Ex-ante Test of Lower Boundary Condition and Market Efficiency: Evidence from Indian Index Options Market


The study examines the efficiency of the Indian options market by ex-ante test of the lower boundary conditions on S&P CNX Nifty index options traded on National Stock Exchange (NSE), India, using spot and futures prices. The data consists of daily closing prices of S&P CNX Nifty index options contracts fromApril 01, 2008 to March 31, 2012.The study reveals a severe fall in the frequency of the violations of boundary conditions when using the ex-ante formulation in comparison to ex-post test results. To analyze the exploitability of such violations, thebehaviour of exante formulated violations are examined with respect to liquidity,maturity and moneyness. The magnitudes of violation are further examined fromthe perspective of retail and institutional investors by incorporating the differential transaction cost.From the results, it can be suggested that the Indian options market during the period of study was sufficiently efficient as majority of violations are un-exploitable.


Index options have emerged as a popular instrument in terms of managing risk and as an exciting investment avenue, since their introduction on the Chicago Board Options Exchange (CBOE) in 1983.In June 2000, National Stock Exchange (NSE) and Bombay Stock Exchange (BSE) commenced trading in index futures followed by index options in June 2001. However, Indianfinancial markets took long to realize the importance of index derivatives. The volume of trade (55,366,038 number of index options contracts traded in 2007-08) was very low for several years since its inception. But in April 2008, the scenario changed completely and the volume of trade increased exponentially (212,088,444 number of index options contracts traded in 2008-09). With the increasing volume in the Indian options market and major trading in the derivatives market using index options, it is imperative to see that the options market should function efficiently. Well-functioning financial markets are critical to a booming economy because financial markets facilitate price discovery, risk hedging and allocating capital to its most productive uses (Ackert and Titan, 2000).Market efficiency implies that economic profits from trading are zero, where economic profits are risk-adjusted returns net of all costs(Jensen, 1978). This means the inability of any trader to consistently generate an above-normal average rate of return.

One of the strategies to test the options market efficiency is to evaluate market prices with the theoretical prices implied by the Black and Scholes (1973) model. If any mispricing is observed, a riskless profit can be generated by dynamic hedging approach which consists of creating risk-neutral hedge positions i.e. buy (sell) one option and sell (buy) a fraction of the underlying stock. But, a major disadvantage of this strategy is that it engages a joint test of two hypotheses, namely, (i) the Black and Scholes pricing model is valid and (ii) the options market is efficient. As an alternative to the dynamic hedging strategy using the Black and Scholes model, one of the methods to test the efficiency of the market is to identify risk-free arbitrage opportunities such as “pure arbitrage test” (Jensen, 1978). The pure arbitrage test has an advantage over the model based tests in a way that it only tests the hypothesis that the options market is efficient. Merton (1973) has developed lower boundary conditions for options which must be fulfilled to prevent pure arbitraging. Arbitrages based on lower boundary conditions do not require a dynamic revision of hedge portfolio; rather, positions taken for arbitrage are held till maturity. Galai (1978) stated that the market cannot be inefficient for these weak conditions and at the same time,needs to be efficient for stronger assumptions like model based test. The index options market is relatively new to Indian investors as compared to developed countries; therefore, it is relevant to test the market efficiency with weaker conditions like lower boundary condition which is a pure arbitrage test. The lower boundary condition shows the intrinsic value of the options contract at a point of time. An arbitrage opportunity occurs if the price of the options contract falls below the lower boundary condition. Thus, for the market to be efficient, the lower boundary condition must be satisfied.

Majority of market efficiency studies are based on expost formulation, i.e. on the basis of information at time t; a trading strategy is developed and a position is set up on the same prices. Generally, traders are unable to execute the trade at the prices viewed at the time of the violations. Therefore, these violations are considered as signals to develop the trading strategies.

However, there is no assurance that the prices used in the trading strategy will be the same as the prices in the observed violations. Thus, the supernormal profits for the ex-post test might specify that either markets are inefficient or markets are non-synchronous. Galai (1978) argued that market efficiency tests should be conducted on ex-ante basis, i.e.on the basis of information at time t;a trading strategy is developed, but the position is set up at time (t + 1) at prices that are unidentified at time t. The reason behind his argument isthat ex-post tests do not mention a trading strategy which an arbitrageur can duplicate. In this paper, the efficiency of the options market is examined by exante test of the lower boundary conditions of both call and put options on S&P CNX Nifty index options traded on National Stock Exchange (NSE), India using spot and futures prices. Thus, the nature of the present study is ex-ante, as a trading strategy has been devised to show the exploitability of mispricing signals (Trippi, 1977and Chiras and Manaster, 1978).Further in this study, a comprehensive analysis of violations is done by incorporating transaction costs incurred during execution of the trading strategy.

The research paper is organized as follows. In section II, the literature and the concept related to lower boundary conditions have been discussed. In section III, the objectives of the study have been presented. Section IV follows the description of the data and transaction costs considered for the analysis. In sections V and VI, the procedure to test the market efficiency using the lower boundary condition and data analysis with empirical evidence is documented respectively. Lastly in section VII, some concluding observationsof the study have been presented.

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