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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Bid, ask and transaction prices in a specialist market with heterogeneously informed traders
Similar reasoning yields a symmetric condition for low type informed traders. If the high type informed traders want to sell at priceincrease their value function at price by.
In fact, in markets with a higher information value, the effect of attention constraints on the liquidity provision ability of market makers is greater. In the section below, I solve for the equilibrium trading intensities and prices numerically. First, observe that since is distributed exponentially, the only relevant state variable is at time. Application to Pricing Using Bid-Ask. The equilibrium trading intensities can be derived from these values analytically.
Let and denote the vector of value function levels over each point in the price grid after iteration.
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Price of risky asset. If the low type informed traders want to buy at pricedecrease their value function at price by.
At each timean equilibrium consists of a pair of bid and ask prices. All glozten have a fixed order size of. In the definition above, the and subscripts denote the realized value and trade directions for the informed traders. Thus, in the equations below, I drop the milgorm dependence wherever it causes no confusion. In all time periods in which the informed trader does not trade, smooth pasting glosyen 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. No arbitrage implies that for all with and since: In order to guarantee a solution to the optimization problem posed above, I restrict the domain of potential trading strategies to those that generate finite mlgrom of game wealth. 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.
Let denote the vector of prices. At the time of a buy or sell order, smooth pasting implies that the informed trader was indifferent between placing the order or not.
The algorithm below computes, and. Along the way, the algorithm checks that neither informed trader type has an incentive to bluff. Empirical Evidence from Italian Listed Companies. Given thatwe can interpret as the probability of the event at time given the information set. Related Party Transactions and Financial Performance: Then, I iterate on these value function guesses until the adjustment error which I define in Step 5 below is sufficiently small. Perfect competition dictates that the market maker sets the price of the risky asset.
Between trade price drift. Thus, for all it must be that and. I interpolate the value function levels at and linearly. There is an informed trader and a stream of uninformed traders who arrive with Poisson intensity.
Notes: Glosten and Milgrom () – Research Notebook
Scientific Gloaten An Academic Publisher. Theoretical Economics LettersVol. 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. Optimal Trading Strategies I now characterize the equilibrium trading intensities of the informed traders.