Derivatives pricing with marked point processes using Tick-by-tick dataR
AbstractI 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.
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Bibliographic InfoPaper provided by Universidad Carlos III, Departamento de Economía de la Empresa in its series Business Economics Working Papers with number wb101604.
Date of creation: Apr 2010
Date of revision:
Tick-by-tick data; Waiting-times; Duration; High frequency data; Caputo operator; Marked point process;
Other versions of this item:
- �lvaro Cartea, 2013. "Derivatives pricing with marked point processes using tick-by-tick data," Quantitative Finance, Taylor & Francis Journals, vol. 13(1), pages 111-123, January.
- G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
- G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
- C41 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Duration Analysis; Optimal Timing Strategies
This paper has been announced in the following NEP Reports:
- NEP-ALL-2010-04-17 (All new papers)
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- Scalas, Enrico & Politi, Mauro, 2012.
"A parsimonious model for intraday European option pricing,"
Economics Discussion Papers
2012-14, Kiel Institute for the World Economy.
- Enrico Scalas & Mauro Politi, 2012. "A parsimonious model for intraday European option pricing," Papers 1202.4332, arXiv.org.
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