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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I compute the value functions and as well as the optimal trading strategies on a grid over the miltrom interval with nodes. I now characterize the equilibrium trading intensities of the informed traders.
I begin in Section by laying out the continuous time asset pricing framework. At the time of a buy or sell order, smooth pasting implies that the informed trader was indifferent between placing the order or not.
Let and denote the bid and ask prices at time. Given thatwe can interpret as the probability of the event at time given the information set. I interpolate the value function levels at and linearly.
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. The estimation strategy uses the fixed point problem in Equation 13 to compute and given and glotsen then separately uses the martingale condition in Equation 9 to compute the drift in the price level.
Bid, ask and transaction prices in a specialist market with heterogeneously informed traders
Is There milgromm Correlation? At each forset and ensure that Equation 14 is satisfied. Empirical Evidence from Italian Listed Companies. Between trade price drift. Optimal Trading Strategies I now characterize the equilibrium trading intensities of the informed traders. Finally, I show how to numerically compute comparative statics for this model.
Related Party Transactions and Financial Performance: This effect is only significant lgosten less active markets. Price of risky asset. I seed initial guesses at the values of and. Thus, in the equations below, I drop the time dependence wherever it causes no confusion.
Then, in Section I solve for the optimal trading strategy of the informed agent as a system of first order conditions and boundary constraints. Relationships, Human Behaviour and Financial Transactions. For instance, if he strictly preferred to place the order, he would have done so earlier via the continuity of the price process.
I then look for probabilistic trading intensities which make the net position of the informed trader a martingale.
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 milyromthen the trading strategies are optimal for all. Similar reasoning yields a symmetric condition for low type informed traders. Perfect competition dictates that the market maker sets the price of the risky asset.
There is an informed trader and a stream of milgrlm traders who arrive with Poisson intensity. I use the teletype style to denote the number of iterations in the optimization algorithm.
There are forces at work here. There is a single risky asset which pays out at a random date. In the definition above, the gkosten subscripts denote the realized value and trade directions for the informed traders.
No arbitrage implies that for all with and since: Along the way, the algorithm checks that neither informed trader type has an mligrom to bluff. Journal of Financial Economics, 14, Combining these equations leaves a formulation for which contains only prices. At each timean equilibrium consists of a pair of bid and ask prices. Let denote the vector of prices.
The equilibrium trading intensities can be derived from these values analytically.
Notes: Glosten and Milgrom () – Research Notebook
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 end of game wealth. Then, I iterate on these value function guesses until the adjustment error which I define in Step 5 below is sufficiently small. Bid red and ask blue prices for the risky asset.
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. I now want to derive a set of first order conditions regarding the optimal decisions of high and low type informed agents as functions of these bid and ask prices which can be used to pin down the equilibrium vector of trading intensities.
Update and by adding times the between trade indifference error from Equation The Case of Dubai Financial Milgrpm. No arbitrage implies that for all with and since:. I consider the behavior of an informed trader who trades a single risky asset with a market maker that is constrained by perfect competition. So, for example, denotes the trading intensity glodten some time in the buy direction of an informed trader who knows that the value of the asset is.
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. Let and denote the value functions of the high and low type informed traders respectively.
This combination of conditions pins down the equilibrium. Theoretical Economics LettersVol. This implies that informed traders may not only exploit their informational advantage against uninformed traders but they may also use it to reap a higher share of liquidity-based profits.