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

Financial Innovation

Table 5 P&L of CTP solutions (RN and RA) versus benchmark policy S1

Currency	Policy	Mean	Median	\(VaR_{1\% }\)	\(CVaR_{1\% }\)
USDCLP \(S_{0} = 800.0\)	RN₁	30.0 (3.7)	27.1	13.5	16.4 (2.1)
	RA_0.75	27.6 (3.5)	22.3	11.6	15.4 (1.9)
	S1	25.6 (3.2)	24.4	− 11.5	− 11.1 (− 1.4)
USDBRL \(S_{0} = 5.5\)	RN₁	0.3298 (6.0)	0.2746	0.0739	0.0920 (1.7)
	RA_0.75	0.3143 (5.7)	0.2541	0.0686	0.0907 (1.6)
	S1	0.1992 (3.6)	0.1695	− 0.0808	− 0.0774 (− 1.4)
USDTRY \(S_{0} = 10.0\)	RN₁	0.7087 (7.1)	0.5760	0.0690	0.0852 (0.9)
	RA_0.75	0.6949 (6.9)	0.5614	0.0659	0.0875 (0.9)
	S1	0.2718 (2.7)	0.1498	− 0.0674	− 0.0648 (− 0.6)
AUDUSD \(S_{0} = 0.7\)	RN₁	0.0254 (3.6)	0.0253	0.0196	0.0246 (3.5)
	RA_0.75	0.0219 (3.1)	0.0201	0.0175	0.0226 (3.2)
	S1	0.0372 (5.3)	0.0363	− 0.0184	− 0.0177 (− 2.5)
GBPUSD \(S_{0} = 1.0\)	RN₁	0.0320 (3.2)	0.0337	0.0350	0.0440 (4.4)
	RA_0.75	0.0279 (2.8)	0.0276	0.0279	0.0368 (3.7)
	S1	0.0536 (5.4)	0.0521	− 0.0242	− 0.0220 (− 2.2)
EURUSD \(S_{0} = 1.5\)	RN₁	0.0544 (3.6)	0.0517	0.0221	0.0287 (1.9)
	RA_0.75	0.0500 (3.3)	0.0429	0.0198	0.0270 (1.8)
	S1	0.0505 (3.4)	0.0495	− 0.0251	− 0.0240 (− 1.6)
USDJPY \(S_{0} = 105.0\)	RN₁	4.3 (4.1)	4.3	2.1	2.6 (2.5)
	RA_0.75	3.9 (3.7)	3.5	1.9	2.4 (2.3)
	S1	4.3 (4.1)	4.3	− 2.2	− 2.1 (− 2.0)

The numbers in parenthesis are the P&L divided by \(S_{0}\), that is, the P&L in terms of the foreign currency (US dollar cents for USDCLP, USDBRL, USDTRY, USDJPY, pennies for GBPUSD, euro cents for EURUSD, Australian dollar cents for AUDUSD). We set \(\pi_{u} = \pi_{d} = 2.5\%\) and D = L = 1