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

Financial Innovation

Table 1 Estimates of parameters \({\kappa }\) and \(\sigma_{v}\) defining the mean-reverting process in (12) are obtained from a sample containing 15-min intraday prices from 9 a.m. to 2 p.m. within the period January 2020 to December 2021

Currency	\(S_{0}\)	\({\kappa }\)	\(\sigma : = \sigma_{v} /S_{0}\)	\(\sigma /\sqrt {2{\kappa }}\)	\(\hat{\mu }\)(pips)	\(\hat{\sigma }\)(pips)
USDCLP	800	0.09	0.13%	0.31%	10	12
USDBRL	5.5	0.07	0.21%	0.56%	17	25
USDTRY	10	0.11	0.08%	0.17%	23	75
AUDUSD	0.7	0.06	0.14%	0.40%	13	24
GBPUSD	1	0.07	0.11%	0.29%	9	14
EURUSD	1.5	0.07	0.07%	0.19%	8	6
USDJPY	105	0.09	0.05%	0.12%	10	12

Estimates of parameters \(\hat{\mu }\) and \(\hat{\sigma }\) defining the GBM process of Eq. (13) are obtained from the sample of daily 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