IMPACT OF RISK LIQUIDITY PREMIUM ON INVENTORY PROCESS IN A MARKET MAKING MODEL

Date

2024-9-5

Author

Ateşağaoğlu Alan, Gizem Damla

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A basic market making model in mathematical finance is the one proposed by Avellaneda and Stoikov (AS), which is formulated as a stochastic optimal control problem. This model includes a risk liquidity premium function ℓ which penalizes the remaining inventory at terminal time. To the best of our understanding, in the currently available literature, at least in the context of the AS model, this function is usually assumed zero or is ignored. One explanation given for this assumption is that the dynamics of the inventory process is mean reverting and the ℓ function has little impact on this. In this thesis, we study numerically whether this assumption holds by computing the dynamics of the inventory process for non-zero ℓ functions. We see that depending on model parameters this function can have a nontrivial impact on inventory process dynamics. We present a numerical study of how this impact depends on model parameters.

Subject Keywords

Stochastic Optimal Control Problem, High-frequency Trading, Market Making, Bid-Ask Probability, Inventory Strategy, Hamilton-Jacobi-Bellman Equation

URI

https://hdl.handle.net/11511/111026

Collections

Graduate School of Applied Mathematics, Thesis