How Frequently Does the Stock Price Jump? – An Analysis of High-Frequency Data with Microstructure Noises

The stock price is assumed to follow a jump-diffusion process which may exhibit time-varying volatilities. An econometric technique is then developed for this model and applied to high-frequency time series of stock prices that are subject to microstructure noises. Our method is based on first devising a localized particle filter and then employing fixed-lag smoothing in the Monte Carlo EM algorithm to perform the maximum likelihood estimation and inference. Using the intra-day IBM stock prices, we find that high-frequency data are crucial to disentangling frequent small jumps from infrequent large jumps. During the trading sessions, jumps are found to be frequent but small in magnitude, which is in sharp contrast to infrequent but large jumps when the market is closed. We also find that at the 5- or 10-minute sampling frequency, the conclusion will critically depend on whether heavy-tailed microstructure noises have been accounted for. Ignoring microstructure noises can, for example, lead to an overestimation of the jump intensity of 50% or more.Particle filtering, jump-diffusion, maximum likelihood, EM-algorithm.

Laser‐driven strong‐field Terahertz sources

A review on the recent development of intense laser‐driven terahertz (THz) sources is provided here. The technologies discussed include various types of sources based on optical rectification (OR), spintronic emitters, and laser‐filament‐induced plasma. The emphasis is on OR using pump pulses with tilted intensity front. Illustrative examples of newly emerging applications are briefly discussed, in particular strong‐field THz control of materials and acceleration and manipulation of charged particles

How frequently does the stock price jump? An analysis of high-frequency data with microstructure noises

The stock price is assumed to follow a jump-diffusion process which may exhibit time-varying volatilities. An econometric technique is then developed for this model and applied to high-frequency time series of stock prices that are subject to microstructure noises. Our method is based on first devising a localized particle filter and then employing fixed-lag smoothing in the Monte Carlo EM algorithm to perform the maximum likelihood estimation and inference. Using the intra-day IBM stock prices, we find that high-frequency data are crucial to disentangling frequent small jumps from infrequent large jumps. During the trading sessions, jumps are found to be frequent but small in magnitude, which is in sharp contrast to infrequent but large jumps when the market is closed. We also find that at the 5- or 10-minute sampling frequency, the conclusion will critically depend on whether heavy-tailed microstructure noises have been accounted for. Ignoring microstructure noises can, for example, lead to an overestimation of the jump intensity of 50% or more

A Generalized^2 Linear^2 Models módszer implementálása Octave rendszerben

Dolgozatomban egy olyan eljárást implementáltam, mely segítségével csökkenthető a nagy adathalmazok feldolgozásához szükséges erőforrás-igény, hiszen egy nagy adatmátrix redukált komponensű becslésével a számítási igény csökken. Erre létezik több megoldás is, ám az adatok sokfélesége miatt egy általános megoldás a G^2L^2M módszer, amely több modellt is magába foglal. Úgy gondolom, hogy az információs társadalom tagjait az szolgálja legjobban, ha az egyes fejlesztésekhez nem csak egy korlátozott csoport fér hozzá, ezért egy olyan matematikai rendszert választottam, melynek bármely platformra létezik implementációja, azok működése nem tér el egymástól, és végül nem utolsó sorban ingyenesen hozzáférhető. Ezeket a kritériumokat a GNU Octave rendszer mind magába foglalja. Az implementált algoritmus kompatibilis a MatLab rendszerrel is, így az azzal rendelkező felhasználók is használhatják a programomat.M