Approximate Transition Density Estimation of the Stochastic Cusp Model
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. Qualitat...
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ftczacademyscien:oai:asep.lib.cas.cz:CavUnEpca/0507383 2024-02-11T10:05:09+01:00 Approximate Transition Density Estimation of the Stochastic Cusp Model Voříšek, J. (Jan) 2016 http://hdl.handle.net/11104/0298681 eng eng urn:isbn: 978-80-7494-296-9 http://hdl.handle.net/11104/0298681 multimodal distributions stochastic cusp model approximate transition density info:eu-repo/semantics/conferenceObject info:eu-repo/semantics/publishedVersion 2016 ftczacademyscien 2024-01-16T17:17:52Z 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. Conference Object Iceland The Czech Academy of Sciences: Publication Activity (ASEP) Krona ENVELOPE(12.432,12.432,65.827,65.827) |
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Open Polar |
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The Czech Academy of Sciences: Publication Activity (ASEP) |
op_collection_id |
ftczacademyscien |
language |
English |
topic |
multimodal distributions stochastic cusp model approximate transition density |
spellingShingle |
multimodal distributions stochastic cusp model approximate transition density Voříšek, J. (Jan) Approximate Transition Density Estimation of the Stochastic Cusp Model |
topic_facet |
multimodal distributions stochastic cusp model approximate transition density |
description |
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. |
format |
Conference Object |
author |
Voříšek, J. (Jan) |
author_facet |
Voříšek, J. (Jan) |
author_sort |
Voříšek, J. (Jan) |
title |
Approximate Transition Density Estimation of the Stochastic Cusp Model |
title_short |
Approximate Transition Density Estimation of the Stochastic Cusp Model |
title_full |
Approximate Transition Density Estimation of the Stochastic Cusp Model |
title_fullStr |
Approximate Transition Density Estimation of the Stochastic Cusp Model |
title_full_unstemmed |
Approximate Transition Density Estimation of the Stochastic Cusp Model |
title_sort |
approximate transition density estimation of the stochastic cusp model |
publishDate |
2016 |
url |
http://hdl.handle.net/11104/0298681 |
long_lat |
ENVELOPE(12.432,12.432,65.827,65.827) |
geographic |
Krona |
geographic_facet |
Krona |
genre |
Iceland |
genre_facet |
Iceland |
op_relation |
urn:isbn: 978-80-7494-296-9 http://hdl.handle.net/11104/0298681 |
_version_ |
1790602033039933440 |