An explicit positivity preserving numerical scheme for CIR/CEV type delay models with jump
For financial modelers needing reliable numerical schemes for mean-reverting processes with delay and jumps, this provides a provably positivity-preserving method.
The paper proves non-negativity of solutions for CIR/CEV type delay models with jumps and proposes an explicit positivity preserving numerical scheme that converges strongly to the exact solution, with minimal numerical experiments illustrating the method.
We consider mean-reverting CIR/CEV processes with delay and jumps used as models on the financial markets. These processes are solutions of stochastic differential equations with jumps, which have no explicit solutions. We prove the non-negativity property of the solution of the above models and propose an explicit positivity preserving numerical scheme,using the semi-discrete method, that converges in the strong sense to the exact solution. We also make some minimal numerical experiments to illustrate the proposed method.