Telegraph Processes with Random Jumps and Complete Market Models

Nikita Ratanov

Research output: Contribution to journalResearch Articlepeer-review

15 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)677-695
Number of pages19
JournalMethodology and Computing in Applied Probability
Issue number3
StatePublished - Sep 10 2015

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • General Mathematics


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