EconPapers    
Economics at your fingertips  
 

Telegraph Processes with Random Jumps and Complete Market Models

Nikita Ratanov ()

Methodology and Computing in Applied Probability, 2015, vol. 17, issue 3, 677-695

Abstract: Abstract We propose a new generalisation of jump-telegraph process with variable velocities and jumps. Amplitude of the jumps and velocity values are random, and they depend on the time spent by the process in the previous state of the underlying Markov process. This construction is applied to markets modelling. The distribution densities and the moments satisfy some integral equations of the Volterra type. We use them for characterisation of the equivalent risk-neutral measure and for the expression of historical volatility in various settings. The fundamental equation is derived by similar arguments. Historical volatilities are computed numerically.

Keywords: Inhomogeneous Jump-telegraph process; Dependence on the past; Historical volatility; Compound poisson process; 60J27; 60J75; 60K99; 91G99 (search for similar items in EconPapers)
Date: 2015
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (6) Track citations by RSS feed

Downloads: (external link)
http://link.springer.com/10.1007/s11009-013-9388-x Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:metcap:v:17:y:2015:i:3:d:10.1007_s11009-013-9388-x

Ordering information: This journal article can be ordered from
https://www.springer.com/journal/11009

DOI: 10.1007/s11009-013-9388-x

Access Statistics for this article

Methodology and Computing in Applied Probability is currently edited by Joseph Glaz

More articles in Methodology and Computing in Applied Probability from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().

 
Page updated 2022-09-03
Handle: RePEc:spr:metcap:v:17:y:2015:i:3:d:10.1007_s11009-013-9388-x