Derivatives pricing with marked point processes using tick-by-tick data
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 InfoArticle provided by Taylor and Francis Journals in its journal Quantitative Finance.
Volume (Year): 13 (2013)
Issue (Month): 1 (January)
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Web page: http://taylorandfrancis.metapress.com/link.asp?target=journal&id=111405
Other versions of this item:
- Álvaro Cartea, 2010. "Derivatives pricing with marked point processes using Tick-by-tick dataR," Business Economics Working Papers wb101604, Universidad Carlos III, Departamento de Economía de la Empresa.
- G12 - Financial Economics - - General Financial Markets - - - Asset Pricing
- 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
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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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