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112 tionship that a trader who requires immediacy of execution is facing. 1 If few limit buy or sell orders are present in the system or if many orders are present but for small trade sizes only, liquidity is low and marketable limit order trades may incur considerable price impacts. For example, Harris (2002) provides a complete taxonomy of the kinds of trades that can be submitted to exchanges and their impact on market liquidity. Broadly speaking and focusing solely on order books, liquidity providers (patient investors) submit non-aggressive limit orders, i.e. limit orders which do not face immediate execution but which provide liquidity to the system by filling the order book. Liquidity demanders (impatient traders) submit market orders which are executed against standing limit orders and which thus deplete the order book and decrease the overall liquidity. 2 Recent studies which focus on the interaction and dynamics of market orders vs limit orders in automated auctions include Biais et al. (1995), Handa and Schwartz (1996), Ahn et al. (2001) or Beltran et al. (2005a). Due to the interaction between limit and market orders, most studies conclude that there exists a dynamical equilibrium between limit order trading and transitory volatility. Examples of impatient traders include traders who wish to transact near the close of the trading session (so that the price of their trade is not far from the official closing price), see Cushing and Madhavan (2000), or momentum traders who are keen on entering immediate long or short positions (Keim and Madhavan 1997). In all cases, this behavior leads to increased volatility and trading costs. Because of the price and time priority rules implemented at automated auction markets, the price impact of a buy (sell) side trade is an increasing (decreasing) function of the trade size. As in recent studies focusing on liquidity in automated auction markets (Gouriéroux et al. 1998; Irvine et al. 2000; Coppejans et al. 2004; Domowitz et al. 2005), we model the available liquidity by focusing on the unit price obtained by selling v shares at time t: btðÞ¼ v P k bk;tvk;t v P. Giot, J. Grammig where v is the volume executed at k different unique bid prices bk,t with corresponding volumes vk,t standing in the limit order book at time t. The unit price at(v) of a buy of size v at time t can be computed analogously. Price impacts of buy and sell trades defined as in Eq. (1) provide important measures of ex-ante liquidity for impatient investors. As phrased in Irvine et al. (2000), “an ex-ante measure of liquidity is useful to investors, because it indicates the cost at which a trade can be immediately executed.” The most obvious measure of ex-ante liquidity is the quoted inside spread. With full order book data, one can however do much better as the price impact of buy and sell trades for any given volume v (i.e. for volumes below or above the quoted inside depths) can be computed as in Eq. (1). In dealer based trading system (such as the over-the-counter trading in FOREX markets for 1 That explains why market participants care about the whole information contained in the book and why order book modelling is of paramount importance. Pascual and Veredas (2004), Cao et al. (2004), Beltran et al. (2005b) or Beltran et al. (2005a), among others, focus on this issue. 2 Several authors, such as Biais et al. (1995), have put forward a scale of aggressiveness for submitted orders. The most aggressive orders are market orders (also called marketable limit orders) that are fully matched with possibly many standing limit orders that sit on the other side of the book. On the other hand, the most patient investors submit limit orders that enter the order book below/above the best bid/ask prices. (1)
How large is liquidity risk in an automated auction market? 113 example), ex-ante measures of liquidity are limited to quoted inside spread and quoted inside depths. It is also important to note that liquidity measures such as defined in Eq. (1) characterize committed liquidity as given by the standing limit orders only. With hybrid trading systems which mix characteristics of order book and dealer systems, unit prices at(v) and b t(v) give an upper bound on the price to be paid for the trade as the additional participants can add liquidity prior to the execution of the trade, decreasing a t(v) or increasing b t(v). 3 This is also the case for automated auction markets which allow so-called hidden or iceberg orders (see below). In order book markets which feature hidden orders, ex-ante costs of trading measures and liquidity risk measures such as computed in this paper give an upper bound on these trading and liquidity costs (see also Beltran et al. 2005a). 4 In this paper we will show that, with suitable data at hand, it is possible to quantify the liquidity risk over short term time horizons in automated auction markets. More precisely, we introduce liquidity risk measures that take into account the potential price impact of liquidating a portfolio. This approach is particularly relevant for short term impatient traders who submit market orders. The core of our methodology relies on the comparison of risk measures for so-called frictionless returns (i.e. no-trade returns) and actual returns (which take into account the actual trade price for a v-share trade). These actual returns are particularly relevant for short-term impatient traders who currently hold the stock and who are committed to shortly submit a marketable sell order. In contrast, frictionless returns refer to traders who hold the stock over the same time period, but do not intend to sell their shares. We rely on measures that originate from the Value-at-Risk methodology (see Section 3) to characterize the liquidity risk. It should however be stressed that our framework is not the usual 10-day VaR framework familiar to financial regulators. Hence, we use the VaR methodology to define our intraday risk measures, but in our paper these risk measures are meant to assess the intraday immediate liquidation risk faced by impatient traders. Consequently, we do not derive implications for financial regulators. In contrast, our approach is more similar to Andersen and Bollerslev (1997); Giot (2000, 2005) or Chanda et al. (2005) who characterize volatility on an intraday basis. In contrast to a standard (frictionless) VaR approach, in which one uses prices based on mid-quotes, the Actual VaR approach pursued in this paper uses as inputs volume-dependent transaction prices. This takes into account the fact that buyer (seller) initiated trades incur increasingly higher (lower) prices per unit share as the trade volume increases. The liquidity risk component naturally originates from the volume dependent price impact incurred when the portfolio is liquidated. Our approach relies on the availability of intraday bid and ask prices valid for the immediate trade of any volume of interest. Admittedly, procuring such data from traditional market maker systems would be an extremely tedious task. However, the advent of modern automated auction systems offers new possibilities for em- 3 Examples are a combination of a limit order book and market markets who bring additional liquidity (Euronext or Xetra, for non-actively traded stocks), or a combination of a limit order book, a specialist and floor traders (NYSE), see Sofianos and Werner (2000) or Venkatamaran (2001). Note that the German Stock Exchange recently adopted the price impact as defined in Eq. (1) as the key liquidity indicator for the automated auction system Xetra (see Gomber et al. 2002). 4 Nevertheless, they do provide meaningful information as they characterize the worst-case scenarios.
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High Frequency Financial Econometri
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Prof. Luc Bauwens CORE Voie du Roma
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vi Contents Intraday stock prices,
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2 L. Bauwens et al. component nicel
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4 L. Bauwens et al. but provides al
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Luc Bauwens . Dagfinn Rime . Genaro
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Exchange rate volatility and the mi
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32 K. Bien et al. Although economet
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34 K. Bien et al. 2.1 Copula functi
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36 K. Bien et al. and x k t ≡ (xk
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38 K. Bien et al. Fig. 3 Multivaria
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40 K. Bien et al. Bivariate model s
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42 K. Bien et al. deviation 0.0099,
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44 K. Bien et al. - Set ˆzt = Âxt
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46 K. Bien et al. % Frequency −0.
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48 K. Bien et al. References Amilon
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50 1 Introduction A. Escribano and
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52 A. Escribano and R. Pascual Jang
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54 A. Escribano and R. Pascual the
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56 The generating processes of mark
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58 with AtðLÞ ¼ 0 B @ 1 ð ÞAab
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60 A. Escribano and R. Pascual cros
Page 68 and 69: 62 Hasbrouck (1991). The system is
Page 70 and 71: 64 unitary seller-initiated shock (
Page 72 and 73: 66 6.1 Estimation of the baseline m
Page 74 and 75: Table 2 The base-line VEC model for
Page 76 and 77: 70 Table 3 Simulation of the base-l
Page 78 and 79: 72 revert towards narrow levels. As
Page 80 and 81: Table 5 Impulse-response functions
Page 82 and 83: 76 We also show that NYSE buyer-ini
Page 84 and 85: 78 As 0 < a m < 1; L ð Þ ¼ 1 a m
Page 86 and 87: 80 NYSE 2000 Stocks AOL America Onl
Page 88 and 89: 82 A. Escribano and R. Pascual Madh
Page 90 and 91: 84 1 Introduction S. Frey, J. Gramm
Page 92 and 93: 86 develops the empirical methodolo
Page 94 and 95: Table 1 Sample descriptives Company
Page 96 and 97: 90 comparability across stocks, we
Page 98 and 99: 92 subtracting the deviations from
Page 100 and 101: 94 market order distribution that c
Page 102 and 103: 96 Table 2 First stage GMM results
Page 104 and 105: Table 4 First stage GMM results bas
Page 106 and 107: 100 S. Frey, J. Grammig quotes on e
Page 108 and 109: 102 S. Frey, J. Grammig approximate
Page 110 and 111: 104 To obtain the estimates in the
Page 112 and 113: 106 Hence, using the liquidity stat
Page 114 and 115: 108 In the main text we discuss the
Page 117: Pierre Giot . Joachim Grammig How l
Page 121 and 122: How large is liquidity risk in an a
Page 137: How large is liquidity risk in an a
Page 140 and 141: 134 A. D. Hall, N. Hautsch In this
Page 142 and 143: 136 includes order book variables,
Page 144 and 145: 138 An important determinant of liq
Page 146 and 147: 140 The innovation term ei is compu
Page 148 and 149: Table 1 Order book characteristics
Page 150 and 151: 144 data covering the normal tradin
Page 152 and 153: 146 Table 3 Descriptive statistics
Page 154 and 155: Table 4 Fully specified ACI models
Page 156 and 157: Table 4 (continued) BHP NAB NCP TLS
Page 158 and 159: Table 5 ACI models without dynamics
Page 162 and 163: Table 6 ACI models without covariat
Page 166 and 167: 160 specification which includes or
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162 5.2.5 The impact of the bid-ask
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164 contrast to those of Pascual an
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Roman Liesenfeld . Ingmar Nolte . W
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Modelling financial transaction pri
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200 W. B. Omrane, H. V. Oppens anal
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202 W. B. Omrane, H. V. Oppens of s
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204 The extrema detection method ba
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206 price 0.8565 0.8575 0.8585 0.85
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208 We distinguish three possible c
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210 originates. The most active tra
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212 Table 2 Predictability of the c
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214 6 Conclusion Using 5-min euro/d
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216 where σk is the standard devia
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218 If we meet a particular case su
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220 C.5. Triple bottom (TB) TB is c
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222 References W. B. Omrane, H. V.
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Juan M. Rodríguez-Poo · David Ver
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Semiparametric estimation for finan
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254 between price changes and durat
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256 simply aggregated. Even after a
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258 is to make use of the fact that
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260 together with the restrictions
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Table 3 Estimated probabilities of
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264 A. S. Tay, C. Ting More interes
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Table 4 Estimated probabilities of
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268 Acknowledgements Tay gratefully
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270 This paper explores the effect
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272 contrast, price responses to po
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274 Fig. 1 Continuous line is the T
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276 the β’s can form a convex sh
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278 fixing some intervals around th
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280 . That is for a given absolute
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282 30 25 20 15 10 5 CC UNEMW ISM U
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Appendix Table A1 Consumer confiden
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Table A3 Non-farm payrolls • ✓
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Table A5 Weekly unemployment claims
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290 Table A8 Retail sales • ✓ 1
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292 Table A12 GDP, BI, TB and PI Re
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294 V. Voev with the problem of how
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296 V. Voev 2.1 A sample covariance
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298 V. Voev Using the equicorrelate
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300 V. Voev where �kl(t) is the (
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302 V. Voev where hkl,k ′ l ′ i
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304 V. Voev is 1.9%. From the daily
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306 V. Voev ACF ACF ACF 0.5 0.5 0.5
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308 V. Voev autocorrelated. Indeed,
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310 V. Voev 5 Conclusion Table 2 Ro
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312 V. Voev Engle R (1982) Autoregr
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