Approximate Transition Density Estimation of the Stochastic Cusp Model

0507383 - ÚTIA 2020 RIV CZ eng C - Konferenční příspěvek (zahraniční konf.)
Voříšek, Jan
Approximate Transition Density Estimation of the Stochastic Cusp Model.
Proceedings of the 34th International Conference Mathematical Methods in Economics MME 2016. Liberec: Technical University, 2016 - (Kocourek, A.; Vavroušek, M.), s. 892-897. ISBN 978-80-7494-296-9.
[MME 2016. International Conference Mathematical Methods in Economics /34./. Liberec (CZ), 06.09.2016-09.09.2016]
Grant CEP: GA ČR(CZ) GBP402/12/G097
Institucionální podpora: RVO:67985556
Klíčová slova: multimodal distributions * stochastic cusp model * approximate transition density
Obor OECD: Statistics and probability
http://library.utia.cas.cz/separaty/2019/E/vorisek-0507383.pdf

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.
Trvalý link: http://hdl.handle.net/11104/0298681