1. (35) Consider a variation of the Glosten-Milgrom sequential trade model where the asset's value V...

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1. (35) Consider a variation of the Glosten-Milgrom sequential trade model where the asset's value V can take three values. Suppose that the true value of stock in Trident Corporation can be, with equal probability, either V = , V = , or some middle value V Let a = of the traders be informed insiders, while the remaining 1 - = 3 are uninformed noise traders. Assume as always that informed traders always buy when V = VH and sell when V = V, while uninformed traders buy or sell with equal probability. The focus of this problem is the traders' behavior when V = VM (a) (5) Draw the tree diagram, leaving uncertain the action of informed traders when V = VM (b) (5) Show that there is no value of VM for which informed traders randomize between buying and selling. (c) (10) Suppose that informed traders always buy when V = VM i. (3) Calculate the conditional probabilities of a buy order at each value V can take and the uncondi- tional probability of a buy. ii. (3) Using Bayes' rule, calculate the posterior probabilities of V taking on each value conditional on a buy, and compute the ask price as a function of VM iii. (4) Find the informed trader's payoff when V = VM and use this to find the lowest value of VM at which the trader is willing to buy. (d) (10) Now suppose the informed traders always sell when V = VM i. (3) Calculate the conditional probabilities of a sell order at each value V can take and the uncondi- tional probability of a sell. ii. (3) Using Bayes' rule, calculate the posterior probabilities of V taking on each value conditional on a sell, and compute the bid price as a function of VM iii. (4) Find the informed trader's payoff when V = VM and use this to find the highest value of VM at which the trader is willing to sell. (e) (5) What happens if VM satisfies neither of the bounds you found above? 1. (35) Consider a variation of the Glosten-Milgrom sequential trade model where the asset's value V can take three values. Suppose that the true value of stock in Trident Corporation can be, with equal probability, either V = , V = , or some middle value V Let a = of the traders be informed insiders, while the remaining 1 - = 3 are uninformed noise traders. Assume as always that informed traders always buy when V = VH and sell when V = V, while uninformed traders buy or sell with equal probability. The focus of this problem is the traders' behavior when V = VM (a) (5) Draw the tree diagram, leaving uncertain the action of informed traders when V = VM (b) (5) Show that there is no value of VM for which informed traders randomize between buying and selling. (c) (10) Suppose that informed traders always buy when V = VM i. (3) Calculate the conditional probabilities of a buy order at each value V can take and the uncondi- tional probability of a buy. ii. (3) Using Bayes' rule, calculate the posterior probabilities of V taking on each value conditional on a buy, and compute the ask price as a function of VM iii. (4) Find the informed trader's payoff when V = VM and use this to find the lowest value of VM at which the trader is willing to buy. (d) (10) Now suppose the informed traders always sell when V = VM i. (3) Calculate the conditional probabilities of a sell order at each value V can take and the uncondi- tional probability of a sell. ii. (3) Using Bayes' rule, calculate the posterior probabilities of V taking on each value conditional on a sell, and compute the bid price as a function of VM iii. (4) Find the informed trader's payoff when V = VM and use this to find the highest value of VM at which the trader is willing to sell. (e) (5) What happens if VM satisfies neither of the bounds you found above?