By Lawrence R. Glosten and Paul Milgrom; Bid, ask and transaction prices in a specialist market Journal of Financial Economics, , vol. Dealer Markets Models. Glosten and Milgrom () sequential model. Assume a market place with a quote-driven protocol. That is, with competitive market. Glosten, L.R. and Milgrom, P.R. () Bid, Ask and Transactions Prices in a Specialist Market with Heterogeneously Informed Traders. Journal.
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This effect is only significant in less mipgrom markets. Bid red and ask blue prices for the risky asset. In all time periods in which the informed trader does not trade, smooth pasting implies that he must be indifferent between trading and delaying an instant. Let be the closest price level to such that and let be the closest price level to such that. Thus, for all it must be that and. For the high type informed trader, this value includes the value change due to the price driftthe value change due to an uninformed trader placing a buy order with probability and the value change due to an uninformed trader placing a sell order with probability.
The around a buy or sell order, the price moves by jumping from or from so we can think about the 9185 process as composed of a deterministic drift component and jump components with magnitudes and. Update and by adding times the between trade indifference error from Equation There is a single risky asset which pays out at a 1958 date.
In fact, in markets with a higher information value, the effect of attention constraints on the liquidity provision ability mligrom market makers is greater. For instance, glossten he strictly preferred to place the order, he would have done so earlier via the continuity of the price process. There are forces at work here. Theoretical Economics LettersVol. This combination of conditions pins down the equilibrium.
Bid, ask and transaction prices in a specialist market with heterogeneously informed traders
I consider the behavior of an informed trader who trades a single risky asset with a market maker that is constrained by perfect competition. If the low type informed traders want to buy at pricedecrease their value function at price by. Asset Pricing Framework There is a single risky asset which pays out at a random date. I then plug in Equation 10 to compute and.
The informed trader chooses a trading strategy in order to maximize his end of game wealth at random date with discount rate.
Notes: Glosten and Milgrom () – Research Notebook
The algorithm updates the value function in each step by first computing how badly the no trade indifference condition in Equation 15 is violated, and then lowering the values of for near when the high type informed trader is too eager to trade and raising them when he is too apathetic about trading and vice versa for the low type trader. Compute using Equation 9. The estimation strategy uses the fixed point problem in Equation 13 to compute and given and and then separately uses the martingale condition in Equation 9 to compute the drift in the price level.
At each forset and ensure that Equation 14 is satisfied. Optimal Trading Strategies I now characterize the equilibrium trading intensities of the informed traders. Application to Miltrom Using Bid-Ask. Let and denote the value functions of the high and low type informed traders respectively.
Furthermore, the aggregate level of market liquidity remains unaltered across both highly active and inactive markets, suggesting a reactive strategy by informed traders who step in to compete with market makers during high information intensity periods when their attention allocation efforts are compromised.
I compute the value functions and as well as the optimal trading strategies on a grid over the unit interval with nodes. Price of risky asset.
Similar reasoning yields a symmetric condition for low type informed traders. Scientific Research An Academic Publisher. The model end date is distributed exponentially with intensity. Thus, in the equations below, I drop the time dependence wherever it causes no confusion.
In the section below, I solve for the equilibrium trading intensities and prices numerically. Between trade price drift. This cost has to be offset by the value delaying.
No arbitrage implies that for all with and since: Along the way, the algorithm checks that neither informed trader type has an incentive to bluff. There is an informed trader and a stream of uninformed traders who arrive with Poisson intensity. At each timean equilibrium consists of a pair of bid and ask prices. Below I outline the estimation procedure in complete detail. If the trading strategies are admissible, is a non-increasing function ofis a non-decreasing function ofboth value functions satisfy the conditions above, and the trading strategies are continuously differentiable on the intervalthen the trading strategies are optimal for all.
In the results below, I set and for simplicity. Let denote the vector of prices. The algorithm below computes, and.
Substituting in the formulas for and from above yields an expression for the price change that is purely in terms of the trading intensities and the price. All traders have a fixed order size of. The equilibrium trading intensities can be derived from these values analytically.
Journal of Financial Economics, 14, Let be the left limit of the price at time. Empirical Evidence from Italian Listed Companies. If the high type informed traders want to sell at priceincrease their value function at price by. Code the for the simulation can be found on my GitHub site. I interpolate the value function levels at and linearly. The Case of Dubai Financial Market. At the time of a buy or sell order, smooth pasting implies that the informed trader was indifferent between placing the order or not.
I now characterize the equilibrium trading intensities of the informed traders.