IMES Discussion Paper Series 98-J

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1 IMES DISCUSSION PAPER SERIES Discuss ssion Paper No. 98-J-1 INSTITUTE FOR MONETARY AND ECONOMIC STUDIES BANK OF JAPAN

2 IMES Discussion Paper Series 98-J

3

4 k profile 1

5 1.2. I R i å R i 2

6 Glosten and Milgrom 1985 Glosten and Milgrom Gennottee and Leland

7 2.2. t I R i t+1 t+2 t+3 t+2 t+3 t t+2 R it R it+1 R it+2 R it+3 S DR i 4 S 1

8 t I F it F it t f it x t Fit = fit ( xt ) S 0 t+1 I x t t+1 f it S 0 = dx F = f ( x ) = f ( x + dx) it + 1 it + 1 t + 1 it t R s å å å R = R = df = s i i fi x dx I f 1 f 2 it + it + t+2 F 2 = f 2( x + dx) it+ it+ t n

9 æ n df ö i dx = G ç å èi= x 1 ø S 1 S1 = dx+ dx = dx R d å( + 2 ) å fit+ 2 ( xt dx) fit ( xt ) R = F - F d it it ( ) = + - æ i ( ) fx dx dx fi = ç + + è t dt ö å ø (1) t (1) fi t dt 6

10 R d t x a t a t = a constant x b t db = b / x b constant x c t dc = c dx t t t t b x t 100 x x t = 100 s x = 02. S0 = 5s = -65. x x t + 1 =

11 F = f ( x ) = 100 x = = it it t t F = f ( x ) = 100 x = = 9350 it + 1 it + 1 t + 1 t + 1 R s R = å R = ådf = 1950 s i i F2 = f2 ( x ) = 100 x = = t t t t ( ) ( ) F = f ( x ) = b/ x x = / = t+ 1 2t+ 1 t+ 1 t+ 1 t+ 1 df 2 F3 = f3 ( x ) = 100 x = = t t t t ( ) { } x t + 1 F = f ( x ) = c dx x = (- 6. 5) = t+ 1 3t+ 1 t+ 1 t+ 1 df 3 x t + 1 =+ 21 = n dx æ ö = G dfi x ç å èi= 1 ø = k( ) =-11. 5k k=0.2 S1 = dx+ dx = =-88. 8

12 R d å( + 2 ) R = F - F d it it æ å Fit + 2ç1 - è x t t + 2 ö ø = =

13 t 10

14 JGB JGB JGB ± ± ± 11

15 71.67% 76.67% 85.42% 12

16 13

17 % t JGB 14

18 JGB 15

19 JGB JGB JGB JGB 16

20 DP = as b DP a s b p p : JGB : / : JGB : VaR (t) * * t VaR t-1 t 17

21

22

23

24 21

25 Factor x Factor y y x ( ) X = x, y t t t t f ( X ) t t Sensitivity data at t : f t ( Xt) f ( ) t Xt x t+1 f ( ) 1( X 1) ft+ 1 Xt+ 1 t+ t+ x f ( X ) t+ 1 t+ 1 y y 22

26 a) b) f f t ( X ) t t+1 x ( Xt) f ( ) t Xt+1 x f x ( X ) t+ 1 t+ 1 f t f t+1 x Network A sell xa Network B buy xb Network C sell xc 23

27 Camargo, F. A., Learning Algorithms in neural Networks, Working Paper, the DOC Laboratory, Computer Science Department, Columbia University, Glosten, L., and P. Milgrom, Bid, Ask, and Transaction Prices in a Specialist Market with Heterogeneously Informed Traders, Journal of Financial Economics, 13, 1985, pp Gennottee, G., and H. Leland, Market Liquidity, Hedges and Crashes, American Economic Review, 80, 1990, pp O hara, M., Market Microstructure Theory, Blackwell Publishers. Shimizu, Tokiko, and Tsukasa Yamashita, Dynamic Micro and Macro Stress Simulation, Disucussion Paper Series, 96-E-4, IMES, Bank of Japan 24

28 180

29 181

30 182

31 183

32 184

33 185

34 186

35 187

36 Table 1 Characteristics of the agents Key for trading Fortrend/contrarian Other characteristics Targeted profit (loss limit), Position limit Agent 1 Charts of market movements (chartist) Fortrend Positive correlation b/w P/L condition and trading volume 3 billion yen/half year, delta limit:± 100 billion Agent 2 Charts of market movements (chartist) Contrarian Frequent writer of options 3 billion yen/half year, delta limit:± 100 billion Agent 3 Fundamental events (fundamentalist) Trading horizon is longer than the others (more an investor-type of trader than a dealer) 2 billion yen/half year, delta limit:± 70 billion Table 2 Steps for inputs adjustments Inputs Agent 1 Agent 2 Agent 3 A: Market data (change on a trading day) B: A + accumulated P/L C: B + recent market movements + news D: C + market trend over a longer horizon (Agent 3) 71.67% 82.08% 80.00% (Figure 5) (Figure 6) 188

37 Table 3 The magnitude of largest daily change Upward change Downward change 3-year swap rate 3.01s -3.43s 5-year swap rate 2.96s -2.59s 10-year swap rate 3.46s -2.54s Table 4 Stress scenarios 3y 5y 10y Period t 3.33% 3.98% 4.49% Scenario % 4.22% 4.72% Scenario % 3.78% 4.33% Scenario % 3.98% 4.49% Scenario % 3.98% 4.49% Scenario % 4.22% 4.49% Scenario % 3.78% 4.49% Scenario % 3.98% 4.72% Scenario % 3.98% 4.33% 189

38 Table 5 Changes of each agent s delta under scenarios (in billions of yen) Agent 1 Agent 2 Agent 3 Total D/S Scenario Scenario Scenario Scenario Scenario Scenario Scenario Scenario Standard deviation 12 Table 6 Risk profiles of each agent (in billions of yen) Agent 1 Agent 2 Agent 3 Total Scenario Scenario Scenario Scenario Scenario Scenario Scenario Scenario VaR(t) * * Agent 3 s VaR figure is measured at period t-1, since its position at period t is square. 190

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

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