IMES DISCUSSION PAPER SERIES Discuss ssion Paper No. 98-J-2 INSTITUTE FOR MONETARY AND ECONOMIC STUDIES BANK OF JAPAN 100-8630 203

IMES Discuss ssion Paper Series 98-J-2 1998 1 VaRVWAP E-mail: ohsawa@boj.co.uk E-mail: jun.muranaga@boj.or.jp BIS THE MEASUREMENT OF AGGREGATE RISK BIS World Wide Web http://www.bis.org 1997 12 WWW http://www.boj.or.jp BIS

1 3 5 5 6 7 8 9 11 12 15

1 Mori, Ohsawa, and Shimizu (1996) VaR Fallon (1996) Alexander (1996) VaR GARCH 1 Wilson (1996) Board of Governors of the Federal Reserve System ed. (1996) Part II Session

2 3 2 1996 3

VaR 4 4 lender of last resort

Glosten and Harris (1988) order-processing cost adverse selection cost Glosten and Milgrom <1985>George, Kaul, and Nimalendran (1991) AMEX/NYSENASDAQ Longstaff (1995) Black-Scholes

Amihud and Mendelson (1987) NYSE open-toopenclose-to-close Stoll and Whaley (1990) Lee and Lin (1995)

Amihud and Mendelson (1987) 5 NYSE Clark, McConnell and Singh (1992) 19821987NYSE Ritter and Chopra (1989) 5 Easley, Kiefer, O hara, and Paperman (1996)

parking-theproceeds Bollerslev and Melvin (1994) Bollerslev and Domowitz (1993) Glassman (1987) Locke and Sarkar (1996) readiness

Hebner <1996> a. b. c. d. Watanabe (1996) 6 1,200 1995 10 2 1996 9 30

VaR NYSE kurtosis VWAP; volume-weighted average price) VWAP kurtosis

500 237 230 5.929.4 NYSE NYSE MOC; market-on-close 7 TSE VWAP VWAP VWAP 2 100,000 7 NYSE

8 VaR VWAP VaR VaR 1 1/2 1 9 8 0 P = P exp s e t + s e ( ) ex VWAP VWAP a H b P ex 0 P VWAP s VWAP 1996 VWAP VWAP s H VWAP 1995 10 1996 9 t e, e a b 9 ( s e ) Pbid = Pm exp m t - f( u) 2 0 1 ( s e ) Pask = Pm exp m t + f( u) 2 P bid 0 1

99 VaR VaR 10 normal market size 1 11 P ask 0 P m t s m f () e u 10 VaR VaR 11

12 90 VaR 3 13 12 Lee and Ready (1991) P P i bid i ask i i V g u i = Pbid æ ( ö -1 2 ) l expç- è NMS ø i i æ V g ( u ö i-1 2 ) l = Pask expç è NMS ø i P bid 0 0 Pbid = Pm exp ( s m e t) - E[ f( u1 )] 0 0 Pask = Pm exp ( s m e t) + E[ f( u1 )] 1 2 1 2

VaR VaR 99 95 VaR herding behavior Shimizu (1997) i P ask 0 P m t s m f () g l () e u u i 1, 2 V i NMS

VaR Shimizu (1997)

0.02000 0.01930 0.01896 0.01999 6.5503 6.7363 7.2008 6.5145

( t ) ( t+1 ) ( t+2 ) VWAP (1929.1) VWAP (1930.5) VWAP (1982.9)

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Lee, C. M. and M. J. Ready (1991), Inferring Trade Direction from Intraday Data, Journal of Finance, 2, 733-746. Locke P.R. and A. Sarkar (1996), Volatility and Liquidity in Futures Markets, Federal Reserve Bank of New York Research Paper No. 9612, May. Longstaff, F.A.(1995), How Much Can Marketability Affect Security Values?, Journal of Finance, 5, 1767-1774. Mori, A., M. Ohsawa, and T. Shimizu (1996), A Framework for More Effective Stress Testing, in FRB, ed., Risk Measurement and Systemic Risk --Proceedings of a Joint Central Bank Research Conference, November 1995, Washington D.C.. Shimizu, T. (1997), Dynamic Macro Stress Exercise Including Feedback Effects, mimeo, Institute for Monetary and Economic Studies, Bank of Japan. Stoll, H.R. and R.E. Whaley (1990), Stock Market Structure and Volatility, Review of Financial Studies, 44, 115-134. Watanabe, T., Intraday Price Volatility and Trading Volume: A Case of the Japanese Government Bond Futures, in FRB, ed., Risk Measurement and Systemic Risk, Washington D.C. (forthcoming). Wilson, T. (1996), Calculating Risk Capital, in C. Alexander, ed., The Handbook of Risk Management and Analysis, West Sussex: John Wiley.