Market Makers' Pricing Strategy Under Simplified Glosten-milgrom Model

Market Maker Rule means that one or a few business legal entities(usually financial institutions)who have the financial strength,and are qualified with good credit quote bid and ask prices in continues time and accept the trade at these prices from the traders,at the same time provide liquidity to the market in the order driven market.In this paper,financial market participants are mainly divided into three categories: market makers,informed traders and uninformed traders.In the process of market making,market makers face inventory risk and information risk.We focus on the information one in this paper.Informed traders bring the information risk of market makers.They have some advantage(or inside)information about the hidden true value of the assets and trades.Uninformed traders have no private information.Market makers and they are all based on historical trades' information to infer private information so that prices can be revealed.Market Maker Rule is an important trading system in financial markets,which are applied initially in the National Equities Exchange and Quotations(i.e.the New OTC)and OTC options so that the research of market makers' pricing problem becomes one of the important research topics of financial calculation field.Because Glosten-Milgrom model is a continuous time model considering market makers' information risk problem,at the same time add an assumption that market makers learn from trading filtration,it is difficult to give the numerical solution of the pricing strategy which indicated the expectations of a hidden true value.However,the analytical solution of cannot be obtained,and the authors do not give a precise numerical solution in the article.At the same time,this model is strict in data requirements,which requires data to meet many constraints.The problem of market makers' pricing strategy studied in this paper is under the perfect competition and risk neutral theory in continuous time.The ask and bid prices are defined as the conditional expectation of the true value of the asset given the market makers partial information which include the trading decisions of the traders.We set the true value as a Markov process,and can be observed by the traders with some noise in Poisson time.The volatility of assets is characterized by the difference between the maximum value and the minimum value.We have strict limitations that the bid and ask prices should be between the maximum value of the asset and the minimum one.Then we consider a static version of the dynamic Glosten-Milgrom model.At last,we apply the pricing model of market makers' to New OTC.We use the real data from the market to get solutions of dynamic and static models,simulate the pricing strategy into several elementary functions in dynamic one,and get the results compared and analyzed.The results show that,compared with the actual bid and ask prices quoted by the market makers in the market,the simulated prices of the market makers in the simplified static model are closer to the actual prices of the market stocks.This also satisfies zero expected profit condition.The simulation of the power function is better than that of the quadratic function under the dynamic model.In practical,market makers can use static model to calculate updated quotes while use dynamic model to simulate quote updates over time.The research can improve the poor topic of market makers' pricing strategy in China.Besides,it can also provide some new ideas and inspirations for the Chinese financial market,especially the OTC derivatives trading.