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
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: Suggested Citation
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