### GLOSTEN MILGROM 1985 PDF

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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Code the for the simulation can be found on my GitHub site. Thus, in the equations below, Glosteh drop the time dependence wherever it causes no confusion. I then look for probabilistic trading intensities which make the net position of the informed trader a martingale. Value function gglosten the high red and low blue type informed trader. Scientific Research An Academic Publisher. Let and denote the bid and ask prices at time. In flosten section below, I solve for the equilibrium trading intensities and prices numerically.

I seed initial guesses at the values of and. Bid red and ask blue prices for the risky asset. Let and denote the vector of value function levels over each point in the price grid after iteration. 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.

Empirical Evidence from Italian Listed Companies. If the high type informed traders want to sell at priceincrease their value function at price by. However, via the conditional expectation price setting rule, must be a martingale meaning tlosten.

## Notes: Glosten and Milgrom (1985)

All traders have a fixed order size of. The informed trader chooses a trading strategy in order to maximize his end of game wealth at random date with discount rate. Then, in Section I solve for the optimal trading strategy of the informed agent as a system of first order conditions and boundary constraints.

This effect is only significant in less active markets. 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.

I then plug in Equation 10 to compute and. I interpolate the value function levels at and linearly.

Let and denote the value functions of the high and low type informed traders respectively. Similar reasoning yields a symmetric condition for low type informed traders. There milgro forces at work here. It is not optimal for the informed traders to bluff.

Journal of Financial Economics, 14, Perfect competition dictates that the market maker sets the price of the risky asset. Finally, I glosteh how to numerically compute comparative statics for this model.

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

Related Party Transactions and Financial Performance: 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. 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.

Numerical Solution In the results below, I set and for simplicity. Below I outline the estimation procedure in complete detail. 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.

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

Optimal Trading Strategies I now characterize the equilibrium trading intensities of the informed milrom. The Case of Dubai Financial Market. No arbitrage implies that for all with and since: This combination of conditions pins down the equilibrium. For instance, if he strictly preferred to place the order, he would have done so earlier via the continuity of the price process. There is a single risky asset which pays out at a random date.

Combining these equations leaves a formulation for which contains only prices. Along the way, the algorithm checks that neither informed trader type has an incentive to bluff. 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.

In the results below, I set and for simplicity. Then, I iterate on these value function guesses until the adjustment error which I define in Step 5 below is sufficiently small. I use the teletype style to denote the number of iterations in the optimization algorithm.

First, observe that since is distributed exponentially, the only relevant state variable is at time. 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.