caa a22 4500 605519692 CHVBK 20210128100731.0 cr unu---uuuuu 210128e20150901xx s 000 0 eng 10.1007/s11009-013-9388-x doi (NATIONALLICENCE)springer-10.1007/s11009-013-9388-x Ratanov Nikita Universidad del Rosario, Cl. 12c, No. 4-69, Bogotá, Colombia aut Telegraph Processes with Random Jumps and Complete Market Models [Elektronische Daten] [Nikita Ratanov] 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. Springer Science+Business Media New York, 2013 Inhomogeneous Jump-telegraph process nationallicence Dependence on the past nationallicence Historical volatility nationallicence Compound poisson process nationallicence Methodology and Computing in Applied Probability Springer US; http://www.springer-ny.com 17/3(2015-09-01), 677-695 1387-5841 17:3<677 2015 17 11009 https://doi.org/10.1007/s11009-013-9388-x text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s11009-013-9388-x text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Ratanov Nikita Universidad del Rosario, Cl. 12c, No. 4-69, Bogotá, Colombia aut NATIONALLICENCE 773 0- Methodology and Computing in Applied Probability Springer US; http://www.springer-ny.com 17/3(2015-09-01), 677-695 1387-5841 17:3<677 2015 17 11009