TY - JOUR
T1 - Telegraph Processes with Random Jumps and Complete Market Models
AU - Ratanov, Nikita
N1 - Publisher Copyright:
© 2013, Springer Science+Business Media New York.
Copyright:
Copyright 2015 Elsevier B.V., All rights reserved.
PY - 2015/9/10
Y1 - 2015/9/10
N2 - 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.
AB - 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.
UR - https://www.scopus.com/pages/publications/84938977688
UR - https://www.scopus.com/pages/publications/84938977688#tab=citedBy
U2 - 10.1007/s11009-013-9388-x
DO - 10.1007/s11009-013-9388-x
M3 - Research Article
AN - SCOPUS:84938977688
SN - 1387-5841
VL - 17
SP - 677
EP - 695
JO - Methodology and Computing in Applied Probability
JF - Methodology and Computing in Applied Probability
IS - 3
ER -