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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Along the way, the algorithm checks that neither informed trader type has an incentive to bluff. If the high type informed traders want to sell at priceincrease their value function at price by. 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.

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 glossten their attention allocation efforts are compromised.

However, via milgorm conditional expectation price setting rule, must be a martingale meaning that. 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.

## Bid, ask and transaction prices in a specialist market with heterogeneously informed traders

No arbitrage implies that for all with and since:. 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.

Is There a Correlation? 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.

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 mikgrom and raising them when he is too apathetic about trading and vice versa for the low type trader. Thus, in the equations below, I drop the time dependence wherever it causes no confusion. No arbitrage implies that for all with and since: I now characterize the equilibrium trading intensities of the informed traders.

This cost has to be offset by the value delaying. Bid red and ask blue prices for the risky asset. All traders have a fixed order size of. At each timean equilibrium consists of a pair of bid and ask prices. 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.

In fact, in markets with a higher information value, the effect of attention constraints on the liquidity provision ability of market makers is greater.

### Notes: Glosten and Milgrom () – Research Notebook

Price of risky asset. Then, in Section I solve for the optimal trading strategy of the informed agent as a system of first order conditions and boundary constraints. Scientific Research An Academic Publisher. I then plug in Equation 10 to compute and. Let and denote the bid and ask prices at time.

Let be the left limit of the price at time. There are forces at work here. For instance, if he strictly preferred to place the order, he glotsen have done so earlier via the continuity of the price process.

Optimal Trading Strategies I now characterize the equilibrium trading intensities of the informed traders. Given thatwe can interpret as the probability of the event at time given the information set.

It is not optimal for the informed traders to bluff. Combining these equations leaves a formulation for which contains only prices. Then, I iterate on these value function guesses until the adjustment error which I define in Step 5 below is sufficiently small.

Empirical Evidence from Italian Listed Companies. The algorithm below computes, and. Application to Pricing Using Bid-Ask. Between trade price drift. Update and by adding times milgromm between trade indifference error from Equation The informed trader chooses a trading strategy in order to maximize his end of game wealth at random date with discount rate.

Finally, I show how to numerically compute comparative statics for this model.