A new model of a market maker

Financial instruments are bought and sold at a financial market. Market makers at a financial market act as intermediaries between the buyer and the seller of the financial instrument. Market makers have the power to quote the bid price and the ask price. This price-setting process is called market-making. With market maker models this price-setting proces of the market maker is studied. To create liquidity in the market the market maker must trade immediately if an order arrives. The market maker bears risk because he does not have optimal portfolios. To protect himself against the losses he quotes the ask price higher than the bid price. The difference between the bid price and the ask price is called the bid-ask spread. The main causes of emergence of bid-ask spread are the fixed costs, the inventory costs and the adverse selection costs. Fixed costs are costs arising from order execution. Inventory costs arise from holding securities in inventory. Adverse selection costs arise from trading with traders who have superior information. In early financial literature the bid-ask spread is modelled with a regression model. Later market makers models are used to study the price setting mechanism of the market maker. There are two types of market makers models: inventory-based models and information-based models. In inventory-based models the behaviour of the market maker as inventory-holder and the inventory cost are studied. In information-based models the adverse selection problem between the market maker and the informed trader is studied. The informed trader has superior information than the market maker, which is why the market maker has adverse selection cost if he trades with the informed trader. Two examples of information based models are the model of Glosten and Milgrom and the Das market maker's model. The market maker of Glosten and Milgrom uses Baysian learning to learn the fundamental value of the underlying security. The market maker of Das expands the Glosten and Milgrom model by keeping a probabilistic density distribution of the fundamental value. We study the market maker's behaviour with a linear pricing strategy and introduce a market maker with bid-ask spread location detection and fundamental value approximation capability. We compare the Das market maker with our market maker with the mean of bid-ask spreads method and the sum of differences between the fundamental value and the bid and ask price method.