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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Value function for the high red and low blue type informed trader. So, for example, denotes the trading intensity at some time in the buy direction of an informed trader who knows that the value of the asset is. 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.
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. Given thatwe can interpret as the probability of the event at time given the information set.
All traders have a fixed order size of. Let and denote the bid and ask prices at time. I now characterize the equilibrium trading intensities of the informed traders. Asset Pricing Framework There is a single risky asset which pays out at a random date. 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 use the teletype style to denote the number of iterations in the optimization algorithm. 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.
Empirical Evidence from Italian Listed Companies.
Notes: Glosten and Milgrom () – Research Notebook
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. Combining these equations leaves a formulation for which contains only prices. Relationships, Human Behaviour and Financial Transactions. Price of risky asset. Glosyen instance, if he strictly preferred to place the order, he would have done so earlier via the continuity of the price process.
In fact, in markets with a higher information value, the effect of attention constraints on the liquidity provision ability of market makers is greater. 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. Similar reasoning yields a symmetric condition for low type 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. In the section below, I solve for the equilibrium trading intensities and prices numerically. Then, in Section I solve for the optimal trading strategy of the informed agent as a system of first order conditions and boundary constraints. The model end date is distributed exponentially with intensity. At each forset and ensure that Equation 14 is satisfied.
In the results below, I set and for simplicity. No arbitrage implies that for all with and since: The equilibrium trading intensities can be derived from these values analytically.
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There is an informed trader and a stream of uninformed traders who arrive with Poisson intensity. If the high type informed traders want to sell at priceincrease their value function at price by.
Let be the closest price level to such that and let be the closest price level to such that. 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. This effect is only significant in less active markets. I compute the value functions and as well as the optimal trading strategies on a grid over the unit interval with nodes.
It is not optimal for the informed traders to bluff. I then look for probabilistic trading intensities which make the net position of the informed trader a martingale. Application to Pricing Using Bid-Ask.