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期貨未平倉量的資訊內涵及其交易活動之研究
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would be consistent with implication (1) in Hypothesis 1.
We use Model (2) to test implication (2) that the “unexpected” component co-moves
with liquidity measures, particularly the depth measure.
EOI
and
UOI
in equation (2) are,
respectively, expected and unexpected open interest, decomposed from
OI
by the ARIMA
model as described in section 3.1. If
φ
2
, the coefficient of depth, for
DEP
regression is
significantly positive, the evidence would support implication (2) in Hypothesis 1.
Hypothesis 2 generates implications about the relationship between open interest and
spot market volatility. To test the implication (3), we regress the expected open interest
against proxies of spot index volatility in Model (3) and the unexpected open interest against
the spot volatility in Model (4). The regression models are specified as:
(3)
(4)
where
EOI
and
UOI
, respectively, stand for expected and unexpected component of open
interest. For spot market volatility (
σ
t
), we apply measures developed by Parkinson (1980),
Garman and Klass (1980) and Rogers and Satchell (1991), respectively and perform
regression for each volatility measure independently (See footnote 7 for the definition of the
three volatility measures). Both Model (3) and (4) include days to expiration (
TTM
) and day-
of-week dummies (
D
j
) as control variables. The finding of positive and significant
β
3
and
β
4
supports the positive association between open interest and spot market volatility predicted
by implication (3).
Implication (4) stresses that open interest increases with unexpected volatility. To test it,
we perform similar regressions to Model (3) and (4) but separate the spot volatility into
expected volatility and unexpected volatility.
(5)
(6)