The paper develops a new class of financial market models. These models are based on generalized telegraph processes with alternating velocities and jumps occurring at switching velocities. The model under consideration is arbitrage-free and complete if the directions of jumps in stock prices are in a certain correspondence with their velocity and with the behaviour of the interest rate. A risk-neutral measure and arbitrage-free formulae for a standard call option are constructed. This model has some features of models with memory, but it is more simple.
|Journal of Applied Mathematics and Stochastic Analysis
|Published - 2007
All Science Journal Classification (ASJC) codes
- Statistics and Probability
- Modeling and Simulation
- Applied Mathematics