Question

Consider the sequential trading model of Glosten and Milgrom (1985). Let us assume that:

• The future value of the asset, can take the value of 5 or 4. The asset takes the value of 5 with probability 0.6. That is,
• Thirty percent of traders are informed. That is .
• Further, assume that the uninformed traders are equally likely to buy or sell.
• The dealer earns zero expected profits, such that:
• 
• 

where a_t is the ask price, b_t is the bid price, B_t indicates a buy order and S_t indicates a sell order all at time .

1. Calculate the unconditional probability of observing a buy order at time t. That is, P(B_t).

2. Calculate the unconditional probability of observing a sell order at time t. That is, P(St).

3. Given Bayes theorem :

solve for the bid price at time t .

d. Solve the ask price at time t.

e. Solve for the bid-ask spread at time t.

f. Solve for the relative bid-ask spread at time t.

V. A=0.6. at = E(VB) by = E(VS) = P(Y) P(Y|Z) = P(ZY) (Y\2PY P(Z) V. A=0.6. at = E(VB) by = E(VS) = P(Y) P(Y|Z) = P(ZY) (Y\2PY P(Z)