A Time-Series Approach to Non-Self-Financing Hedging in a Discrete-Time Incomplete Market

Table 1

Algorithmic results for options with 30 days to expiration.

	Resid-min	Resid-max	Shortfall-min	Shortfall-max	PosProb-min	PosProb-max
BAC+CJ30	0.3446	−0.2167	−0.0226	0.71	1.00	0.2446
BAC+CW30	0.3592	−0.0952	−0.0035	0.98	1.00	0.0776
BAC+CX30	0.3253	−0.3301	−0.0865	0.52	0.87	0.1368
BAC+JV30	0.4406	−0.4111	−0.0425	0.74	0.98	0.0301
CYQ+CE30	0.5328	−0.2833	−0.1226	0.60	0.97	0.1280
CYQ+CX30	0.2995	−0.1182	−0.0301	0.83	1.00	−0.0750
CYQ+CY30	1.0162	−0.5349	−0.2480	0.55	0.86	0.1542
GE+CF30	0.1778	−0.0308	−0.0004	1.00	1.00	0.0959
GE+CG30	0.1862	−0.2934	−0.0441	0.60	0.94	0.1482
GE+CY30	0.1776	−0.0073	0.0000	1.00	1.00	0.0799
GE+CZ30	0.1805	−0.0964	−0.0049	0.92	1.00	0.0259
GE+JF30	0.0600	−0.1824	−0.0159	0.35	0.95	0.3118
HNZ+CI30	0.6032	−0.2572	−0.0166	0.95	1.00	0.1243
HNZ+CJ30	0.6220	−0.3183	−0.0442	0.77	1.00	−0.3530
INTC+JE30	0.0502	−0.3145	−0.0344	0.06	0.83	0.0945
MER+CP30	0.3211	−0.2597	−0.0101	0.85	1.00	0.1665
MQF+JX30	0.1921	−0.0504	−0.0020	0.99	1.00	0.4038
MS+CO30	0.7941	−0.4197	−0.0319	0.89	1.00	0.0266
MSQ+CK30	0.5451	−0.2825	−0.0419	0.45	1.00	0.0062
MSQ+CY30	0.1225	−0.0918	−0.0072	0.55	1.00	0.0915
MSQ+JE30	0.1234	−0.1689	−0.0201	0.69	0.98	−0.1216
NQ+CD30	0.1762	−0.3961	−0.0885	0.18	0.93	0.2945
WMT+CH30	0.3740	−0.1248	−0.0019	1.00	1.00	−0.0872
WMT+CJ30	0.0787	−0.3912	−0.0777	0.29	0.84	−0.1892
WMT+JJ30	0.2226	−0.4898	−0.0514	0.54	0.90	0.0058
XOM+CN30	0.5323	−0.5517	−0.0542	0.31	0.98	−0.0748
XOM+CO30	1.2703	−0.9711	−0.1213	0.35	0.89	−0.1373
XOM+JI30	0.1527	−0.2978	−0.0545	0.15	0.93	0.0528
XOM+JV30	0.2231	−0.1508	−0.0117	0.59	1.00	𝐸(Δ𝑛)