0507383 20240111141022.320190807235959.9 000385239500153 6 s. E cav_un_epca*0462920978-80-7494-296-9892-897LiberecTechnical University2016KocourekA. multimodal distributions stochastic cusp model approximate transition density cav_un_auth*0256753 100 Voříšek Jan UTIA-B Ekonometrie Department of Econometrics E E CZ K Ústav teorie informace a automatizace AV ČR, v. v. i. pdf http://library.utia.cas.cz/separaty/2019/E/vorisek-0507383.pdf cav_un_auth*0281000 GBP402/12/G097 GA ČR CZ 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. cav_un_auth*0333702 MME 2016. International Conference Mathematical Methods in Economics /34./ 06.09.2016-09.09.2016 Liberec CZ BB 10000 10100 10103 2020 1 PR RVO:67985556 http://hdl.handle.net/11104/0298681 S n.a. Proceedings Paper Economics|Social Sciences Mathematical Methods 2016 SCOPUS PUBMED 000385239500153 WOS pdf cav_un_epca*0462920 Proceedings of the 34th International Conference Mathematical Methods in Economics MME 2016 978-80-7494-296-9 892 897 Liberec Technical University 2016 340 Kocourek A. 340 Vavroušek M.