Inventory process dynamics of a market making model with regime switch

Date

2025-1-07

Author

Alkan, Nazlan Belemir

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We study a version of the Avellaneda Stoikov (AS) market-making model, which optimizes the bid and ask spread of the market maker, with regime switch as proposed in the preprint ``Short Term Market Changes and Market Making with Inventory'' by Kim et al. As in the ordinary AS model, under a structural assumption for the value function, the Hamilton Jacobi Bellman equation for the value function reduces to an ordinary differential equation. We note that, as opposed to the ordinary AS model, the resulting ODE is nonlinear and, therefore, cannot be solved via matrix exponentials. We numerically solve the ODE via finite differences and study the dynamics of the inventory process and their dependence on model parameters. We note that the inventory process of the model with regime switch behaves like a process with regime switch where in each regime, the inventory process has dynamics similar to the inventory process of an AS model with no regime switch.

Subject Keywords

Market making model, Stochastic optimal control, Regime switching, Inventory management

URI

https://hdl.handle.net/11511/113452

Collections

Graduate School of Applied Mathematics, Thesis