Limited Attention and News Arrival in Limit Order Markets

Transcription

1 Limited Attention and News Arrival in Limit Order Markets Jérôme Dugast Banque de France Market Microstructure: Confronting many Viewpoints #3 December 10, 2014 This paper reflects the opinions of the authors and does not necessarily express the views of the Banque de France.

2 Motivation Understanding the mechanisms of price formation in financial markets focus on public news arrival Classical view on financial markets : public information releases are immediately integrated into prices, with no role for trades. However numerous empirical studies, for different asset classes, attribute explanatory power to order flow (e.g around macro announcements in FX markets : Evans and Lyons (2008), Love and Payne (2008)) Theoretical literature on price formation mechanisms, following public information releases, in modern markets is scarce

3 Research Question What are the effects of news arrival in limit order markets? How do prices adjust to news? (duration, role of order flows) How does it impact market liquidity? Why news arrival should affect how financial markets work? People have limited attention... and machines, at lower time scale, face latencies

4 Limited attention How does limited attention affect investors behaviour? Investors have a limited attention capacity. They don t continuously pay attention to a single market. Information processing takes time. Investors react to news with a delay. Prices don t adjust immediately. Investors who react first have a short time of informational advantage. News arrivals generate information asymmetry.

5 Findings Investors strategies depend on the news arrival frequency. When the frequency of news arrival increases, liquidity supply, measured by market depth, declines, prices adjust faster to information conveyed by news, the number of limit order executions increases compared to limit order cancellations during the price adjustment Economic channel Following news arrival, limit orders incur a picking-off risk (winner s curse).

6 Dynamic of prices adjustment P 1 P 0 News Arrival time

7 Dynamic of prices adjustment A 1 P 1 B 1 A 0 P 0 B 0 News Arrival time

8 Dynamic of prices adjustment LO : Limit Order MO : Marker Order A 1 LO cancel & resubmit P 1 B 1 P 0 A 0 B 0 MO News Arrival time

9 Dynamic of prices adjustment LO : Limit Order MO : Marker Order A 1 LO cancel & resubmit P 1 B 1 P 0 A 0 B 0 MO LO cancel & resubmit News Arrival Transition End time

10 Dynamic of prices adjustment LO : Limit Order MO : Marker Order A 1 LO cancel & resubmit P 1 B 1 P 0 A 0 B 0 MO LO cancel & resubmit News Arrival Transition End time

11 Literature Market reaction to public information : Kim and Verrecchia (1994), Eredington and Lee (1995), Fleming and Remolona (1999), Green (2004), Tetlock (2010). Imperfect market monitoring : Foucault, Roell and Sandas (2003), Biais and Weill (2009), Foucault, Kadan and Kandel (2012), Biais, Hombert and Weill (2012), Pagnotta and Philippon (2012). Limit order markets : Parlour (1998), Foucault (1999), Foucault, Kadan and Kandel (2005), Rosu (2009,2010). Financial markets modelling based on Duffie, Garleanu and Pedersen (2005,2007) : Weill (2007, 2008), Lagos and Rocheteau (2009), Lagos, Rocheteau and Weill (2011).

12 Modelling Approach 1. I depart from the model of OTC markets with search friction introduced by Duffie, Garleanu and Pedersen [2005, 2007]. 2. I introduce uncertainty for the asset value to model news arrival events. 3. I replace the search friction by an attention friction. 4. I adapt the model to a limit order market framework. I provide a tractable model of limit order markets.

13 Baseline model - Duffie, Garleanu and Pedersen, OTC markets [2005,2007] Time line. Continuous time trading game on a stochastic interval [0,τ]. τ follows a Poisson distribution, with intensity r. Asset value. At t [0,τ] the asset value is v t. At τ, The asset pays-off v τ. Asset supply. s = 1/2 so that half of the population owns the asset. Investors : A continuum of investors, [0,1], who can hold 1 or 0 asset unit. Two types of preferences : h : high private valuation for the asset (buyer). l : low private valuation for the asset (seller), asset holding cost δ per time unit. Investor switch from h to l or conversely at Poisson times with intensity ρ 4 types of investors : ho, hn, lo, ln, with population sizes L ho, L hn, L lo, L ln.

14 Asset value dynamic The news arrival event is a random jump of the asset value. At time t = 0 the asset value is v 0. News arrival : between t and t+dt, a piece of news arrives with prob µ.dt. µ is the news arrival frequency. Asset value change : following news arrival, the new asset value is either high, v u = v 0 +ω, or low, v d = v 0 ω, with equal probabilities. The asset value changes only once. Assumption : ω is big compared to δ.

15 Attention friction Because of limited attention, investors imperfectly monitor the market. Market Monitoring : An investor monitors the market at Poisson times with intensity λ. Assumption : An investor also monitors the market when his preference for the asset changes, at Poisson times with intensity ρ. When an investor monitors the market, he observes the asset value and can take an action. The higher is λ, the more investors are attentive to the market.

16 Trading mechanism : the limit order market Trading takes place a in a limit order market. Investors can consume liquidity with market orders. PROS : execution immediacy CONS : suboptimal execution price Investors can provide liquidity with limit orders. PROS : optimal execution price CONS : risk of being picked-off following news arrival Trading prices. The set of possible trade prices is discrete. The difference between two subsequent prices is, the tick size. Execution priority. All limit orders at the same price have the same probability of being executed by a market order (no time priority). Action set. An investor can have at most a one-unit limit order in the book. When an investor monitors the market, he can cancel a limit order, send a limit order, send a market order or do nothing.

17 Equilibrium Proposition There exists a symmetric Markov perfect equilibrium in which Prior to news arrival the market is in a steady-state phase. The best bid and ask prices are symmetric w.r.t v 0 δ, 2r B 0 = v 0 δ 2r 2, A0 = v 0 δ 2r + 2. Investors trade because of differences in private valuations. Following news arrival the market starts a transition phase. Investors trade for information reasons. Then the market migrates to a new steady-state phase at price (A u,b u ) if v = v 0 +ω or (A d,b d ) if v = v 0 ω

18 Equilibrium market dynamic LO : Limit Order MO : Marker Order A 1 LO cancel & resubmit P 1 B 1 P 0 A 0 B 0 MO LO cancel & resubmit News Arrival Transition End time

19 Focus on the steady-state phase LO : Limit order MO : Market order sell LO s : α 0 A 0 One tick market : All LO s are submitted at B 0 and A 0. bid-ask spread, A 0 B 0 =. Number of buy limit orders = number of investors hn. MO vente buy LO s : α 0 MO achat B 0 Number of sell limit orders = Number of investors lo. hn s and lo s are indifferent between MO and LO. indifference conditions determines α 0.

20 Steady state populations The aggregate distribution of investor s types is constant. The flows of investors switching from h to l and conversely must be equal to each other, ρ(l ho +L hn ).dt = ρ(l lo +L ln ).dt L lo +L ln = L ho +L hn = 1 2 The asset supply equal to 1/2 implies L lo +L ho = 1 2 There remains one degree of freedom. L lo = α 0, L ho = 1 2 α0, L ln = 1 2 α0, L hn = α 0 This free parameter α 0 is determined at equilibrium.

21 Trading strategies prior to news arrival Investors with type ho or ln do not trade. Investors with types hn and lo are willing to trade. They are indifferent between using market and limit orders. hn : buy market order at A 0 with probability m or a buy limit order at B 0 with probability 1 m. lo : sell market order at B 0 with probability m or a sell limit order at A 0 with probability 1 m. All limit orders are concentrated at the two best prices A 0 and B 0. All limit orders are exclusively owned by investors with types lo and hn. D A 0 = L lo = α 0, D B 0 = L hn = α 0.

22 Micro-level dynamic of the limit order book in steady state limit order cancellations : by lo s switching to ho s ρl lo.dt = ρα 0.dt, by lo s sending market orders mλl lo.dt = mλα 0.dt. limit order submissions by ho s switching to lo s : (1 m)ρl ho.dt = (1 m)ρ ( 1 2 α0).dt. α 0 A 0 limit order executions by hn s buy market orders : m(λl hn +ρl ln ).dt = m [ λα 0 +ρ ( 1 2 α0)].dt. Steady state condition : ρα 0 +2m [ λα 0 +ρ ( 1 2 α0)] = ρ ( 1 2 α0) m = f(α 0 )

23 Indifference condition At equilibrium investors with types hn and lo are indifferent between limit and market orders. V lo A 0(m,α 0 ) = V ln (m,α 0 )+B 0, V hn B 0(m,α 0 ) = V ho (m,α 0 ) A 0 This indifference condition implies a second linkage between m and α 0 m = g(α 0 ) Proposition the equation f(α 0 ) = g(α 0 ) has a unique admissible solution that defines the equilibrium value α 0 eq.

24 Trading strategies following news arrival If v = v 0 + ω, sell limit orders providers try to avoid being picked-off while potential buyers try to pick-off the formers. Until there is no limit order left at A 0 : - Investors with type ho do not trade. - Investors with type lo cancel any sell limit order at A 0 and resubmit a limit order at price A u - Investors with type hn or ln send a buy market order to pick-off limit orders at A 0 If v = v 0 ω, we are in the symmetric situation.

25 Dynamic of the market depth following news arrival limit order cancellations : (λ+ρ)d A 0(t).dt At t = τ the asset value switches to v 0 +ω. Initial condtion : D A 0(τ) = α 0 D A 0(t) A 0 limit order executions by hn s and ln s buy market orders : (λ+ρ) (L hn (t)+l ln (t)).dt = λ+ρ 2.dt. Market dynamic equation : Duration : T s.t D A0(τ +T) = 0 D A 0(t) = 1 2 +[α ]e (ρ+λ)(t τ) T = 1 ρ+λ ln(1+2α0 )

26 Market depth and trading intensity prior to news arrival The market depth decreases with the news arrival frequency µ : α 0 eq µ < 0. The trading intensity increases with the news arrival frequency µ : TI µ > Α 0 eq Μ Trading intensity Μ Figure: (i) Market depth and (ii) trading intensity in function of µ [2,3].

27 Effect of the market monitoring intensity Anything goes for α 0 eq, with respect to the monitoring intensity λ Α 0 eq Λ Α 0 eq Λ Figure: Evolution of α 0 eq w.r.t λ. The effect is small, 0. the absolute speed of reaction does not really matter.

28 Price adjustment delay The delay of the price adjustment after news arrival is equal to T = 1 ρ+λ ln(1+2α0 ) T decreases with the news arrival frequency µ, T µ < 0. When news are frequent, the limit order book is thin It takes less time to execute or cancel all stale limit orders.

29 Limit order cancellations and executions during the price adjustment phase Number of limit order executions during the price adjustment phase, LOE = ln(1+2α0 ). 2 Number of limit order cancellations during the price adjustment phase, LOC = α 0 ln(1+2α0 ) 2 The number of limit order executions and cancellations decline with the news arrival frequency, LOE µ < 0, LOC µ < 0. The relative importance of trades in the price adjustment phase increases with the news arrival frequency, LOE µ LOC > 0.

30 Conclusion Limited attention can explain price reaction delays around news arrival. It generates information asymmetry that affects investors trading strategies. The paper delivers novel predictions on the linkage between news arrival frequency, market liquidity and order flows in the price formation process.

31 Value functions Type ho : Type hn : ( ) V u rv ho = rv +ρ(v lo V ho )+µ ho (0)+Vho(0) d V ho 2 rv hn = ρ(v ln V hn )+mλ(v ho A 0 V hn )+l 0 (V ho B V hn ) ( ) V u +µ hn (0)+Vhn(0) d V hn 2 l 0 is the limit order execution rate defined as l 0.dt = m(λl lo +ρl ho ).dt L hn. The equilibrium execution rate l 0 is such that an investor hn is indifferent between limit and market orders V hn = V ho A 0