Problem 7. [Call auction] Graph total market demand and supply curves in {price, quantity} space for...

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Problem 7. [Call auction] Graph total market demand and supply curves in {price, quantity} space for a call auction market where the following orders are submitted to a central auctioneer: Limit orders to buy: 100 shares at $3.00, 200 shares at $4.00, 200 shares at $3.50, and 500 shares at $2.50. Limit orders to sell: 500 shares at $5.00, 600 shares at $3.00, and 500 shares at $4.00. Market orders to buy: a total of 500 shares. Market orders to sell: a total of 200 shares. What is the market clearing price? What quantity of stock is traded? Are all orders that are executable at the market clearing price fully filled? Problem 8. [Continuous order-driven market] Now suppose that the above orders arrive on the market over time, in the order of arrival that is listed above (that is, at time t = 1 the limit order to buy 100 at $3.00 is submitted, at time t = 2 the limit order for 200 at $4.00, and so on, continuing until time t = 9, when the market order to sell 200 arrives). Track the state of the LOB (show it after each new order has arrived and any transactions are triggered, for t = 0, ..., 9, in the trading screen format of figure 1.2) and the time, price and quantity of any transactions that take place. Record the dollar bid-ask spread, that is, the difference between the lowest ask and the highest bid, in the continuous market as it evolves from t = 5 onwards. Problem 9. [Comparison: efficiency and market presence] Consider again the two markets described in questions 7 and 8. Assume that the limit order prices are equal to the order placer's valuation for the block of shares submitted in the order, and think of market orders as placed by agents whose valuation is well outside (above for buyers, below for sellers) the relevant range of trading prices. Which market is Pareto efficient, in the sense that at the end of the trading day there is no pair of agents who could both benefit by trading with each other (i.e., after t = 9 in the continuous order-driven market)? Intuitively, why? Problem 7. [Call auction] Graph total market demand and supply curves in {price, quantity} space for a call auction market where the following orders are submitted to a central auctioneer: Limit orders to buy: 100 shares at $3.00, 200 shares at $4.00, 200 shares at $3.50, and 500 shares at $2.50. Limit orders to sell: 500 shares at $5.00, 600 shares at $3.00, and 500 shares at $4.00. Market orders to buy: a total of 500 shares. Market orders to sell: a total of 200 shares. What is the market clearing price? What quantity of stock is traded? Are all orders that are executable at the market clearing price fully filled? Problem 8. [Continuous order-driven market] Now suppose that the above orders arrive on the market over time, in the order of arrival that is listed above (that is, at time t = 1 the limit order to buy 100 at $3.00 is submitted, at time t = 2 the limit order for 200 at $4.00, and so on, continuing until time t = 9, when the market order to sell 200 arrives). Track the state of the LOB (show it after each new order has arrived and any transactions are triggered, for t = 0, ..., 9, in the trading screen format of figure 1.2) and the time, price and quantity of any transactions that take place. Record the dollar bid-ask spread, that is, the difference between the lowest ask and the highest bid, in the continuous market as it evolves from t = 5 onwards. Problem 9. [Comparison: efficiency and market presence] Consider again the two markets described in questions 7 and 8. Assume that the limit order prices are equal to the order placer's valuation for the block of shares submitted in the order, and think of market orders as placed by agents whose valuation is well outside (above for buyers, below for sellers) the relevant range of trading prices. Which market is Pareto efficient, in the sense that at the end of the trading day there is no pair of agents who could both benefit by trading with each other (i.e., after t = 9 in the continuous order-driven market)? Intuitively, why?