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Some explicit results on one kind of sticky diffusion

Part of: Mathematical finance Markov processes

Published online by Cambridge University Press:  30 July 2019

Yiming Jiang ,
Shiyu Song  and
Yongjin Wang
Yiming Jiang*
Affiliation:
Nankai University
Shiyu Song*
Affiliation:
Tianjin University
Yongjin Wang*
Affiliation:
Nankai University
*
*Postal address: School of Mathematical Sciences, Nankai University, Tianjin 300071, China.
**Postal address: School of Mathematics, Tianjin University, Tianjin 300354, China.
****Postal address: School of Business, Nankai University, Tianjin 300071, China.
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Abstract

In this paper we derive several explicit results on one special sticky diffusion process which is constructed as a time-changed version of a diffusion with no sticky points. A theorem concerning the process-related Green operators defined on some nonnegative piecewise continuous functions is provided. Then, based on this theorem, we explore the distributional properties of the sticky diffusion. A financial application is presented where we compute the value of the European vanilla call option written on the underlying with sticky price dynamics.

Keywords

Sticky diffusionfirst hitting timeGreen’s operatordistributional propertiesoption pricing

MSC classification

Primary: 60J60: Diffusion processes
Secondary: 91G20: Derivative securities
Type
Research Papers
Information
Journal of Applied Probability , Volume 56 , Issue 2 , June 2019 , pp. 398 - 415
Copyright
© Applied Probability Trust 2019 

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