–Š‡‡””‘”…‘‡ˆϐ‹…‹‡–Ƚ1‹’Ž‹‡•–Šƒ– –Š‡”‡‹•ƒ’‡”•‹•–‡…‡‘ˆ•Š‘…•™‹–Š‡ˆˆ‡…–•‹–Š‡Ž‘‰”—ǡ–Šƒ–‹•ǡ˜‘Žƒ–‹Ž‹–› †‘‡•‘–†‡…ƒ›”ƒ’‹†Ž›„—––‡†•–‘”‡ƒ‹ƒ†‹–•‡ˆˆ‡…–†‹‡•‘ˆˆ‰”ƒ†—ƒŽŽ›Ǥ Š‡ …‘‡ˆϐ‹…‹‡–• ‘ˆ –Š‡ †—› ˜ƒ”‹ƒ„Ž‡• ‹–”‘†—…‡† ‹ –Š‡ ˜ƒ”‹ƒ…‡ ‡“—ƒ–‹‘ȋ †—›Ȍƒ”‡’‘•‹–‹˜‡ǡ‡š…‡’–ˆ‘”–Š‡…ƒ•‡‘ˆƒƒ†ƒǢ–Š‡› ƒ”‡ƒŽ•‘•–ƒ–‹•–‹…ƒŽŽ›‹•‹‰‹ϐ‹…ƒ–‹–Š‡…ƒ•‡‘ˆ‡š‹…‘ƒ†ƒƒ†ƒƒ†‹–Š‡ ǤǤ…ƒ•‡–Š‡…‘‡ˆϐ‹…‹‡–‹••–ƒ–‹•–‹…ƒŽŽ›•‹‰‹ϐ‹…ƒ–ƒ–ͳͲΨ•‹‰‹ϐ‹…ƒ…‡Ž‡˜‡ŽǢ –Š‹• •—‰‰‡•–• –Šƒ– ˜‘Žƒ–‹Ž‹–› ‹…”‡ƒ•‡† ‹ –Š‡ Ǥ Ǥ ƒ”‡– ƒˆ–‡” –Š‡ …”‹•‹•Ǥ ‘™‡˜‡”ǡ–Š‡•‡”‡•—Ž–•‹†‹…ƒ–‡–Š‡‡‡†–‘ƒ’’Ž›ƒ‘†‡Ž–‘‡šƒ‹‡ –Š‡’”‡•‡…‡‘ˆƒ•›‡–”‹…˜‘Žƒ–‹Ž‹–›ƒ†ƒ‹…”‡ƒ•‡‹˜‘Žƒ–‹Ž‹–›ˆ‘ŽŽ‘™‹‰

80

Volumen 7, número 1, enero - junio 2017, pp. 67-88

Estocástica:

Global Financial Crisis Volatility Impact and Contagion Effect…

FINANZAS Y RIESGO

Table 5. GARCH models coefficients -January 1, 2001 to February 27, 2015 

&RHI¿FLHQWV

0H[LFR

86

&DQDGD

Į

7.47E-06

2.52E-06

1.93E-06

(0.00)*

(0.00)

(0.00)

0.0946

0.1027

0.0668

(0.00)

(0.00)

(0.00)

0.8782

0.8746

0.9236

(0.00)

(0.00)

(0.00)

0.9728

0.9701

0.9905

Dummy

1.24E-06

7.20E-07

-3.17E-07

0.2198

0.0732

0.3007

$5&+/0

0.0077

3.3911

0.1118

(0.9297)

(0.0657)

(0.7381)

Į

ȕ

Įȕ *$5&+

*Values within parentheses indicate probabilities.

–Š‡ϐ‹ƒ…‹ƒŽ…”‹•‹•ǤŠ‡ ‘†‡Ž‹•–‡•–‡†ˆ‘”‹–•ϐ‹–‡••ƒ†ƒ†‡“—ƒ…› —•‹‰Ǧ–‡•–Ǥ‡•—Ž–•‹†‹…ƒ–‡–Šƒ––Š‡”‡™ƒ•‘‡ˆˆ‡…–ƒˆ–‡” ƒ’’Ž›‹‰ –Š‡  ‘†‡Ž•ǡ •‹…‡   –‡•–• ƒ”‡ ‘– •–ƒ–‹•–‹…ƒŽŽ› •‹‰‹ϐ‹…ƒ–ƒ•–Š‡‹”’”‘„ƒ„‹Ž‹–›˜ƒŽ—‡‹•Š‹‰Š‡”–ŠƒͲǤͲͷǤ

3.4 Crisis and volatility changes applying a TARCH model Š‡ϐ‹ƒ…‹ƒŽŽ‹–‡”ƒ–—”‡ǡ’”‘˜‹†‡•ƒ’Ž‡‡˜‹†‡…‡’”‘˜‹‰–Šƒ–…Šƒ‰‡•‹–Š‡ …‘†‹–‹‘ƒŽ˜‘Žƒ–‹Ž‹–›‘ˆ•–‘…”‡–—”•‘–‘Ž›†‡’‡†•‘–Š‡ƒ‰‹–—†‡‘ˆ –Š‡•Š‘…•ǡ„—–ƒŽ•‘‘‹–••‹‰•Ǣƒ‡Ž›ǡ‰‘‘†ƒ†„ƒ†‡™•Ž‡ƒ†•–‘†‹ˆˆ‡”‡– ”‡•—Ž–•Ǥƒ†‡™•›‹‡Ž†•‰”‡ƒ–‡”…Šƒ‰‡•‹˜‘Žƒ–‹Ž‹–›–Šƒ‰‘‘†‡™•™Š‹…Š …ƒ„‡–‡•–‡†ƒ’’Ž›‹‰ƒȋͳǡͳȌ‘†‡Ž™‹–Šƒ†—›˜ƒ”‹ƒ„Ž‡‹–Š‡ ˜ƒ”‹ƒ…‡‡“—ƒ–‹‘Ǥ‡•—Ž–•‘ˆ‹–•‹’Ž‡‡–ƒ–‹‘ƒ”‡•Š‘™‹ƒ„Ž‡͸Ǥ

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ISSN 2007-5375 versión impresa

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Estocástica:

Miriam Sosa y Edgar Ortiz

FINANZAS Y RIESGO

ƒ„Ž‡͸ǡ–Š‡Ž‡˜‡”ƒ‰‡–‡”ȋɀȌ”‡’”‡•‡–‡†„› δͲȋͳȌ‹• ‰”‡ƒ–‡” –Šƒ œ‡”‘ ƒ† •–ƒ–‹•–‹…ƒŽŽ› •‹‰‹ϐ‹…ƒ–ǡ ”‡‹ˆ‘”…‹‰ –Š‡ ƒ••—’–‹‘ –Šƒ–’‘•‹–‹˜‡ƒ†‡‰ƒ–‹˜ƒ•Š‘…•Šƒ˜‡†‹ˆˆ‡”‡–‡ˆˆ‡…–•‘–Š‡˜‘Žƒ–‹Ž‹–›‘ˆ †ƒ‹Ž›•–‘…”‡–—”•Ǥ ‘‘†‡™•Šƒ•ƒ‹’ƒ…–‘ˆȽ1ǡ™Š‹Ž‡„ƒ†‡™•Ʋ‹’ƒ…– ‹•Ƚ1Ϊɀǡ–Š‡”‡ˆ‘”‡ǡ–Š‡‹’ƒ…–‘ˆ„ƒ†‡™•‹•Žƒ”‰‡”–Šƒ–Šƒ–‘ˆ‰‘‘†‡™•‹ ƒŽŽϐ‹ƒ…‹ƒŽƒ”‡–•ƒƒŽ›œ‡†Ǥ –Š‹•”‡‰ƒ”†ǡ–Š‡ƒƒ†‹ƒƒ”‡–•Š‘™• ƒ ‘”‡ ’”‘‘—…‡† ‡ˆˆ‡…– ‘ –Š‡ ƒ•›‡–”› ‘ˆ ˜‘Žƒ–‹Ž‹–›ǡ ˆ‘ŽŽ‘™‡† „› –Š‡ ‡š‹…ƒƒ†–Š‡ǤǤƒ”‡–•ǤŠ‡”‡ˆ‘”‡ǡ–Š‡‡˜‹†‡…‡…‘ϐ‹”•–Šƒ–‡‰ƒ–‹˜‡‹’ƒ…–•’”‘†—…‡†ƒŽ‡˜‡”ƒ‰‡‡ˆˆ‡…–Ǥ ‡•—Ž–•”‡’‘”–‡†ˆ‘”–Š‡†—›˜ƒ”‹ƒ„Ž‡‹†‹…ƒ–‡–Šƒ––Š‡ϐ‹ƒ…‹ƒŽ…”‹•‹• †‹†‘–‹…”‡ƒ•‡–Š‡ƒ‰‹–—†‡‘ˆ–Š‡Ž‡˜‡”ƒ‰‡‡ˆˆ‡…–‘–Š‡ ϐ‹ƒ…‹ƒŽ ƒ”‡–•ǡ™Š‡”‡–Š‡’”‘„ƒ„‹Ž‹–›ƒ••‘…‹ƒ–‡†™‹–Š–Š‡†—›˜ƒ”‹ƒ„Ž‡‹•‘– •–ƒ–‹•–‹…ƒŽŽ›•‹‰‹ϐ‹…ƒ–ƒ†ǡ‹–Š‡…ƒ•‡‘ˆ‡š‹…‘ƒ†ƒƒ†ƒǡ–Š‡†—› …‘‡ˆϐ‹…‹‡–‹•‡‰ƒ–‹˜‡Ǥ‡ƒ™Š‹Ž‡ǡ–Š‡˜ƒŽ—‡•‘  ˆ–Š‡‘‡Žƒ‰Ǧ˜ƒŽ—‡• ƒ”‡•–ƒ–‹•–‹…ƒŽŽ›‹•‹‰‹ϐ‹…ƒ–ǡ™‹–Šƒ’”‘„ƒ„‹Ž‹–›˜ƒŽ—‡Š‹‰Š‡”–ŠƒͲǤͲͷǤ Table 6. TARCH models coefficients -January 1, 2001 to February 27, 2015 

&RHI¿FLHQWV

0H[LFR

86

&DQDGD

Į

6.70E-06

1.17E-05

2.29E-06

(0.00)*

(0.00)

(0.00)

0.003568

0.17777

0.035707

0.5261

(0.00)

(0.00)

0.130937

0.199725

0.052788

(0.00)

(0.00)

(0.00)

0.90793

0.703279

0.924504

(0.00)

(0.00)

(0.00)

ĮȖ

0.911498

0.881049

0.960211

Dummy in variance

-1.09E-06

5.01E-07

-6.24E-07

(0.1346)

(0.7707)

(0.0381)

0.4542

0.7475

0.2126

(0.5004)

(0.4548)

(0.6447)

Į

ȕ

5(6,'$5&+ Ȗ

$5&+/0

*Values within parentheses indicate probabilities.

82

Volumen 7, número 1, enero - junio 2017, pp. 67-88

Global Financial Crisis Volatility Impact and Contagion Effect…

Estocástica:

FINANZAS Y RIESGO

• ’”‡˜‹‘—•Ž› ‡–‹‘‡†ǡ –Š‡ ƒƒ†‹ƒ ƒ”‡– ’”‡•‡–‡† Š‹‰Š‡” ˜‘Žƒ–‹Ž‹–›ƒ†Ž‡˜‡”ƒ‰‡‡ˆˆ‡…–ǡˆ‘ŽŽ‘™‡†„›–Š‡‡š‹…ƒƒ”‡–Ǥ –…‘—Ž†„‡ „‡…ƒ—•‡‘ˆ–Š‡•‹œ‡‘ˆ–Š‡ƒƒ†‹ƒƒ”‡–ƒ†‹–•”‡…‡–‡”‰‡”’”‘…‡•• –Šƒ– •–ƒ”–‡† ‹ ʹͲͳͳ ƒ† ‘ˆϐ‹…‹ƒŽŽ› ϐ‹‹•Š‡† ‹ ʹͲͳͶǤ Š‹• ‡”‰‡” ’”‘…‡•• Šƒ• ‰‹˜‡ ’Žƒ…‡ –‘ –Š‡ •‡…‘† Š‹‰Š‡” –”ƒ•ƒ–Žƒ–‹… ƒ”‡–ǡ …‘„‹‹‰ –Š‡ ‘†‘–‘…š…Šƒ‰‡ ”‘—’’Ž…ȋ Ȍ™‹–Š–Š‡ ”‘—’ǤŠ‡•‡–›’‡• ‘ˆ‹–‡”ƒ–‹‘ƒŽ‘’‡”ƒ–‹‘•…‘—Ž†‹…”‡ƒ•‡–Š‡‰Ž‘„ƒŽ”‹•‡š’‘•—”‡Ǥ

4. Conclusion Š‹•’ƒ’‡”ƒƒŽ›œ‡•–Š‡…‘–ƒ‰‹‘‡ˆˆ‡…–ƒ†˜‘Žƒ–‹Ž‹–›…Šƒ‰‡•‘ˆ–Š‡•–‘… ƒ”‡– ‹†‡š‡• ˆ‘” –Š‡ …‘—–”‹‡• …‘’”‹•‹‰ –Š‡   „Ž‘…ǣ ‡š‹…‘ǡ ƒƒ†ƒ ƒ† –Š‡ Ǥ Ǥ –• ƒ‹ ™ƒ• –‘ —˜‡‹Ž ™Š‡–Š‡” ‘” ‘– –Š‘•‡ ƒ”‡–• ™‡”‡…Šƒ”ƒ…–‡”‹œ‡†„›ƒ•›‡–”‹…˜‘Žƒ–‹Ž‹–›ƒ•™‡ŽŽƒ•‹ˆ•—…Š‡ˆˆ‡…–„‡…ƒ‡ ƒ……‡–—ƒ–‡† †—‡ –‘ –Š‡ ‰Ž‘„ƒŽ ϐ‹ƒ…‹ƒŽ …”‹•‹•ǡ ™Š‹…Š „‡‰ƒ ‹ ʹͲͲ͹ ™‹–Š †‹•‡“—‹Ž‹„”‹ƒ ‹ –Š‡ Ǥ Ǥ ƒ”‡–Ǥ ƒ–ƒ ‡šƒ‹‡† ‹…Ž—†‡† ƒ—ƒ”› ͳǡ ʹͲͲ͵ –‘ ‡„”—ƒ”› ʹ͹ǡ ʹͲͳͷǤ Š‡ ‡–Š‘†‘Ž‘‰› ‡’Ž‘›‡† –‘ ’”‘˜‡ –Š‡ …‘–ƒ‰‹‘ ‡ˆˆ‡…–™ƒ•”‘ŽŽ‹‰™‹†‘™…‘””‡Žƒ–‹‘ǡƒ†–‘…ƒ’–—”‡–Š‡†›ƒ‹…•‘ˆ–Š‡ ˜‘Žƒ–‹Ž‹–› ”‡–—”• ‘ˆ –Š‡ ǡ  ƒ† ƬͷͲͲ ‹†‡š‡•ǡ  ȋͳǡͳȌ ƒ† ȋͳǡͳȌ‘†‡Ž•™‡”‡—•‡†Ǥ Š‡”‘ŽŽ‹‰™‹†‘™…‘””‡Žƒ–‹‘ƒƒŽ›•‹•‘ˆˆ‡”•‡˜‹†‡…‡ƒ„‘—–…‘–ƒ‰‹‘ ‡ˆˆ‡…–ƒ‘‰–Š‡ …‘—–”‹‡••–‘…ƒ”‡–•ǤŠ‡‡“—‹–›‹†‡š‡•‘”‡ …Ž‘•‡Ž› ”‡Žƒ–‡† ƒ”‡  ƒ† Ƭ ˆ‘ŽŽ‘™‡† „›  ƒ† ƬǤ Š‹• ‡˜‹†‡…‡ Šƒ• ‹’‘”–ƒ– ‹’Ž‹…ƒ–‹‘• ‘ ƒ••‡– ƒŽŽ‘…ƒ–‹‘ ƒ† ”‹• †‹˜‡”•‹ϐ‹…ƒ–‹‘ …‘…‡”‹‰ –”‹Ǧƒ–‹‘ƒŽ ’‘”–ˆ‘Ž‹‘• ƒ‘‰ –Š‡•‡ ‡“—‹–› ƒ”‡–•Ǥ ‘”–ˆ‘Ž‹‘ ™‡‹‰Š–••Š‘—Ž†„‡…ƒ”‡ˆ—ŽŽ›‘’–‹‹œ‡†–‘„‡‡ϐ‹–ˆ”‘Š‹‰Š‡””‹•”‡–—”• ˆ”‘–Š‡‡š‹…ƒƒ”‡–ƒ†Ž‘™‡””‹•Ǧ”‡–—”’‡”ˆ‘”ƒ…‡ˆ”‘–Š‡‘–Š‡” –™‘„Ž‘…‡„‡”•ǡ’ƒ”–‹…—Žƒ”Ž›–Š‡Ž‘™…‘””‡Žƒ–‹‘„‡–™‡‡–Š‡ƒƒ†‹ƒ ƒ†‡š‹…ƒ•–‘…ƒ”‡–•Ǥ ’‹”‹…ƒŽŽ›ǡ–Š‡•–ƒ–‹‘ƒ”‹–›‘ˆ–Š‡•‡”‹‡•ǡ–Š‡’”‡•‡…‡‘ˆ‡ˆˆ‡…– ƒ† ‘”ƒŽ‹–› ™‡”‡ ϐ‹”•– ˜‡”‹ϐ‹‡†Ǥ Š‡ǡ ”‡Ž‡˜ƒ– ‘†‡Ž• ™‡”‡ …Š‘•‡ ƒ’’Ž›‹‰ƒš‹—Ž‹‡Ž‹Š‘‘†ƒƒŽ›•‹•‹†‡–‹ˆ›‹‰ƒ ȋͳǡͳȌ‘†‡Žƒ• –Š‡‘•–•—‹–ƒ„Ž‡ǤŠ‡‡’‹”‹…ƒŽ‡˜‹†‡…‡•—‰‰‡•–•–Š‡’‡”•‹•–‡…‡‘ˆ•Š‘…• ™‹–ŠŽ‘‰”—‡ˆˆ‡…–•Ǥ‡•—Ž–•ƒ••‘…‹ƒ–‡†™‹–Š–Š‡†—›˜ƒ”‹ƒ„Ž‡‹†‹…ƒ–‡† –Šƒ– ˜‘Žƒ–‹Ž‹–› ‹ –Š‡ ‡š‹…ƒ ƒ† ƒƒ†‹ƒ ƒ”‡–• ™‡”‡ ‘– ˜‡”› Žƒ”‰‡ ˆ‘ŽŽ‘™‹‰ –Š‡ …”‹•‹•ǡ ‡˜‡”–Š‡Ž‡•• ‹ –Š‡ …ƒ•‡ ‘ˆ –Š‡ Ǥ Ǥǡ ‡“—‹–› ƒ”‡–• ‹†‡š‡•‹…”‡ƒ•‹‰˜‘Žƒ–‹Ž‹–›•‹…‡–Š‡‰Ž‘„ƒŽϐ‹ƒ…‹ƒŽ…”‹•‹•ǡ™ƒ•…‘ϐ‹”‡†Ǥ

ISSN 2007-5383 versión digital,

ISSN 2007-5375 versión impresa

83

Estocástica:

Miriam Sosa y Edgar Ortiz

FINANZAS Y RIESGO

‹ƒŽŽ›ǡƒȋͳǡͳȌ‘†‡Ž™ƒ•ƒ’’Ž‹‡†–‘†‡–‡”‹‡–Š‡’”‡•‡…‡‘ˆ ƒ•›‡–”‹… ˜‘Žƒ–‹Ž‹–› ‹’ƒ…–• ‘ –Š‡ ”‡–—”• ‘ˆ –Š‡   ƒ”‡–• ƒ†ǡ Ž‹‡™‹•‡ǡ‹ˆ•—…Šƒ•›‡–”›‹…”‡ƒ•‡†ˆ‘ŽŽ‘™‹‰–Š‡ϐ‹ƒ…‹ƒŽ…”‹•‹•Ǥ ‹†‹‰• •Š‘™–Šƒ–ˆ‘”–Š‡–Š”‡‡•–‘…‡š…Šƒ‰‡•–Š‡”‡™ƒ•ƒŽ‡˜‡”ƒ‰‡‡ˆˆ‡…–‹–Š‡‹” ”‡–—”•‡”‹‡•Ǣ–Šƒ–‹•ǡ‡‰ƒ–‹˜‡‡™•Šƒ˜‡ƒŽƒ”‰‡”‹’ƒ…––Šƒ’‘•‹–‹˜‡‘‡• ‘˜‘Žƒ–‹Ž‹–›ǤŠ‡ƒƒ†‹ƒƒ”‡–•Š‘™•–Š‡Žƒ”‰‡•–ƒ•›‡–”›‹˜‘Žƒ–‹Ž‹–›ǡ ˆ‘ŽŽ‘™‡†„›–Š‡•–‘…ƒ”‡–•ˆ”‘‡š‹…‘ƒ†–Š‡ǤǤǡ”‡•’‡…–‹˜‡Ž›Ǥ‹–Š ”‡‰ƒ”†–‘–Š‡‡ˆˆ‡…–•‘ˆ–Š‡ϐ‹ƒ…‹ƒŽ…”‹•‹•‘˜‘Žƒ–‹Ž‹–›„‡Šƒ˜‹‘”ǡ”‡•—Ž–•ƒ„‘—– –Š‡†—›˜ƒ”‹ƒ„Ž‡‹†‹…ƒ–‡–Šƒ––Š‡ϐ‹ƒ…‹ƒŽ…”‹•‹•†‹†‘–ƒ……‡–—ƒ–‡–Š‡ ƒ•›‡–”‹…ƒŽ„‡Šƒ˜‹‘”‘ˆ˜‘Žƒ–‹Ž‹–›ǤŠ‡•‡Žƒ––‡””‡•—Ž–•ƒ›„‡‹†‹…ƒ–‹˜‡ ‘ˆƒ‰”‡ƒ–‡”‹–‡‰”ƒ–‹‘ƒ‘‰–Š‡‡š‹…ƒǡƒƒ†‹ƒƒ†–Š‡ǤǤƒ”‡–• †—‡–‘–Š‡‹”•‹‹Žƒ””‡ƒ…–‹‘–‘‡š‘‰‡‘—••Š‘…•Ǥ Š‡ ‹’‘”–ƒ…‡ ‘ˆ –Š‹• –›’‡ ‘ˆ ƒƒŽ›•‹• …‘•‹•–• ‹ ‡’Šƒ•‹œ‹‰ –Šƒ– Ž‘‰‡‘”›ƒ†Ž‡˜‡”ƒ‰‡‡ˆˆ‡…–‹Š‹„‹–‹˜‡•–‡–‘’‡”ƒ–‹‘•ǡƒ†Š‹‰Š‡” ƒ”‡–›‹‡Ž†•‹’Ž›Š‹‰Š‡”…‘•–•ˆ‘”…‘”’‘”ƒ–‹‘•‹••—‹‰•Šƒ”‡•ƒ†„‘†•ǡ ™Š‹…Šƒˆˆ‡…––Š‡”‡ƒŽ‡…‘‘›ǡ‰‡‡”ƒ–‡•‘”‡‡š’‡•‹˜‡ˆ—†‹‰ǡ‹…”‡ƒ•‡• ’”‹…‡• ƒ† †‹•…‘—”ƒ‰‡• ‹˜‡•–‡–Ǥ • ƒ …‘”‘ŽŽƒ”›ǡ ˆ‘” ’‘Ž‹…› ƒ‡”•ǡ ϐ‹†‹‰•‹’Ž›–Š‡‡‡†–‘‡Šƒ…‡–Š‡‹”•–‘…ƒ”‡–•–‘ˆ—”–Š‡”‡…‘‘‹… ‹–‡‰”ƒ–‹‘ƒ††‡˜‡Ž‘’‡–Ǥ

Referencias bibliográficas ‹œ‡ƒǡ Ǥǡ ‹Œƒ”ƒǡǤǡ‡‡ǡǤǡƬƒ”ǡǤȋʹͲͳʹȌǤDz‡˜‡Ž‘’‹‰‘—–”‹‡•ǯ ‹ƒ…‹ƒŽ—Ž‡”ƒ„‹Ž‹–›–‘–Š‡—”‘”‹•‹•ǣ˜‡––—†›‘ˆ“—‹–›ƒ†‘† ƒ”‡–•ȋ‘Ǥ™ͳͺͲʹͺȌǤNational Bureau of Economic ResearchǤ †”‹‘•‘’‘—Ž‘•ǡǤǤǡ ƒŽƒ”‹‘–‹•ǡǤǤǡƬ’›”‘—ǡǤ ǤȋʹͲͳ͸ȌǤDz‘–ƒ‰‹‘ǡ‘Žƒ–‹Ž‹–›‡”•‹•–‡…‡ǡƒ†‘Žƒ–‹Ž‹–›’‹ŽŽǦ˜‡”•ǣŠ‡ƒ•‡‘ˆ‡”‰›ƒ”‡–• —”‹‰–Š‡—”‘’‡ƒ ‹ƒ…‹ƒŽ”‹•‹•ǤdzAvailable at SSRN 2718841Ǥ ƒ‡ Ǥ Ǥ ƒ† Ǥ Ǥ ƒ”‘Ž›‹ ȋͳͻͻͶȌǤ Dz ‘‘† ‡™•ǡ ƒ† ‡™• ƒ† –‡”ƒ–‹‘ƒŽ ’‹ŽŽ‘˜‡”•‘ˆ–‘…‡–—”‘Žƒ–‹Ž‹–›‡–™‡‡ ƒ’ƒƒ†–Š‡dzǤƒ…‹ϔ‹…Ǧƒsin Finance Journalǡ ʹǡ’’ǤͶͲͷǦͶ͵ͺǤ ‘ŽŽ‡”•Ž‡˜ǡǤȋͳͻͺ͸ȌǤDz ‡‡”ƒŽ‹œ‡†—–‘”‡‰”‡••‹˜‡‘†‹–‹‘ƒŽ‡–‡”‘•‡†ƒ•–‹…‹–›dz. Journal of Econometrics ͵ͳǡ’’Ǥ͵Ͳ͹Ǧ͵ʹ͹Ǥ ‘ŽŽ‡”•Ž‡˜ǡǤǡ‰Ž‡ǡǤ ǤǡƬ‡Ž•‘ǡǤǤȋͳͻͻͶȌǤDz‘†‡Ž•dzǤHandbook of econometricsǡͶǡ’’ǤʹͻͷͻǦ͵Ͳ͵ͺǤ

84

Volumen 7, número 1, enero - junio 2017, pp. 67-88

Global Financial Crisis Volatility Impact and Contagion Effect…

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ƒ•ƒ•ǡǤƒ†‡’‡†ƒǡǤȋʹͲͲͺȌǤDz‘†‡Ž‘•”…Šǡ ƒ”…Š› ƒ”…Šǣ’Ž‹…ƒ…‹‘‡• ƒ‡”‹‡• ‹ƒ…‹‡”ƒ•dzǤCuadernos de Economía, ˜‘ŽǤ ǡïǤͶͺǡ‘‰‘–ž ʹͲͲͺǡ’’Ǥʹͺ͹Ǧ͵ͳͻǤ Š‹––‡†‹ǡ Ǥ Ǥ ȋʹͲͳͷȌǤ Dz ‹ƒ…‹ƒŽ ”‹•‹• ƒ† ‘–ƒ‰‹‘ ˆˆ‡…–• –‘ †‹ƒ –‘… ƒ”‡–ǣǮȂ ǯƒŽ›•‹•dzǤGlobal Business Reviewǡͳ͸ȋͳȌǡ’’ǤͷͲǦ͸ͲǤ ‹‰ Ǥǡ ”ƒ‰‡” Ǥ Ǥ Ǥ ƒ† ‰Ž‡ Ǥ Ǥ ȋͳͻͻ͵ȌǤ Dz ‘‰ ‡‘”› ”‘’‡”–› ‘ˆ –‘…ƒ”‡–‡–—”•ƒ†ƒ‡™‘†‡ŽdzǤJournal of Empirical Finance.ͳȋͳȌǡ ’’Ǥͺ͵ǦͳͲ͸Ǥ ‰Ž‡ǡ Ǥ Ǥǡ Ƭ ‘ŽŽ‡”•Ž‡˜ǡ Ǥ ȋͳͻͺ͸ȌǤ Dz‘†‡ŽŽ‹‰ –Š‡ ‡”•‹•–‡…‡ ‘ˆ ‘†‹–‹‘ƒŽ ƒ”‹ƒ…‡•dzǤEconometric reviewsǡͷȋͳȌǡ’’ǤͳǦͷͲǤ

Ž‘•–‡ǤǤǡǤ ƒ‰ƒƒ–Šƒƒ†ǤǤ—Ž‡ȋͳͻͻ͵ȌǤDz–Š‡‡Žƒ–‹‘•Š‹’‡–™‡‡–Š‡š’‡…–‡†ƒŽ—‡ƒ†–Š‡‘Žƒ–‹Ž‹–›‘ˆ–Š‡‘‹ƒŽš…‡••‡–—” ‘–‘…•dzǤThe Journal of Finance.ͶͺȋͷȌǡ’’Ǥͳ͹͹ͻǦͳͺͲͳ •‹ Ǥ Ǥ ȋʹͲͲͶȌǤ Dz —Ž–‹Žƒ–‡”ƒŽ ’’”‘ƒ…Š –‘ šƒ‹‹‰ –Š‡ ‘‘˜‡‡–• ‘‰ ƒŒ‘” ‘”Ž† “—‹–› ƒ”‡–•dzǤ International Review of Financial Analysisǡͳ͵ȋͶȌǡ’’ǤͶ͵͵ǦͶ͸ʹǤ

ƒ™ƒ†‹ǡ Ǥǡ‘—Š‹…Š‹ǡǤǡƬŠ‡ˆˆ‘—ǡǤ ǤȋʹͲͳͷȌǤDz‡•–‹‰ƒ†‘†‡Ž‹‰ —’‘–ƒ‰‹‘…”‘•• –‡”ƒ–‹‘ƒŽ–‘…ƒ”‡–•ǣ‘’ƒ”ƒ‡–”‹… –”ƒ†ƒ›’’”‘ƒ…ŠdzǤJournal of Financial Marketsǡʹ͸ǡ’’Ǥ͸ͶǦͺͶǤ

‹ǡǤǡƬǡǤȋʹͲͳ͸ȌǤDz Ž‘„ƒŽ ‹ƒ…‹ƒŽ”‹•‹•ƒ†‡”‰‹‰–‘…ƒ”‡–‘–ƒ‰‹‘ǣ‘Žƒ–‹Ž‹–› ’—Ž•‡‡•’‘•‡ —…–‹‘’’”‘ƒ…ŠdzǤResearch in International Business and Financeǡ͵͸ǡ’’Ǥͳ͹ͻǦͳͻͷǤ

‘•Š‹ǡǤȋʹͲͳʹȌǤDz ‹ƒ…‹ƒŽ”‹•‹•ƒ†‘Žƒ–‹Ž‹–›‡Šƒ˜‹‘—”‘ˆ–‘…ƒ”‡–•‘ˆ •‹ƒdzǤQuest-Journal of Management and ResearchǡʹȋʹȌǡ’’Ǥ͵ͷǦͶͶǤ ƒŽ•‹‡ǡ Ǥǡ Ƭ ”‘”ƒǡ Ǥ ȋʹͲͳ͸ȌǤ DzƒŽ›•‹• ‘ˆ –Š‡ ’ƒ…– ‘ˆ  ‹ƒ…‹ƒŽ ”‹•‹• ‘   …‘‘‹‡• —•‹‰ dzǤ FOCUS. Journal of International Businessǡ ʹȋʹȌǤ —Ž•Š”‡•Š–ŠƒǡǤǡƬ‹––ƒŽǡǤȋʹͲͳͷȌǤDz‘Žƒ–‹Ž‹–›‹–Š‡ †‹ƒ ‹ƒ…‹ƒŽƒ”‡– ‡ˆ‘”‡ǡ—”‹‰ƒ†ˆ–‡”–Š‡ Ž‘„ƒŽ ‹ƒ…‹ƒŽ”‹•‹•dzǤJournal of Accounting and Financeǡͳͷȋ͵Ȍǡ’ǤͳͶͳǤ ƒ”–‹ǡ ǤǡƬŽƒ‰—›‡ǡǤȋʹͲͳͷȌǤDz•›‡–”‹…›ƒ‹…•‹–Š‡‘””‡Žƒ–‹‘• ‘ˆ‡†‰‡ —†–”ƒ–‡‰› †‹…‡•ǣŠƒ–‡••‘•„‘—– ‹ƒ…‹ƒŽ‘–ƒ‰‹‘ǫdz Economics Bulletinǡ͵ͷȋͶȌǡ’’ǤʹͳͳͲǦʹͳʹͷǤ ‹‹ƒ‘—‹ǡǤǡƒ›ƒ‹ǡǤǡƬŠƒ‹„‹ǡǤȋʹͲͳͷȌǤDzŠ‡ ’ƒ…–‘ˆ ‹ƒ…‹ƒŽ”‹•‹•‘ •Žƒ‹…ƒ†‘˜‡–‹‘ƒŽ †‹…‡•‘ˆ–Š‡ ‘—–”‹‡•dzǤJournal of Applied Business Researchǡ͵ͳȋʹȌǡ’Ǥ͵ͷ͹Ǥ

ISSN 2007-5383 versión digital,

ISSN 2007-5375 versión impresa

85

Estocástica:

Miriam Sosa y Edgar Ortiz

FINANZAS Y RIESGO

‘Šƒƒ†‹ǡǤǡƬƒǡǤȋʹͲͳͷȌǤDz‡–—”ƒ†‘Žƒ–‹Ž‹–›’‹ŽŽ‘˜‡”•ƒ…”‘••“—‹–› ƒ”‡–•‹ƒ‹Žƒ†Š‹ƒǡ‘‰‘‰ƒ†–Š‡‹–‡†–ƒ–‡•dzǤEconometricsǡ͵ȋʹȌǡ’’ǤʹͳͷǦʹ͵ʹǤ ‘ŽŽƒŠǡǤǡ—‘”‡•Š‹ǡǤǤǡƬƒϐ‹”‘˜ǡ ǤȋʹͲͳ͸ȌǤDz“—‹–›ƒ”‡–‘–ƒ‰‹‘—”‹‰

Ž‘„ƒŽ ‹ƒ…‹ƒŽƒ†—”‘œ‘‡”‹•‡•ǣ˜‹†‡…‡ ”‘ƒ›ƒ‹…‘””‡Žƒ–‹‘ƒŽ›•‹•dzǤJournal of International Financial Markets, •–‹–—–‹‘•ƒ† ‘‡›Ǥ ‡Ž•‘ǡǤǤȋͳͻͻͳȌǤDz‘†‹–‹‘ƒŽ‡–‡”‘•‡†ƒ•–‹…‹–›‹••‡–‡–—”•ǣ‡™ ’’”‘ƒ…ŠdzǤ…‘‘‡–”‹…ƒǣ ‘—”ƒŽ‘ˆ–Š‡…‘‘‡–”‹…‘…‹‡–›ǡ’’Ǥ͵Ͷ͹Ǧ͵͹ͲǤ ƒ—Žǡ Ǥ Ǥǡ Ƭ ‹ƒ–ƒǡ Ǥ Ǥ ȋʹͲͳ͸ȌǤ DzŠ‡ ‹ƒ‰‡•ǡ ‡”•‹•–‡…‡ǡ •›‡–”› ‹ –Š‡‘Žƒ–‹Ž‹–›ǡ–Š‡”‹…‡‹•…‘˜‡”›ƒ†ˆϐ‹…‹‡…›ǡƒ†–Š‡ˆˆ‡…–‘ˆ–Š‡ —„’”‹‡‘”–‰ƒ‰‡ ‹ƒ…‹ƒŽ”‹•‹•‘–Š‡’‘–ƒ†–Š‡ —–—”‡•ƒ”‡–ǯ• ‡–—”•ǣ–Š‡ƒ•‡‘ˆ †‹ƒdzǤApplied EconomicsǡͶͺȋͺȌǡ’’Ǥ͸͸ͻǦ͸ͺ͵Ǥ ”ƒ‰‹†‹•ǡ Ǥ Ǥǡ ‹‡ŽŽ‹ǡ Ǥ Ǥǡ Š‹‘‹•ǡ Ǥǡ Ƭ …Š‹œƒ•ǡ Ǥ ȋʹͲͳͷȌǤ Dz‘–ƒ‰‹‘ ˆˆ‡…–• —”‹‰ ‹ƒ…‹ƒŽ ”‹•‹•ǣ ˜‹†‡…‡ ”‘ –Š‡ ”‡‡ ‘˜‡”‡‹‰ ‘†• ƒ”‡–dzǤJournal of Financial Stabilityǡͳͺǡ’’Ǥͳʹ͹Ǧͳ͵ͺǤ ‡›‡•ǡ Ǥ ǤǤǡƬ”–‹œǡǤȋʹͲͳ͵ȌǤDz‘†‡Ž‘•Ǧ ›’‘”–ƒˆ‘Ž‹‘•†‡‹˜‡”•‹× –”‹ƒ…‹‘ƒŽ‡•‡Ž‘•‡”…ƒ†‘•ƒ……‹‘ƒ”‹‘•†‡ŽdzǤRevista Mexicana de Economía y Finanzas. Nueva Época/Mexican Journal of Economics and FinanceǡͺȋʹȌǡ’’ǤͳʹͻǦͳͷͷǤ ƒ†‡”ǡ Ǥǡ Ƭ Ž‡‹‡‹‡”ǡ Ǥ ȋʹͲͲ͵ȌǤ Dz‘–ƒ‰‹‘ ƒ† ƒ—•ƒŽ‹–›ǣ ƒ ’‹”‹…ƒŽ ˜‡•–‹‰ƒ–‹‘‘ˆˆ‘—”•‹ƒ”‹•‹•’‹•‘†‡•dzǤJournal of International Financial Markets, Institutions and Moneyǡͳ͵ȋʹȌǡ’’Ǥͳ͹ͳǦͳͺ͸Ǥ ‹ŠƒǡǤȋʹͲͳͷȌǤDzƒ–—”‡‘ˆ‡”‰› †‡š‘Žƒ–‹Ž‹–›‹‘•– ‹ƒ…‹ƒŽ”‹•‹•‡”‹‘†ǣ˜‹†‡…‡•ˆ”‘ †‹ƒdzǤEnergy Procediaǡ͹ͷǡ’’Ǥʹͷͷ͸Ǧʹͷ͸ʹǤ ›”‹‘’‘—Ž‘•ǡ Ǥǡ ƒ”ƒǡ Ǥǡ Ƭ ‘—„ƒ‡”ǡ Ǥ ȋʹͲͳͷȌǤ Dz–‘… ƒ”‡– ‘Žƒ–‹Ž‹–› ’‹ŽŽ˜‡”•ƒ†‘”–ˆ‘Ž‹‘‡†‰‹‰ǣ ƒ†–Š‡ ‹ƒ…‹ƒŽ”‹•‹•dzǤInternational Review of Financial Analysisǡ͵ͻǡ’’Ǥ͹ǦͳͺǤ ƒ›Ž‘”ǡǤȋͳͻͺ͸ȌǤModeling Financial Time SeriesǤ ‘Š‹Ž‡›Ƭ‘•ǡ‡™‘”Ǥ ƒ›Ž‘”ǡ ǤǤǡƬ‹ŽŽ‹ƒ•ǡ ǤǤȋʹͲͲͻȌǤDzŽƒ…™ƒ‹–Š‡‘‡›ƒ”‡–dzǤAmer‹…ƒ…‘‘‹… ‘—”ƒŽǣƒ…”‘‡…‘‘‹…•ǡͳȋͳȌǡ’’ǤͷͺǦͺ͵Ǥ ƒ‘‹ƒ ǤǤȋͳͻͻͶȌǤDzŠ”‡•Š‘Ž†‡–‡”‘•‡†ƒ•–‹…‘†‡Ž•dzǤJournal of Economic ›ƒ‹…•ƒ†‘–”‘Žǡͳͷǡ’’Ǥͻ͵ͳǦͻͷͷǤ ‡•–‘•ǡ ǤǤȋʹͲͳͷȌǤŠ‡ Ž‘„ƒŽ ‹ƒ…‹ƒŽ”‹•‹•ǣ ”‘—„’”‹‡‘”–‰ƒ‰‡•–‘ —”‘’‡ƒ‘˜‡”‡‹‰‡„–Ǥ‘—–Ž‡†‰‡Ǥ

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Volumen 7, número 1, enero - junio 2017, pp. 67-88

Global Financial Crisis Volatility Impact and Contagion Effect…

Estocástica:

FINANZAS Y RIESGO

APPENDIX 1 Rolling window correlation, pre-crisis period (Jan 1, 2003- Ago 8, 2007)

Rolling window correlation, crisis period (Ago 9, 2007- Feb 27, 2015).

ISSN 2007-5383 versión digital,

ISSN 2007-5375 versión impresa

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