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Financial Innovation

Table 4 Estimates of parameters \({\kappa }\) and \(\sigma_{v}\) defining the mean-reverting process in (12) are obtained from daily prices within the period January-2000 to December-2021

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

  

Normal TPU

High TPU

  

Currency

\(S_{0}\)

\({\kappa }\)

\(\sigma\)(%)

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

\({\kappa }\)

\(\sigma\)(%)

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

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

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

USDCLP

800

0.07

0.42

1.12

0.06

0.58

1.67

45

58

USDBRL

5.5

0.09

0.41

0.97

0.07

0.72

1.92

75

44

USDTRY

10

0.08

0.19

0.48

0.09

0.54

1.27

95

46

AUDUSD

0.7

0.09

0.80

1.89

0.07

0.57

1.52

45

50

GBPUSD

1

0.08

0.83

2.08

0.08

0.71

1.78

30

32

EURUSD

1.5

0.1

0.47

1.05

0.1

0.32

0.72

40

26

USDJPY

105

0.09

0.58

1.37

0.1

0.47

1.05

34

9

  1. Normal (high) TPU corresponds to the months below (above) the 75th percentile within the sample, which is at approximately level 47. Estimates of parameters \(\hat{\mu }\) and \(\hat{\sigma }\) defining the GBM process of Eq. (13) are obtained from the sample of monthly currency returns within the period January 2000 to December 2021. We determine the mean and volatility of returns above the 90th and below the 10th percentile of the sample to capture the degree of the trends (drifts). \(S_{0}\) is the spot price to be used at the beginning of every simulation. Estimates are shown on a daily scale. 1 pip = 10.−4
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