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Table 10 Sensitivity analysis of \(\hat{\sigma }\) in the GBM intraday price process for the USDCLP. The rest of the parameters 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

\(VaR_{99\% }\)

\(CVaR_{99\% }\)

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

RN1

795.2 (− 0.6)

796.9

805.0

805.8 (0.7)

RA0.7

796.8 (− 0.4)

798.1

804.0

805.2 (0.7)

B1

794.0 (− 0.8)

795.9

800.0

800.0 (0.0)

B2

798.9 (− 0.1)

799.1

808.7

808.8 (1.1)

NH

796.5 (− 0.4)

797.1

816.8

816.9 (2.1)

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

RN1

795.3 (− 0.6)

797.1

805.0

806.1 (0.8)

RA0.7

797.9 (− 0.3)

798.9

803.2

804.7 (0.6)

B1

793.9 (− 0.8)

796.0

800.0

800.0 (0.0)

B2

798.9 (− 0.1)

799.2

809.0

810.5 (1.3)

NH

796.5 (− 0.4)

797.3

818.8

821.3 (2.7)

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

RN1

795.3 (− 0.6)

797.6

806.0

807.7 (1.0)

RA0.7

799.7 (0.0)

799.9

800.7

801.2 (0.1)

B1

793.2 (− 0.9)

795.9

800.0

800.0 (0.0)

B2

798.9 (− 0.1)

799.4

811.0

813.4 (1.7)

NH

796.5 (− 0.4)

797.9

824.0

828.3 (3.5)

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

RN1

795.5 (− 0.6)

798.4

818.9

824.0 (3.0)

RA0.7

799.9 (− 0.0)

799.8

802.6

804.7 (0.6)

B1

790.9 (− 1.1)

795.4

800.0

800.0 (0.0)

B2

798.9 (− 0.1)

799.5

815.9

819.9 (2.5)

NH

796.6 (− 0.4)

798.5

835.5

842.8 (5.3)

  1. The numbers in parenthesis are the rates of increase (reduction) (%) relative to \(S_{0} = 800\). 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)