Derivatives Pricing with Marked Point Processes Using Tick-by-Tick Data

Quantitative Finance, Volume13 (1), 2013, Pages 111-123

32 Pages Posted: 25 Mar 2010 Last revised: 11 Mar 2013

See all articles by Álvaro Cartea

Álvaro Cartea

University of Oxford; University of Oxford - Oxford-Man Institute of Quantitative Finance

Date Written: March 18, 2010

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 I derive 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

JEL Classification: G12, G13, C41

Suggested Citation

Cartea, Álvaro, Derivatives Pricing with Marked Point Processes Using Tick-by-Tick Data (March 18, 2010). Quantitative Finance, Volume13 (1), 2013, Pages 111-123, Available at SSRN: https://ssrn.com/abstract=1574171 or http://dx.doi.org/10.2139/ssrn.1574171

Álvaro Cartea (Contact Author)

University of Oxford ( email )

Mansfield Road
Oxford, Oxfordshire OX1 4AU
United Kingdom

University of Oxford - Oxford-Man Institute of Quantitative Finance ( email )

Eagle House
Walton Well Road
Oxford, Oxfordshire OX2 6ED
United Kingdom

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