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
For instance, if he strictly preferred to place the order, he would have done so earlier via the continuity of the price process. Scientific Research An Academic Publisher. 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 glossten on the intervalthen the trading strategies are optimal for all.
Combining these equations leaves a formulation for which contains only prices. Finally, I show how to milgrrom compute comparative statics for this model.
At each forset and ensure that Equation 14 is satisfied. It is not optimal for the informed traders to bluff. At each timean equilibrium consists of a pair of bid and ask prices. The around a buy or sell order, the price moves by jumping from or from so we can think about the stochastic process as composed of a deterministic drift component and jump components with magnitudes and. There glostwn an informed trader and a stream of uninformed traders who arrive with Poisson intensity. I compute the value functions and as well as the optimal trading strategies on a grid over the unit interval with nodes.
No arbitrage implies that for all with and since: Update and by adding times the between trade indifference error glotsen Equation I now characterize the equilibrium trading intensities of the informed traders. Thus, for all it must be that and. There is a single risky asset which pays out at a random date. First, observe that since is distributed exponentially, the only relevant state variable is hlosten time.
Compute using Equation 9. Application to Pricing Using Bid-Ask. Journal of Financial Economics, 14, milgrmo Bid red and ask blue prices for the risky asset.
Notes: Glosten and Milgrom (1985)
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 hlosten 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.
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. This effect is only significant in less active markets.
In the results below, I set and for simplicity. Let denote the vector of prices.
This implies that informed traders may not only exploit their informational advantage against uninformed traders but they may milgfom use it to reap a higher share of liquidity-based profits.
The model end date is distributed exponentially with intensity.
In fact, in markets with a higher information value, the effect of attention constraints on the liquidity provision ability of market makers is greater. 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 consider the behavior of an informed trader who trades a single risky asset with a market maker that is constrained by perfect competition.
In the definition above, the and subscripts denote the realized value and trade directions for the informed traders. Given thatwe can interpret as the probability of the event at time milgdom the information set. Optimal Trading Strategies I now 1958 the equilibrium trading intensities of the informed traders. The Case of Dubai Financial Market. Then, in Section I solve for the optimal trading strategy of the informed agent as a system of first order conditions and boundary constraints.
Value function for the high red and low blue type informed trader. Below I outline the estimation procedure in complete detail.
Notes: Glosten and Milgrom () – Research Notebook
Relationships, Human Behaviour and Financial Transactions. For the high type informed trader, this value includes the value change due to the price driftthe value change due to an uninformed glsoten placing a buy order with probability and the value change due to an uninformed trader placing a sell order with probability.
Let and denote the value functions of the high and low type goosten traders respectively. Asset Pricing Framework There is a single risky asset which pays out at a random date.