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.
%0 Journal Article
%1 cartea2013
%A Cartea, Álvaro
%D 2013
%J Quantitative Finance
%K data derivatives pricing tick
%N 1
%P 111-123
%R 10.1080/14697688.2012.661447
%T Derivatives pricing with marked point processes using tick-by-tick data
%U /brokenurl# http://dx.doi.org/10.1080/14697688.2012.661447
%V 13
%X 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.
@article{cartea2013,
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. },
added-at = {2015-10-14T22:21:29.000+0200},
author = {Cartea, Álvaro},
biburl = {https://www.bibsonomy.org/bibtex/25ff06e947008ec3e202fea363aea62be/krassi},
doi = {10.1080/14697688.2012.661447},
eprint = {http://dx.doi.org/10.1080/14697688.2012.661447},
interhash = {44f790dad3c7d7908aba3364a1d5895e},
intrahash = {5ff06e947008ec3e202fea363aea62be},
journal = {Quantitative Finance},
keywords = {data derivatives pricing tick},
number = 1,
pages = {111-123},
timestamp = {2015-12-31T14:42:44.000+0100},
title = {Derivatives pricing with marked point processes using tick-by-tick data},
url = {/brokenurl# http://dx.doi.org/10.1080/14697688.2012.661447 },
volume = 13,
year = 2013
}