Abstract
The article provides the necessary background information about the microstructure of the market, presents a market model, and derives pricing equations based on the market-making algorithm. This article introduces the Market Making Algorithm, an online probability density estimation method used by a market maker to track the true underlying value of a stock. Taking into account the desire of the market maker to make a profit and the desire to control the risk of the portfolio, the practical implementation of the market making algorithm is described. Under various market conditions, an empirical analysis of the market making algorithm is presented, including the presence of several competing market makers. Modeling markets based on the market making algorithm provides information about the behavior of price processes. A comparison of the properties of time series price data obtained as a result of modeling with the known properties of real markets is presented. This makes it possible to simulate real financial time series, such as the leptokurtic return distribution, without postulating complex models of agent interactions and herd behavior of agents. The influence of competition, volatility and jumps in the value of the underlying asset on the profit of market makers, the spread between the purchase and sale price and the execution of transactions is analyzed.
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