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Derivatives pricing with marked point processes using Tick-by-tick data

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URI: https://hdl.handle.net/10016/7583
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wb101604.pdf (200.73 KB)
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2010-04
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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.
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Tick-by-tick data, Waiting-times, Duration, High frequency data, Caputo operator, Marked point process
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DEE - Working Papers. Business Economics. WB
Economists Online