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Table 8 Performance of CTP solutions RN and RA versus benchmark policies B1, B2 and NH. The subscript in RN and RA is the ÎČ used in Eq. (5), which defines the degree of risk aversion

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

798.3 (− 0.2)

798.7

4.6

806.3

810.7 (1.3)

RA0.8

799.3 (− 0.1)

799

2.6

804.2

805.3 (0.7)

B1

796.6 (− 0.4)

797.7

3.9

800

800.0 (0.0)

B2

801.2 (0.1)

800.8

3.8

810.9

812.0 (1.5)

NH

802.8 (0.4)

801.8

8.9

821.9

824.0 (3.0)

USDBRL \(S_{0} = 5.5\)

RN1

5.4798 (− 0.4)

5.4879

0.0537

5.5647

5.5792 (1.4)

RA0.8

5.4989 (− 0.0)

5.4985

0.0049

5.5108

5.5163 (0.3)

B1

5.4602 (− 0.7)

5.4742

0.0477

5.5000

5.5000 (0.0)

B2

5.5137 (0.2)

5.5088

0.0458

5.6345

5.6511 (2.7)

NH

5.5353 (0.6)

5.5214

0.1065

5.7787

5.808 (5.6)

USDTRY \(S_{0} = 10.0\)

RN1

9.9595 (− 0.4)

9.9948

0.1660

10.2397

10.4491 (4.5)

RA0.7

9.9920 (− 0.1)

9.9940

0.0919

10.1888

10.3897 (3.9)

B1

9.9007 (− 1.0)

9.9690

0.1595

10.0000

10.0000 (0.0)

B2

10.0349 (0.3)

10.0058

0.1326

10.4577

10.5451 (5.5)

NH

10.0923 (0.9)

10.0086

0.3211

11.0052

11.1607 (11.6)

AUDUSD \(S_{0} = 0.7\)

RN1

0.6986 (− 0.2)

0.6990

0.0061

0.7139

0.7198 (2.8)

RA0.8

0.6994 (− 0.1)

0.6994

0.0038

0.7092

0.7160 (2.3)

B1

0.6961 (− 0.6)

0.6974

0.0049

0.7000

0.7000 (0.0)

B2

0.7013 (0.2)

0.7008

0.0046

0.7140

0.7160 (2.3)

NH

0.7033 (0.5)

0.7018

0.0107

0.7294

0.7327 (4.7)

GBPUSD \(S_{0} = 1.0\)

RN1

0.9983 (− 0.2)

0.9989

0.0055

1.0079

1.0111 (1.1)

RA0.7

0.9998 (− 0.0)

0.9996

0.0014

1.0035

1.0060 (0.6)

B1

0.9961 (− 0.4)

0.9974

0.0047

1.0000

1.0000 (0.0)

B2

1.0013 (0.1)

1.0008

0.0044

1.0131

1.0147 (1.5)

NH

1.0031 (0.3)

1.0018

0.0103

1.0268

1.0297 (3.0)

EURUSD \(S_{0} = 1.5\)

RN1

1.4975 (− 0.2)

1.4990

0.0064

1.5054

1.5063 (0.4)

RA0.7

1.4997 (− 0.0)

1.4996

0.0016

1.5021

1.5031 (0.2)

B1

1.4959 (− 0.3)

1.4979

0.0057

1.5000

1.5000 (0.0)

B2

1.5017 (0.1)

1.5010

0.0053

1.5143

1.5153 (1.0)

NH

1.5040 (0.3)

1.5019

0.0126

1.5283

1.5308 (2.1)

USDJPY \(S_{0} = 105.0\)

RN1

104.8 (− 0.2)

105.0

0.6

105.3

105.3 (0.3)

RA0.8

104.8 (− 0.1)

104.9

0.5

105.3

105.3 (0.3)

B1

104.7 (− 0.3)

104.9

0.5

105.0

105.0 (0.0)

B2

105.2 (0.1)

105.1

0.5

106.4

106.5 (1.4)

NH

105.4 (0.4)

105.1

1.1

107.8

108.1 (2.9)

  1. The statistics are obtained from the total cost in domestic currency divided by total demand D = 1. The table shows the results when \(\left( {\pi_{u} , \pi_{d} } \right) = \left( {3.75\% , 1.25\% } \right)\). The numbers in parenthesis are the rate of increase (reduction) (%) relative to \(S_{0}\)