Derivatives pricing with marked point processes using tick-by-tick data Articles uri icon

authors

  • CARTEA GONZALEZ, ALVARO IVAN

publication date

  • February 2013

start page

  • 111

end page

  • 123

issue

  • 1

volume

  • 13

International Standard Serial Number (ISSN)

  • 1469-7688

Electronic International Standard Serial Number (EISSN)

  • 1469-7696

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 MittagLeffler 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 Levy process of either finite or infinite activity.