hard · Quantitative Finance Market Microstructure & Statistical Arbitrage

In Kyle's (1985) single-period model, the market maker sets price p = p_0 + λ(x+u), where x is the informed trader's order and usim N(0,σ_u^2) is noise-trader order flow. The asset's true value is vsim N(p_0,σ_v^2) with σ_v=5 and σ_u=2.5 (same price units). In the unique linear Bayesian-Nash equilibrium, the informed trader submits x^ast=β(v-p_0) with β=σ_u/σ_v, and the market maker sets λ=σ_v/(2σ_u).

What is the equilibrium price-impact coefficient λ?

  1. 2.00
  2. 0.25
  3. 1.00
  4. 0.50

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