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Table 2 Performance of CTP solutions RN and RA versus benchmark policies (B1, B2 and NH), when \(\left( {\pi_{u} , \pi_{d} } \right) = \left( {1.25\% , 3.75\% } \right)\)

From: Foreign exchange trading and management with the stochastic dual dynamic programming method

Currency

Policy

Mean

Median

Volatility

\(VaR_{99\% }\)

\(CVaR_{99\% }\)

USDCLP \(S_{0} = 800.0\)

RN1

795.3 (− 0.6)

797.1

6.4

805.0

806.1 (0.8)

RA0.7

797.9 (− 0.3)

798.9

4.4

803.2

804.7 (0.6)

B1

793.9 (− 0.8)

796.0

5.5

800.0

800.0 (0.0)

B2

798.9 (− 0.1)

799.2

3.8

809.0

810.5 (1.3)

NH

796.5 (− 0.4)

797.3

8.7

818.8

821.3 (2.7)

USDBRL \(S_{0} = 5.5\)

RN1

5.4463 (− 1.0)

5.4687

0.078

5.5687

5.5857 (1.6)

RA0.7

5.4807 (− 0.4)

5.4890

0.0484

5.5312

5.5514 (0.9)

B1

5.4287 (− 1.3)

5.4544

0.0671

5.5000

5.5000 (0.0)

B2

5.4872 (− 0.2)

5.4908

0.0451

5.6101

5.6294 (2.4)

NH

5.4616 (− 0.7)

5.4717

0.1037

5.7359

5.7692 (4.9)

USDTRY \(S_{0} = 10.0\)

RN1

9.8758 (− 1.2)

9.9863

0.2386

10.2803

10.4226 (4.2)

RA0.7

9.9519 (− 0.5)

9.9920

0.1589

10.1324

10.2663 (2.7)

B1

9.8154 (− 1.8)

9.9458

0.2319

10.0000

10.0000 (0.0)

B2

9.9696 (− 0.3)

9.9941

0.1285

10.3530

10.4423 (4.4)

NH

9.9107 (− 0.9)

9.9813

0.3069

10.7926

10.9571 (9.6)

AUDUSD \(S_{0} = 0.7\)

RN1

0.6949 (− 0.7)

0.6974

0.0083

0.7113

0.7183 (2.6)

RA0.7

0.6974 (− 0.4)

0.6989

0.0058

0.7048

0.7075 (1.1)

B1

0.6929 (− 1.0)

0.6958

0.007

0.7000

0.7000 (0.0)

B2

0.6987 (− 0.2)

0.6992

0.0045

0.7114

0.7136 (1.9)

NH

0.6962 (− 0.5)

0.6974

0.0105

0.7243

0.7291 (4.2)

GBPUSD \(S_{0} = 1.0\)

RN1

0.9948 (− 0.5)

0.9974

0.0076

1.0061

1.0083 (0.8)

RA0.7

0.9972 (− 0.3)

0.9989

0.0059

1.0049

1.0074 (0.7)

B1

0.9931 (− 0.7)

0.9956

0.0066

1.0000

1.0000 (0.0)

B2

0.9988 (− 0.1)

0.9991

0.0044

1.0107

1.0126 (1.3)

NH

0.996 (− 0.4)

0.9971

0.0101

1.0227

1.0259 (2.6)

EURUSD \(S_{0} = 1.5\)

RN1

1.4930 (− 0.5)

1.4970

0.0092

1.5058

1.5071 (0.5)

RA0.7

1.4945 (− 0.4)

1.4981

0.0085

1.5049

1.5065 (0.4)

B1

1.4917 (− 0.6)

1.4957

0.0081

1.5000

1.5000 (0.0)

B2

1.4983 (− 0.1)

1.4989

0.0052

1.5123

1.5138 (0.9)

NH

1.4946 (− 0.4)

1.4964

0.0125

1.5256

1.5279 (1.9)

USDJPY \(S_{0} = 105.0\)

RN1

104.4 (− 0.6)

104.9

0.8

105.3

105.4 (0.4)

RA0.7

104.5 (− 0.5)

104.9

0.8

105.2

105.3 (0.3)

B1

104.3 (− 0.6)

104.8

0.8

105.0

105.0 (0.0)

B2

104.9 (− 0.1)

104.9

0.5

106.2

106.3 (1.3)

NH

104.5 (− 0.4)

104.8

1.1

107.4

107.7 (2.6)

  1. The subscript in RN and RA is the ÎČ used in Eq. (5), which defines the degree of risk aversion. The statistics are obtained from the total cost in domestic currency divided by total demand D = 1. The numbers in parenthesis are the rate of increase (reduction) (%) relative to \(S_{0}\)
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