Approximate Transition Density Estimation of the Stochastic Cusp Model

Kód výsledku v IS VaVaI

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Nalezeny alternativní kódy

RIV/00216208:11320/16:10329834

Výsledek na webu

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DOI - Digital Object Identifier

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Jazyk výsledku

angličtina

Název v původním jazyce

Approximate Transition Density Estimation of the Stochastic Cusp Model

Popis výsledku v původním jazyce

Stochastic cusp model is defined by stochastic differential equation with cubic drift. Its stationary density allows for skewness, different tail shapes and bimodality. There are two stable equilibria in bimodality case and movement from one equilibrium to another is interpreted as a crash. Qualitative properties of the cusp model were employed to model crashes on financial markets, however, practical applications of the model employed the stationary distribution, which does not take into account the serial dependence between observations. Because closed-form solution of the transition density is not known, one has to use approximate technique to estimate transition density. This paper extends approximate maximum likelihood method, which relies on the closed-form expansion of the transition density, to incorporate time-varying parameters of the drift function to be driven by market fundamentals. A measure to predict endogenous crashes of the model is proposed using transition density estimates. Empirical example estimates Iceland Krona depreciation with respect to the British Pound in the year 2001 using differential of interbank interest rates as a market fundamental.

Název v anglickém jazyce

Approximate Transition Density Estimation of the Stochastic Cusp Model

Popis výsledku anglicky

Stochastic cusp model is defined by stochastic differential equation with cubic drift. Its stationary density allows for skewness, different tail shapes and bimodality. There are two stable equilibria in bimodality case and movement from one equilibrium to another is interpreted as a crash. Qualitative properties of the cusp model were employed to model crashes on financial markets, however, practical applications of the model employed the stationary distribution, which does not take into account the serial dependence between observations. Because closed-form solution of the transition density is not known, one has to use approximate technique to estimate transition density. This paper extends approximate maximum likelihood method, which relies on the closed-form expansion of the transition density, to incorporate time-varying parameters of the drift function to be driven by market fundamentals. A measure to predict endogenous crashes of the model is proposed using transition density estimates. Empirical example estimates Iceland Krona depreciation with respect to the British Pound in the year 2001 using differential of interbank interest rates as a market fundamental.

Druh

D - Stať ve sborníku

CEP obor

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OECD FORD obor

10103 - Statistics and probability

Projekt

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Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2016

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název statě ve sborníku

Proceedings of the 34th International Conference Mathematical Methods in Economics MME 2016

ISBN

978-80-7494-296-9

ISSN

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e-ISSN

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Počet stran výsledku

6

Strana od-do

892-897

Název nakladatele

Technical University

Místo vydání

Liberec

Místo konání akce

Liberec

Datum konání akce

6. 9. 2016

Typ akce podle státní příslušnosti

EUR - Evropská akce

Kód UT WoS článku

000385239500153