2007/12/20 by Nikita Ratanov, Alexander Melnikov, Ratanov, Nikita +1
Economics, Econometrics and Finance · Mathematics · #60J75 #91B28 #Complex Systems and Time Series Analysis #FOS: Economics and business #FOS: Mathematics #Financial Risk and Volatility Modeling #Probability (math.PR) #Stochastic processes and financial applications #Trading and Market Microstructure (q-fin.TR) #math.PR #msc:60J75 #msc:91B28 #q-fin.TR
paper · pdf · doi:10.48550/arxiv.0712.3428
To appear in a Special Volume of Stochastics: An International Journal of Probability and Stochastic Processes (http://www.informaworld.com/openurl?genre=journal%26issn=1744-2508) edited by N.H. Bingham and I.V. Evstigneev which will be reprinted as Volume 57 of the IMS Lecture Notes Monograph Series (http://imstat.org/publications/lecnotes.htm)
arxiv created 2007/12/20 · openalex publication_date 2007/12/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The paper develops a new class of financial market models. These models are based on generalized telegraph processes: Markov random flows with alternating velocities and jumps 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. An analog of the Black-Scholes fundamental differential equation is derived, but, in contrast with the Black-Scholes model, this equation is hyperbolic. Explicit formulas for prices of European options are obtained using perfect and quantile hedging.