ECON0001: ECONOMICS OF FINANCIAL MARKETS Assignment 4
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ECON0001: ECONOMICS OF FINANCIAL MARKETS
Assignment 4
1. Noise trading in Kyle’s model. Consider the Kyle (1985) model, changing only the assumption about noise trading: assume that there are two groups (1 and 2) of noise traders, whose orders are respectively u1 ~N(0, Gu(2)1 ) and u2 ~N(0, Gu(2)2 ) both uncorrelated with the asset’s future value (i.e., Cov(v, u1 ) = Cov(v, u2). All the other assumptions of the model are unchanged: (i) market makers are risk neutral and perfectly competitive, (ii) the asset value is v~N(u, Gv(2)) (iii) the informed investor’s order is x = F(v − u), and (iv) market makers only observe the total net order q = x + u1 + u2 . [Hint: think whether your answers require computing the results of the Kyle model again.]
a) Derive (i) the price schedule p = µ+λq chosen by competitive market makers, under the assumption that the informed trader’s order is x = F(v − u), (ii) the optimal informed trader’s order, given the price schedule chosen by market makers; and (iii) the equilibrium values of λ and β .
b) Now suppose that market makers can observe the actual realization of the order placed by group 1 (for instance, because these are local investors, while those of group 2 are foreign investors) before trading occurs. Under this further assumption, derive again (i) the price schedule p = µ + λq chosen by competitive market makers, under the assumption that the informed trader’s order is x = F(v − u); (ii) the optimal informed trader’s order, given the price schedule chosen by market makers; and (iii) the equilibrium values of λ and β .
c) Compare the results obtained under (a) and under (b): does the assumption made under (b) change the equilibrium market depth and informed traders’ aggressiveness and, if so, what is the intuitive reason for this difference?
2. Kyle with multiple insiders. Consider the Kyle (1985) model, but assume that instead of a single informed trader there are N > 1 informed traders, who all perfectly observe the final value of the security v but not the equilibrium price at the time that they determine their quantity demanded qi .
a) Suppose that market makers post the price schedule described by equation p(q) = µ + λq, where q is the net order flow ∑
1 x1 + u and µ = E[v]. Assuming that each informed trader uses the following order submission strategy:
xi = Xi (v) = F(v − 
) for i ∈ {1, … , N}
find the value of β for which a Nash equilibrium exists, determine how β is affected by N, and explain intuitively why.
b) Suppose now that investors follow the order submission strategy derived in step (a). Show that in this case the market makers’ pricing strategy is given by equation p(q) = µ + λq, and find the value of λ that they optimally choose.
c) What is the market depth in equilibrium, and how is it affected by an increase in the number of informed traders, N? What is the economic intuition for this result?
2023-05-07