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The temporal relationship between the equities market and
the derivatives market segments of the stock market has
been studied using various methods and by identifying lead-lag
relationship between the value of a representative index
of the equities market and the price of a corresponding
index futures contract in the derivatives market. It has
been generally observed that price innovations appear first
in the derivatives market and are then transmitted to the
equities market. In this paper, the dynamics of such information
transport between stock market and derivatives market are
studied using the information theoretic concept of entropy,
which captures non-linear dynamic relationship also.
Interactions between different sub-systems of financial
market are considered to be an important internal force
of the market. Deciphering the role played by highly correlated
product lines is an important question faced particularly
in the stock market. The identification and quantification
of causal relationships between the equities and the derivatives
segments of the stock market, by analyzing the prices over
time of an equities market index and a futures contract
on the index, furthers the understanding of the market's
internal dynamics and has a lot of implications for all
the participants of the market.
Since we have a set of simultaneously recorded variablesindex
futures price and stock index value - over a period of time,
it is required to measure to what extent the time series
corresponding to such variables contribute to the generation
of information and at what rate they exchange information.
Various methods have been proposed for the simultaneous
analysis of two series, and generally, cross-correlation
and cross-spectrum are used for measuring relationships
between such time series.Introducing time delay in the observations pertaining to
one market segment may facilitate identifying asymmetric
relationship and hence, direction of information flow, however,
non-linear relationships will still remain unexplored.
Garbade and Silber (1983) have presented an analytical
model of simultaneous price dynamics which suggests that
over short intervals, the correlation of price changes is
a function of the elasticity of arbitrage between an asset
in spot market and its counterpart futures contract. Granger
(1969 and 1991) has introduced an error correction model
which takes into account non-stationarity of cointegrated
variables and distinguishes between short run deviations
from equilibrium indicative of price discovery and long
run deviations which account for efficiency and stability.
These approaches involve estimation of simultaneous linear
equations in a pair of variables with time lags and have
been used in a number of studies examining the source of
price discovery. In the Indian context, Raju and Karande
(2003), applying error correction model to daily closing
values of the stock index Nifty and futures contract on
Nifty in National Stock Exchange (NSE) of India over the
period June 2000-October 2002, have concluded that information
gets reflected first in the futures market segment.
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