Numerical Simulation in the Case of Spot Market Intervention

Given the base parameter set, the first part of the numerical simulation is conducted by allowing υ which measures trader’s sensitivity to central bank’s spot intervention to vary from 0 to 1. The degree of the spot rate variability measured by equation (30a) is calculated for each given value of υ, given other parameters held at their base values. The same procedure is applied to ω,

φ

,

µ

andτ .The second part is sensitivity analysis, in which given other parameters held constant, the degree of the spot rate variability is calculated for each possible combination of υ and

φ

, υ and

µ

, υ andτ as well as υ and ω.

The numerical results for the first part of simulation are presented in Tables 4-8 and summarized in Table 3. It is clear that increase in trader’s sensitivity to central bank’s spot intervention υ tends to stabilize fluctuations of the spot rate in the presence of all disturbances. It is also clear that increase in the preference weight placed by the central bank on reaching the target spot rate ω tends to stabilize

fluctuations of the spot rate in the presence of all disturbances.¹²

Increases in the price flexibility

φ

tend to stabilize fluctuations of the spot rate if the random disturbance originates in domestic money u3 or foreign interest rate u6. However, in the presence of domestic absorption disturbance u1, spot trade disturbance u2, foreign expenditure disturbance u4, or foreign price disturbance u5, price flexibility tends to be destabilizing. On the contrary, increases in capital mobility

µ

or speculative elasticityτ tend to stabilize fluctuation of the spot rate in the presence of spot trade disturbance u2, foreign expenditure disturbance u4, or foreign price disturbance u5. If the random disturbance originates in domestic absorption u1, domestic money u3, or foreign interest rate u6, capital mobility and speculation tends to be destabilizing.

Table 3 Summary of Qualitative Results with Base Parameter Values: Spot Rate Effect on Spot Exchange Rate Volatility Source of Disturbance (dampen)spot rate variability

It is also found from Tables 4-8 that domestic monetary disturbance u3 acts as the main source of spot rate variability, regardless of the degree of υ, ω,

φ

,

µ

orτ .

The outcomes of sensitivity analysis are reported in Tables 9-12. All of the tentative conclusions drawn under the base parameter set remain robust. The domestic monetary disturbance u3 remains to be the main source of spot rate variability. In conclusion, the sensitivity analysis finds that the desirability of central bank spot intervention is generally insensitive to the degree of price flexibility, capital mobility, speculation and central bank’s commitment to the target spot rate.

12 Increase in υ or ω has the same effect, both in terms of direction and magnitude, on spot exchange rate volatility can be seen clearly on the specification of equation (30a).

Table 4 Variance of Spot Rate under the Base Parameter Set for Different Values of v

v u

1

u

2

u

3

u

4

u

5

u

6

0 0.0763 0.0022 0.3827 0.00020 0.000022 0.2453 0.3 0.0577 0.0017 0.2894 0.00015 0.000017 0.1855 0.5 0.0488 0.0014 0.2449 0.00013 0.000014 0.1570 0.8 0.0389 0.0011 0.1952 0.00010 0.000011 0.1252 1 0.0339 0.0010 0.1701 0.00009 0.000010 0.1090

Table 5 Variance of Spot Rate under the Base Parameter Set for Different Values of ω

ω u

1

u

2

u

3

u

4

u

5

u

6

0 0.0763 0.0022 0.3827 0.0002 2.2*10^-5 0.2453 1 0.0339 0.0010 0.1701 9*10^-5 1.0*10^-5 0.1090 10 0.0021 6*10^-5 0.0106 6*10^-6 6.0*10^-7 0.0068 100 3*10^-5 9*10^-7 0.0002 8*10^-8 9.0*10^-9 9*10^-5 1000 3*10^-7 9*10^-9 2*10^-6 8*10^-10 9.0*10^-11 1*10^-6

Table 6 Variance of Spot Rate under the Base Parameter Set for Different Values of

φ

φ _u

₁

_u

₂

_u

₃

_u

₄

_u

₅

_u

₆

0.001 2.9*10^-7 0.0002 0.3573 1.6*10^-5 1.8*10^-6 0.1589 0.05 0.0007 0.0003 0.3431 2.3*10^-5 2.6*10^-6 0.1587

1 0.1410 0.0030 0.1787 0.00027 0.00003 0.1556 5 0.8587 0.0116 0.0401 0.00100 0.00012 0.1515 10 1.0270 0.0157 0.0157 0.00140 0.00016 0.1501

Table 7 Variance of Spot Rate under the Base Parameter Set for Different Values of

µ

µ _u

₁

_u

₂

_u

₃

_u

₄

_u

₅

_u

₆

1 0.0354 0.1506 0.2089 0.01360 0.001500 0.1305 5 0.0460 0.0117 0.2375 0.00110 0.000120 0.1515 30 0.0486 0.0020 0.2442 0.00018 0.000020 0.1565 100 0.0490 0.0012 0.2452 0.00011 0.000012 0.1572 200 0.0490 0.0011 0.2454 0.00010 0.000011 0.1574

Table 8 Variance of Spot Rate under the Base Parameter Set for Different Values of τ

τ

u

1

u

2

u

3

u

4

u

5

u

6

1 0.0395 0.0765 0.2201 0.00690 0.000800 0.1386 5 0.0462 0.0103 0.2382 0.00090 0.000100 0.1520 30 0.0486 0.0019 0.2442 0.00017 0.000019 0.1565 100 0.0489 0.0012 0.2452 0.00011 0.000012 0.1572 200 0.0490 0.0011 0.2454 0.00010 0.000011 0.1574

Table 9-1 Variance of Spot Rate against Domestic Absorption Disturbance u1 under the Sensitivity Analysis: Parameter

φ

υ φ

0.001 0.05 1 5 10

0 4.5*10^-7 0.0010 0.2204 1.1356 1.6047 0.3 3.4*10^-7 0.0008 0.1666 1.0301 1.2133 0.5 2.9*10^-7 0.0007 0.1410 0.8587 1.0270 0.8 2.3*10^-7 0.0006 0.1124 0.7268 0.8187 1 2.0*10^-7 0.0005 0.0979 0.5794 0.7132

Table 9-2 Variance of Spot Rate against Spot Trade Balance Disturbance u2 under the Sensitivity Analysis: Parameter

φ

υ φ

0.001 0.05 1 5 10

0 0.00028 0.00041 0.0047 0.0181 0.0246 0.3 0.00021 0.00031 0.0036 0.0137 0.0186 0.5 0.00018 0.00026 0.0030 0.0116 0.0157 0.8 0.00014 0.00021 0.0024 0.0092 0.0125 1 0.00012 0.00018 0.0021 0.0080 0.0109

Table 9-3 Variance of Spot Rate against Excess Supply of Domestic Nominal Money Disturbance u3 under the Sensitivity Analysis: Parameter

φ

υ φ

0.001 0.05 1 5 10

0 0.5583 0.5361 0.2793 0.0626 0.0245 0.3 0.4222 0.4054 0.2112 0.0474 0.0185 0.5 0.3573 0.3431 0.1787 0.0401 0.0157 0.8 0.2849 0.2735 0.1425 0.0320 0.0125 1 0.2481 0.2383 0.1241 0.0278 0.0109

Table 9-4 Variance of Spot Rate against Foreign Expenditure Disturbance u4 under the Sensitivity Analysis: Parameter

φ

υ φ

0.001 0.05 1 5 10

0 0.000025 0.000037 0.00042 0.0016 0.0022 0.3 0.000019 0.000028 0.00032 0.0012 0.0017 0.5 0.000016 0.000023 0.00027 0.0010 0.0014 0.8 0.000013 0.000019 0.00022 0.0008 0.0011 1 0.000011 0.000016 0.00019 0.0007 0.0010

Table 9-5 Variance of Spot Rate against Foreign Price Level Disturbance u5 under the Sensitivity Analysis: Parameter

φ

υ φ

0.001 0.05 1 5 10

0 0.0000028 0.0000041 0.000047 0.00018 0.00025 0.3 0.0000021 0.0000031 0.000036 0.00014 0.00019 0.5 0.0000018 0.0000026 0.000030 0.00012 0.00016 0.8 0.0000014 0.0000021 0.000024 0.00009 0.00013 1 0.0000012 0.0000018 0.000021 0.00008 0.00011

Table 9-6 Variance of Spot Rate against Nominal Foreign Rate of Interest Disturbance

u

6 under the Sensitivity Analysis: Parameter

φ

υ φ

0.001 0.05 1 5 10

0 0.2483 0.2480 0.2432 0.2367 0.2346 0.3 0.1878 0.1875 0.1839 0.1790 0.1774 0.5 0.1589 0.1587 0.1556 0.1515 0.1501 0.8 0.1267 0.1265 0.1241 0.1208 0.1197 1 0.1104 0.1102 0.1081 0.1052 0.1043

Table 10-1 Variance of Spot Rate against Domestic Absorption Disturbance u1 under the Sensitivity Analysis: Parameter

µ

υ µ

^{1 5 30 100 200}

0 0.0554 0.0718 0.0759 0.0765 0.0766 0.3 0.0419 0.0543 0.0574 0.0578 0.0579 0.5 0.0354 0.0460 0.0486 0.0490 0.0490 0.8 0.0282 0.0367 0.0387 0.0390 0.0391 1 0.0246 0.0319 0.0337 0.0340 0.0340

Table 10-2 Variance of Spot Rate against Spot Trade Balance Disturbance u2 under the Sensitivity Analysis: Parameter

µ

υ µ

^{1 5 30 100 200}

0 0.2353 0.0183 0.0031 0.0019 0.0017 0.3 0.1779 0.0138 0.0023 0.0015 0.0013 0.5 0.1506 0.0117 0.0020 0.0012 0.0011 0.8 0.1201 0.0093 0.0016 0.0010 0.0009 1 0.1046 0.0081 0.0014 0.0009 0.0008

Table 10-3 Variance of Spot Rate against Excess Supply of Domestic Nominal Money Disturbance u3 under the Sensitivity Analysis: Parameter

µ

υ µ

^{1 5 30 100 200}

0 0.3265 0.3710 0.3816 0.3831 0.3834 0.3 0.2468 0.2806 0.2885 0.2897 0.2899 0.5 0.2089 0.2375 0.2442 0.2452 0.2454 0.8 0.1666 0.1893 0.1947 0.1955 0.1956 1 0.1451 0.1649 0.1696 0.1703 0.1704

Table 10-4 Variance of Spot Rate against Foreign Expenditure Disturbance u4 under the Sensitivity Analysis: Parameter

µ

υ µ

^{1 5 30 100 200}

0 0.0212 0.0016 0.00027 0.00017 0.00015 0.3 0.0160 0.0012 0.00021 0.00013 0.00012 0.5 0.0136 0.0011 0.00018 0.00011 0.00010 0.8 0.0108 0.0008 0.00014 0.00009 0.00008 1 0.0094 0.0007 0.00012 0.00008 0.00007

Table 10-5 Variance of Spot Rate against Foreign Price Level Disturbance u5 under the Sensitivity Analysis: Parameter

µ

υ µ

^{1 5 30 100 200}

0 0.0024 0.00018 0.000031 0.000019 0.000017 0.3 0.0018 0.00014 0.000023 0.000015 0.000013 0.5 0.0015 0.00012 0.000020 0.000012 0.000011 0.8 0.0012 0.00009 0.000016 0.000010 0.000009 1 0.0010 0.00008 0.000014 0.000009 0.000008

Table 10-6 Variance of Spot Rate against Nominal Foreign Rate of Interest Disturbance u6 under the Sensitivity Analysis: Parameter

µ

υ µ

^{1 5 30 100 200}

0 0.2038 0.2367 0.2445 0.2456 0.2459 0.3 0.1541 0.1790 0.1849 0.1857 0.1859 0.5 0.1305 0.1515 0.1565 0.1572 0.1574 0.8 0.1040 0.1208 0.1247 0.1253 0.1254 1 0.0906 0.1052 0.1087 0.1092 0.1093

Table 11-1 Variance of Spot Rate against Domestic Absorption Disturbance u1 under the Sensitivity Analysis: Parameter τ

υ

τ ^{1 5 30 100 200}

0 0.0617 0.0723 0.0759 0.0765 0.0766 0.3 0.0466 0.0546 0.0574 0.0578 0.0579 0.5 0.0395 0.0462 0.0486 0.0489 0.0490 0.8 0.0315 0.0369 0.0387 0.0390 0.0391 1 0.0274 0.0321 0.0337 0.0340 0.0340

Table 11-2 Variance of Spot Rate against Spot Trade Balance Disturbance u2 under the Sensitivity Analysis: Parameter τ

υ

τ ^{1 5 30 100 200}

0 0.1195 0.0160 0.0030 0.0019 0.0017 0.3 0.0903 0.0121 0.0023 0.0015 0.0013 0.5 0.0765 0.0103 0.0019 0.0012 0.0011 0.8 0.0610 0.0082 0.0015 0.0010 0.0009 1 0.0531 0.0071 0.0013 0.0009 0.0008

Table 11-3 Variance of Spot Rate against Excess Supply of Domestic Nominal Money Disturbance u3 under the Sensitivity Analysis: Parameter τ

υ

τ ^{1 5 30 100 200}

0 0.3439 0.3722 0.3816 0.3831 0.3834 0.3 0.2600 0.2814 0.2886 0.2897 0.2899 0.5 0.2201 0.2382 0.2442 0.2452 0.2454 0.8 0.1754 0.1899 0.1947 0.1955 0.1956 1 0.1528 0.1654 0.1696 0.1703 0.1704

Table 11-4 Variance of Spot Rate against Foreign Expenditure Disturbance u4 under the Sensitivity Analysis: Parameter τ

υ

τ ^{1 5 30 100 200}

0 0.0108 0.0014 0.00027 0.00017 0.00015 0.3 0.0081 0.0011 0.00021 0.00013 0.00012 0.5 0.0069 0.0009 0.00017 0.00011 0.00010 0.8 0.0055 0.0007 0.00014 0.00009 0.00008 1 0.0048 0.0006 0.00012 0.00008 0.00007

Table 11-5 Variance of Spot Rate against Foreign Price Level Disturbance u5 under the Sensitivity Analysis: Parameter τ

υ

τ ^{1 5 30 100 200}

0 0.0012 0.00016 0.000030 0.000019 0.000017 0.3 0.0009 0.00012 0.000023 0.000015 0.000013 0.5 0.0008 0.00010 0.000019 0.000012 0.000011 0.8 0.0006 0.00008 0.000015 0.000010 0.000009 1 0.0005 0.00007 0.000013 0.000009 0.000008

Table 11-6 Variance of Spot Rate against Nominal Foreign Rate of Interest Disturbance u6 under the Sensitivity Analysis: Parameter τ

υ

τ ^{1 5 30 100 200}

0 0.2166 0.2375 0.2445 0.2456 0.2459 0.3 0.1638 0.1796 0.1849 0.1857 0.1859 0.5 0.1386 0.1520 0.1565 0.1572 0.1574 0.8 0.1105 0.1212 0.1248 0.1253 0.1254 1 0.0963 0.1056 0.1087 0.1092 0.1093

Table 12-1 Variance of Spot Rate against Domestic Absorption Disturbance u1 under the Sensitivity Analysis: Parameter ω

υ ω

^{0 1 10 100 1000}

0 0.0763 0.0763 0.0763 0.0763 0.0763 0.3 0.0763 0.0452 0.0048 8*10^-5 8*10^-7 0.5 0.0763 0.0339 0.0021 3*10^-5 3*10^-7 0.8 0.0763 0.0236 0.0009 1*10^-5 1*10^-7 1 0.0763 0.0191 0.0006 7*10^-6 8*10^-8

Table 12-2 Variance of Spot Rate against Spot Trade Balance Disturbance u2 under the Sensitivity Analysis: Parameter ω

υ ω

^{0 1 10 100 1000}

0 0.0022 0.0022 0.0022 0.0022 0.0022 0.3 0.0022 0.0013 0.0001 2*10^-6 3*10^-8 0.5 0.0022 0.0010 6*10^-5 9*10^-7 9*10^-9 0.8 0.0022 0.0007 3*10^-5 3*10^-7 3*10^-9 1 0.0022 0.0006 2*10^-5 2*10^-7 2*10^-9

Table 12-3 Variance of Spot Rate against Excess Supply of Domestic Nominal Money Disturbance u3 under the Sensitivity Analysis: Parameter ω

υ ω

^{0 1 10 100 1000}

0 0.3827 0.3827 0.3827 0.3827 0.3827 0.3 0.3827 0.2264 0.0239 0.0004 4*10^-6 0.5 0.3827 0.1701 0.0106 0.0002 2*10^-6 0.8 0.3827 0.1181 0.0047 6*10^-5 6*10^-7 1 0.3827 0.0957 0.0032 4*10^-5 4*10^-7

Table 12-4 Variance of Spot Rate against Foreign Expenditure Disturbance u4 under the Sensitivity Analysis: Parameter ω

υ ω

^{0 1 10 100 1000}

0 0.0002 0.0002 0.0002 0.0002 0.0002 0.3 0.0002 0.0001 0.0001 2*10^-7 2*10^-9 0.5 0.0002 9*10^-5 6*10^-6 8*10^-8 8*10^-10 0.8 0.0002 6*10^-5 3*10^-6 3*10^-8 3*10^-10 1 0.0002 5*10^-5 2*10^-6 2*10^-8 2*10^-10

Table 12-5 Variance of Spot Rate against Foreign Price Level Disturbance u5 under the Sensitivity Analysis: Parameter ω

υ ω

^{0 1 10 100 1000}

0 2.2*10^-5 2.2*10^-5 2.2*10^-5 2.2*10^-5 2.2*10^-5 0.3 2.2*10^-5 1.3*10^-5 1.4*10^-6 2.3*10^-8 2.5*10^-10 0.5 2.2*10^-5 1.0*10^-5 6.0*10^-7 9.0*10^-9 9.0*10^-11 0.8 2.2*10^-5 7.0*10^-6 3.0*10^-7 3.0*10^-9 3.0*10^-11 1 2.2*10^-5 6.0*10^-6 2.0*10^-7 2.0*10^-9 2.0*10^-11

Table 12-6 Variance of Spot Rate against Nominal Foreign Rate of Interest Disturbance u6 under the Sensitivity Analysis: Parameter ω

υ ω

^{0 1 10 100 1000}

0 0.2453 0.2453 0.2453 0.2453 0.2453 0.3 0.2453 0.1452 0.0153 0.0003 3*10^-6 0.5 0.2453 0.1090 0.0068 9*10^-5 1*10^-6 0.8 0.2453 0.0757 0.0030 4*10^-5 4*10^-7 1 0.2453 0.0613 0.0020 2*10^-5 2*10^-7

在文檔中 匯率波動性與中央銀行最適干預 (頁 22-31)