Cartea, ÁlvaroUniversidad Carlos III de Madrid. Departamento de Economía de la Empresa2010-04-072010-04-072010-04https://hdl.handle.net/10016/7583I propose to model stock price tick-by-tick data via a non-explosive marked point process. The arrival of trades is driven by a counting process in which the waiting-time between trades possesses a Mittag-Leffler survival function and price revisions have an infinitely divisible distribution. I show that the partial-integro-differential equation satisfied by the value of European-style derivatives contains a non-local operator in time-to-maturity known as the Caputo fractional derivative. Numerical examples are provided for a marked point process with conditionally Gaussian and with conditionally CGMY price innovations. Furthermore, the infinitesimal generator of the marked point process derived to price derivatives coincides with that of a Lévy process of either finite or infinite activity.application/pdfengAtribución-NoComercial-SinDerivadas 3.0 EspañaTick-by-tick dataWaiting-timesDurationHigh frequency dataCaputo operatorMarked point processworking paperG12G13C41Empresaopen accesswb101604