Wednesday, May 4, 2016

high frequency - Finding parameters of an utility function in a market making strategy to apply it in practice


I am reading this paper below about optimal bid-ask spread in a market making strategy. It finds an approximation for optimal solution, but I cannot understand how it's practice to set the parameters for a sample stock (eg. AAPL). Assuming, I have this stock below, how I can find all the parameters for the optimal bid-ask spread?


-> How to set $A$ and $k$, for my example stock? Which is the parameter for the tick size?


Example:


Stock: AAPL


$\sigma = 0.2$



$\mu = 0.01$


$S_t$= 169.23 USD


Tick=0.01 USD




Utility function to maxime


enter image description here


Intensity function


How fast my order (bid/ask) will be filled respect to the mid-price in the market at t enter image description here enter image description here


Optimal bid/ask quote (final solution)


Page 13



page 13


Paper source: Dealing with the Inventory Risk. A solution to the market making problem https://arxiv.org/abs/1105.3115




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