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

Reus, Lorenzo; Sepúlveda-Hurtado, Guillermo Alexander

doi:10.1186/s40854-022-00433-7

Financial Innovation

Table 9 (Up): Sensitivity analysis of the long-term volatility \(\sigma /\sqrt {2\kappa }\) in the mean reverting intraday price process for USDCLP

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

Case	Policy	Mean	Median	\(VaR_{99\% }\)	\(CVaR_{99\% }\)
\(\sigma /\sqrt {2\kappa } = 0.1\%\)	RN₁	795.4 (− 0.6)	798.9	801.8	804.9 (0.6)
	RA_0.7	795.8 (− 0.5)	799.2	801.7	802.5 (0.3)
	B1	794.9 (− 0.6)	798.5	800.0	800.0 (0.0)
	B2	798.9 (− 0.1)	799.6	808.8	810.0 (1.3)
	NH	796.5 (− 0.4)	798.6	818.5	820.8 (2.6)
Base Case \(\sigma /\sqrt {2\kappa } = 0.31\%\)	RN₁	795.3 (− 0.6)	797.1	805.0	806.1 (0.8)
	RA_0.7	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)
\(\sigma /\sqrt {2\kappa } = 0.5\%\)	RN₁	795.1 (− 0.6)	795.9	807.9	809.2 (1.1)
	RA_0.7	798.4 (− 0.2)	798.4	803.7	806.0 (0.7)
	B1	793.0 (− 0.9)	794.3	800.0	800.0 (0.0)
	B2	798.9 (− 0.1)	799.0	809.8	811.2 (1.4)
	NH	796.5 (− 0.4)	796.8	819.6	822.0 (2.8)
\(\sigma /\sqrt {2\kappa } = 1.0\%\)	RN₁	794.6 (− 0.7)	793.4	815.8	819.1 (2.4)
	RA_0.7	797.9 (− 0.3)	796.9	809.3	815.3 (1.9)
	B1	790.5 (− 1.2)	791.1	800.0	800.0 (0.0)
	B2	798.9 (− 0.1)	798.9	813.2	814.9 (1.9)
	NH	796.5 (− 0.4)	796.0	823.0	825.6 (3.2)
\(\hat{\mu } = 0\) pips	RN₁	799.6 (0.0)	799.0	806.4	807.8 (1.0)
	RA_0.7	800.0 (0.0)	800.0	800.2	800.3 (0.0)
	B1	797.1 (− 0.4)	797.2	800.0	800.0 (0.0)
	B2	800.0 (0.0)	800.0	804.8	805.6 (0.7)
	NH	799.6 (0.0)	799.6	808.4	809.8 (1.2)
Base case \(\hat{\mu } = 10\) pips	RN₁	795.3 (− 0.6)	797.1	805.0	806.1 (0.8)
	RA_0.7	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)
\(\hat{\mu } = 20\) pips	RN₁	790.7 (− 1.2)	796.5	804.9	805.8 (0.7)
	RA_0.7	791.9 (− 1.0)	797.7	804.7	805.8 (0.7)
	B1	789.4 (− 1.3)	795.4	800.0	800.0 (0.0)
	B2	797.8 (− 0.3)	798.9	816.1	817.8 (2.2)
	NH	793.5 (− 0.8)	796.5	833.9	836.8 (4.6)
\(\hat{\mu } = 30\) pips	RN₁	786.2 (− 1.7)	796.2	804.8	805.8 (0.7)
	RA_0.7	786.8 (− 1.6)	797.1	805.1	805.9 (0.7)
	B1	784.9 (− 1.9)	795.0	800.0	800.0 (0.0)
	B2	796.7 (− 0.4)	798.7	823.5	825.5 (3.2)
	NH	790.6 (− 1.2)	796.2	850.0	853.0 (6.6)

(Down): Sensitivity analysis of \(\hat{\mu }\) in the GBM intraday price process for the USDCLP. The rest of the parameters are kept unchanged and we set \(\left( {\pi_{u} , \pi_{d} } \right) = \left( {1.25\% , 3.75\% } \right)\). 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)

Back to article page