Derivatives pricing with marked point processes using Tick-by-tick data

Álvaro Cartea ()

DEE - Working Papers. Business Economics. WB from Universidad Carlos III de Madrid. Departamento de Economía de la Empresa

Abstract: I 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.

Keywords: Tick-by-tick; data; Waiting-times; Duration; High; frequency; data; Caputo; operator; Marked; point; process (search for similar items in EconPapers)
JEL-codes: C41 G12 G13 (search for similar items in EconPapers)
Date: 2010-04
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Citations: View citations in EconPapers (1)

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