Abstract: A new class of financial market models is proposed. These models are based on continuous time random motions with alternating constant velocities c± (so called "telegraph" process) and with jumps h± occurring when the velocities are switching. While such markets may admit an arbitrage opportunity, the model under consideration is arbitrage-free and complete if directions of jumps in stock prices are in a certain correspondence with their velocity and interest rate behaviour. In the framework of this model we capture bullish and bearish trends in a market evolution. Values h± describes sizes of possible crashes, jumps and spikes. Thus, we study a model that is both realistic and general enough to enable us to incorporate different trends and extreme events. We construct financial market model based on the random processes with finite velocities which possess a simplicity of Black-Scholes model. Replicating strategies for European options are constructed in detail. Explicit formulae for option prices are obtained. Some peculiarities as memory effects and a detailed description of volatility are discussed also.

Brief Biography of the Speaker:
Nikita Ratanov is affiliated as a professor of Economics faculty of University of Rosario, Bogota, Colombia. He was trained in Moscow State University (Diploma, 1976; PhD degree in Mathematics, 1984). He has DrSci degree also (Russian Academy of Sciences, 1999).
His research interests concern with stochastic analysis with application in financial modelling and mathematical physics. He is author of more than 70 papers published in reviewed journals or presented at international conferences. He wrote two textbooks of stochastic analysis in financial modelling for students of economics and applied mathematics faculties (in Russian and in Spanish).