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Financial Innovation

Table 11 (Up): Sensitivity analysis in the intraday mean-reverting price process for USDCLP. When one parameter changes, the rest are kept unchanged and we set \(\left( {\pi_{u} , \pi_{d} } \right) = \left( {1.25\% , 3.75\% } \right)\)

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

Case

Policy

Mean

Median

\(VaR_{1\% }\)

\(CVaR_{1\% }\)

\(\sigma /\sqrt {2\kappa } = 0.1\%\)

RN1

7.0 (0.9)

5.6

1.0

1.3 (0.2)

RA0.5

6.7 (0.8)

5.4

0.3

0.4 (0.1)

S1

7.8 (1.0)

6.2

− 1.1

− 1.0 (− 0.1)

Base case \(\sigma /\sqrt {2\kappa } = 0.31\%\)

RN1

7.1 (0.9)

6.2

3.6

4.8 (0.6)

RA0.5

6.2 (0.8)

4.7

0.7

1.2 (0.1)

S1

9.6 (1.2)

7.8

− 3.3

− 3.0 (− 0.4)

\(\sigma /\sqrt {2\kappa } = 0.5\%\)

RN1

7.9 (1.0)

7.8

6.1

7.5 (0.9)

RA0.5

6.3 (0.8)

4.9

0.8

1.6 (0.2)

S1

11.5 (1.4)

10.4

− 4.9

− 4.6 (− 0.6)

\(\sigma /\sqrt {2\kappa } = 1.0\%\)

RN1

10.3 (1.3)

10.9

12.3

14.9 (1.9)

RA0.5

6.7 (0.8)

5.3

1.1

4.1 (0.5)

S1

17.1 (2.1)

16.7

− 8.3

− 7.3 (− 0.9)

\(\hat{\mu } = 0\) pips

RN1

0.5 (0.1)

0.4

6.4

7.8 (1.0)

RA0.5

0.1 (0.0)

0.0

2.9

4.9 (0.6)

S1

5.9 (0.7)

5.7

− 2.9

− 2.7 (− 0.3)

Base case \(\hat{\mu } = 10\) pips

RN1

7.1 (0.9)

6.2

3.6

4.8 (0.6)

RA0.5

6.2 (0.8)

4.7

0.7

1.2 (0.1)

S1

9.6 (1.2)

7.8

− 3.3

− 3.0 (− 0.4)

\(\hat{\mu } = 20\) pips

RN1

13.3 (1.7)

11.8

3.5

4.4 (0.6)

RA0.5

12.5 (1.6)

10.7

1.0

1.8 (0.2)

S1

15.6 (1.9)

13.0

− 3.4

− 3.1 (− 0.4)

\(\hat{\mu } = 30\) pips

RN1

19.5 (2.4)

17.5

3.6

4.6 (0.6)

RA0.5

18.6 (2.3)

16.4

1.4

2.6 (0.3)

S1

21.7 (2.7)

18.8

− 3.4

− 3.1 (− 0.4)

\(\hat{\sigma } = 0\) pips

RN1

7.3 (0.9)

7.0

3.4

4.4 (0.5)

RA0.5

6.3 (0.8)

5.8

0.8

1.5 (0.2)

S1

9.4 (1.2)

8.2

− 3.3

− 3.1 (− 0.4)

Base case \(\hat{\sigma } = 12\) pips

RN1

8.4 (1.0)

7.6

2.2

2.9 (0.4)

RA0.5

6.7 (0.9)

5.8

0.2

0.4 (0.0)

S1

9.7 (1.2)

7.7

− 3.1

− 2.9 (− 0.4)

\(\hat{\sigma } = 25\) pips

RN1

7.0 (0.9)

4.8

5.3

7.5 (0.9)

RA0.5

0.5 (0.1)

0.0

1.7

4.4 (0.5)

S1

10.9 (1.4)

8.3

− 3.4

− 3.1 (− 0.4)

\(\hat{\sigma } = 50\) pips

RN1

6.8 (0.9)

3.2

20.3

25.1 (3.1)

RA0.5

0.4 (0.0)

0.0

8.5

15.9 (2.0)

S1

15.5 (1.9)

12.8

− 3.4

− 3.1 (− 0.4)

  1. The numbers in parenthesis are the profits divided by \(S_{0} = 800\). Recall that the base case has the following values: \(\left( {\sigma /\sqrt {2\kappa } ,\;\hat{\mu },\;\hat{\sigma }} \right)\) = (0.31%, 10 pips, 12 pips)
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