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116 price b t(v), as defined in Eq. (1), implied by selling at time t volumes v of 1, 5,000, 20,000, and 40,000 shares, respectively. Our choice of volumes is motivated by the descriptive statistics and trading statistics for the three stocks (see below). Midquote prices were computed as the average of best bid and ask prices prevailing at time t. Of course these are equivalent to bt(1) and a t(1), respectively. If the trade volume v exceeds the depth at the prevailing best quote then b t(v) will be smaller than b t(1) (and a t(v)>a t(1)). By varying the trade volume v one can plot the slope of the instantaneous offer and demand curves. Because Xetra did not allow iceberg type orders during the time period under study, our reconstructed order book is the actual order book faced by market participants. This implies that the computed liquidity risk (see below) is the actual risk incurred by an impatient trader who submits aggressive buy or sell orders for a v-share volume. Table 1 reports descriptive statistics on trading and liquidity supply activity for the three stocks. Trading activity is high, with 600 to 1,300 trades per day. The large number of (nonmarketable) limit order submissions, of which on average 60% are cancelled before execution, reflects active and competitive liquidity suppliers. The cumulative depth figures show that the order books can sustain large Table 1 Data descriptives P. Giot, J. Grammig DCX DTE SAP Trade descriptives Avg. no. of trades per day 1,297 922 661 Avg. transaction price (price per share in euros) 69.9 40.7 402.5 Avg. volume per trade (shares) 1,888 3,352 408 Median volume per trade (shares) 1,000 2,000 300 0.25 quantile volume per trade (shares) 500 900 100 0.75 quantile volume per trade (shares) 2,300 4,200 500 0.95 quantile volume per trade (shares) 5,000 9,900 1,000 Liquidity supply descriptives Avg. inside spread (euros) 0.076 0.069 0.732 Avg. volume (shares) at best ask 2,908 4,855 467 Avg. cumulated volume (shares) first two ask quotes 6,230 10,130 986 Avg. cumulated volume (shares) first three ask quotes 9,781 15,575 1,558 Avg. total ask side volume (shares) 350,063 317,725 32,300 Avg. volume (shares) at best bid 2,378 4,648 452 Avg. cumulated volume (shares) first two bid quotes 5,168 9,993 936 Avg. cumulated volume (shares) first three bid quotes 8,145 15,745 1,456 Avg. total bid side volume (shares) 346,334 322,311 33,885 Daily avg. no. submitted non-marketable limit orders per day 3,139 2,311 3,038 Daily avg. no. limit order cancelations per day 1,968 1,395 2,346 The table reports descriptives of the liquidity demand reflected in trade events and liquidity supply reflected in the Xetra order book for Daimler Chrysler (DCX), Deutsche Telekom (DTE) and SAP. The sample period extends from August 2, 1999 to October 29, 1999 and comprises 65 trading days. The descriptives are computed using observations from the continuous trading hours. Until September 17, 1999 the continuous trading period extended from 8.30 A.M.to5.00P.M. CET. Beginning with September 20, 1999 the trading hours were shifted to 9.00 A.M. to 5.30 P.M. CET. Except for the daily figures we compute averages over the trade events using the snapshots of the order book immediately before the trade for the liquidity supply variables
How large is liquidity risk in an automated auction market? 117 trades, also those hypothetical trade sizes that we consider in this paper. Looking at the distribution of trade sizes one can see that the majority of the trades is relatively small, and that the distribution is right-skewed. The hypothetical trade sizes that we consider for the liquidity adjusted VaR method proposed in this paper can thus be considered as large trades, i.e. beyond the 95% quantile of the trade size distribution. This is quite intended as we want to assess the risk associated with liquidating large positions. 3 Methodology In this section, we detail the econometric methodology used to characterize the liquidity risk faced by impatient traders. We first present an existing model that focuses on liquidity risk in the VaR framework. Then we put forward our new methodology that capitalizes on the ex-ante known state of the order book to derive actual measures of liquidity risk. Throughout this section, we focus on the mean component of the liquidity risk and on the ‘uncertainty’ component (the standard deviation combined with the quantile), with both measures being combined in a single number akin to a VaR measure. VaR type market risk measures can be traced back to the middle of the 1990s. First, the 1988 Basel Accord specified the total market risk capital requirement for a financial institution as the sum of the requirements of the equities, interest rates, foreign exchange and gold and commodities positions. 10 Secondly, the 1996 Amendment proposed an alternative approach for determining the market risk capital requirement, allowing the use of an internal model in order to compute the maximum loss over 10 trading days at a 1% confidence level. This set the stage for Value-at-Risk models which take into account the statistical features of the return distribution to quantity the market risk. 11 Although the use of VaR models was a breakthrough with respect to the much cruder models used earlier, the notion of liquidity risk has been conspicuously absent from the VaR methodology until the end of the 1990s. Subramanian and Jarrow (2001) characterize the liquidity discount (the difference between the market value of a trader’s position and its value when liquidated) in a continuous time framework. Empirical models incorporating liquidity risk are developed in Jorion (2000), or Bangia et al. (1999), but none of the methods does explicitly take into account the price impact incurred when liquidating a portfolio of assets. Bangia et al. (1999), henceforth referred to as BDSS, suggest a liquidity risk correction procedure for the VaR framework. BDSS relate the liquidity risk component to the distribution of the inside half-spread. In the first step of the procedure, the VaR is computed as the α percent quantile of the mid-quote return distribution (assuming normality). This quantile is then increased by a factor based on the excess kurtosis of the returns. In a second step, liquidity costs are allowed for by taking as inputs the historical average half-inside-spread and its volatility. This adjusts the VaR for the fact that buy and sell orders are not executed at the quote mid-point, but that 10 This sum is a major determinant of the eligible capital of the financial institution based on the 8% rule. 11 Further general information about VaR techniques and regulation issues are available in Dowd (1998), Jorion (2000), Saunders (2000) or at the Bank of International Settlement website http:// www.bis.org.
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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
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62 Hasbrouck (1991). The system is
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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 and 118: Pierre Giot . Joachim Grammig How l
Page 119 and 120: How large is liquidity risk in an a
Page 121: 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
Page 168 and 169: 162 5.2.5 The impact of the bid-ask
Page 170 and 171: 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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