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Original title:
Approximate Transition Density Estimation of the Stochastic Cusp Model
Authors: Voříšek, Jan
Document type: Papers
Conference/Event: MME 2016. International Conference Mathematical Methods in Economics /34./, Liberec (CZ), 2016-09-06 / 2016-09-09
Year: 2016
Language: eng
Abstract: 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.
Keywords: approximate transition density; multimodal distributions; stochastic cusp model
Project no.: GBP402/12/G097 (CEP)
Funding provider: GA ČR
Host item entry: Proceedings of the 34th International Conference Mathematical Methods in Economics MME 2016, ISBN 978-80-7494-296-9
Institution: Institute of Information Theory and Automation AS ČR (web)
Document availability information: Fulltext is available at external website.
External URL: http://library.utia.cas.cz/separaty/2019/E/vorisek-0507383.pdf
Original record: http://hdl.handle.net/11104/0298681
Permalink: http://www.nusl.cz/ntk/nusl-399087
The record appears in these collections:
Research > Institutes ASCR > Institute of Information Theory and Automation
Conference materials > Papers
Authors: Voříšek, Jan
Document type: Papers
Conference/Event: MME 2016. International Conference Mathematical Methods in Economics /34./, Liberec (CZ), 2016-09-06 / 2016-09-09
Year: 2016
Language: eng
Abstract: 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.
Keywords: approximate transition density; multimodal distributions; stochastic cusp model
Project no.: GBP402/12/G097 (CEP)
Funding provider: GA ČR
Host item entry: Proceedings of the 34th International Conference Mathematical Methods in Economics MME 2016, ISBN 978-80-7494-296-9
Institution: Institute of Information Theory and Automation AS ČR (web)
Document availability information: Fulltext is available at external website.
External URL: http://library.utia.cas.cz/separaty/2019/E/vorisek-0507383.pdf
Original record: http://hdl.handle.net/11104/0298681
Permalink: http://www.nusl.cz/ntk/nusl-399087
The record appears in these collections:
Research > Institutes ASCR > Institute of Information Theory and Automation
Conference materials > Papers
Record created 2019-08-26, last modified 2022-09-29