Равновесное соотношение между деривативами на индекс

Efficient markets are vital for capital allocation, price discovery and risk management. Growth of financial markets can be determined by the degree of how efficiently they operate (Capelle-Blancard, Chaudhury, 2001). Derivatives market efficiency, in turn, to a big extent affects the general financial market efficiency, because derivatives provide liquidity and information to spot markets in terms of what the market anticipates towards these or those assets, also allowing for risk management and hedging. If derivatives market does not operate efficiently, risk management strategies may be hindered.
Efficient market hypothesis (EMH), coined by Fama (1970), states that in an efficient market prices fully reflect all available information. Available information that the author refers to depends upon the form of market efficiency. E.g., in the weak form of market efficiency past trading information of securities is reflected in market prices. There are three forms of market efficiency in total, which are discussed in more detail later in the paper. An efficient market can also be referred to as one where a single investor is not able to make substantially larger profits without having to bear additional risk. Therefore, arbitrage opportunities must be rare, insignificant and quickly eliminated in an efficient market.
The basis for no-arbitrage conditions is that investment strategies with the same future cashflows should be priced the same. In other words, there is no ‘free lunch’ in an efficient market. Investors prefer more to less, and take advantage of any riskless profits earning opportunity. Since no-arbitrage tests use only the observed daily market prices, these tests can be considered as tests of the weak form of market efficiency (Capelle-Blancard and Chaudhury, 2001).
Two distinct directions concerning the option market efficiency can be observed in the academic literature. The first approach is the model-based approach (Black-Scholes, Binomial, other models), which involves deriving a theoretical price of the option and then comparing it with the observed market price, thus calculating the mispricing, which is checked for statistical significance. The problem with this approach is that it tests two hypotheses simultaneously: first, that the model is valid itself, and second, that the market is efficient, while the test is unable to distinguish between the two (Galai, 1977). The second approach tests cross-market efficiency between spot and option prices (put-call parity) and internal market efficiency (box spread, etc.). The second approach is less restrictive in that it is not based upon assumptions about the normal distribution of the price of the underlying and estimation of its volatility (Bhat & Arekar, 2015). That is why the model-free approach is selected in this paper.
One framework for research in this field is provided by Stoll (1969), who was the first in the academic literature to describe the principle of put-call parity. His approach was later generalized and extended to employ futures prices instead of spot prices (Tucker, 1991). The main
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specificity of put-call parity and of put-call-futures parity concepts is that they can be utilized for European-type options only. It is shown in the academic literature that the discrepancies in the pricing of American-type options (i.e., situations when the put-call parity (PCP) does not hold) can be explained by the additional value of early exercise opportunity (Zivney, 1991). The general model has an obvious limitation in that it exists in a frictionless world, that is, no transaction costs are considered. So, for the sake of a realistic revision of the model, transaction costs have to be added into consideration.
According to the efficient market hypothesis, an efficient market is an equilibrium market. It is a market, where an agent is unable to make a riskless profit on the basis of the available information. If the market deviates from the equilibrium, and arbitrage opportunity appears, and the investors immediately take advantage of this discrepancy by buying low and selling high, thus obtaining a risk-free profit. Therefore, an equilibrium relationship between put and call options for the same underlying asset should be reflected in an efficient market. If numerous significant arbitrage opportunities appear (that are not explained away by the level of transaction costs) and so riskless profits can be made, then it can be concluded that there is no equilibrium relationship, and the derivatives’ market efficiency has to be increased. It is important from investor’s point of view, because an inefficient market exposes an investor to non-diversifiable risks. The practical implementation of an existing inefficiency in a market is in two main areas: first, economic agents can make riskless profits in such inefficient market. This is beneficial for economic agents like brokerage houses, investment banks and other investors, such as, for example, retail investors (even though they usually encounter higher levels of transaction costs), because they all can make profits without bearing additional risk. Second, a clear signal to increase market efficiency appears. This is useful for the agent that organizes trading of securities (stock exchange), who is signaled to increase market efficiency. As shown in Chen, Chin and Chung (2020), arbitrageurs may also decrease liquidity in the markets. In addition, as mentioned above, most investors are in search of effective markets, where risks can be effectively diversified or hedged. Therefore, the stock exchange is better off in case it manages to attract more investors with an efficient market.
In this paper, market efficiency in derivatives markets is examined. A great deal of attention is given to the analysis of transaction costs. More precisely, options’ market intra-market efficiency and cross-market efficiency between options and futures markets are researched. A specific type of derivatives is chosen: index derivatives. This type of derivatives is, essentially, one of the most liquid derivatives in any financial market, together with forex (currency) derivatives. Index derivatives let investors track the performance of the broad market with lower transaction costs. Investors do not need to construct a basket of shares that constitute an index, instead they may purchase an index futures security. May an investor need to hedge against the
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performance of the market, she can purchase index options, which oftentimes have even lower trading costs than futures. Derivatives also add liquidity into the markets, because investors obtain an additional source of information about market prices, as well as market expectations about the future movement of these prices.
The issue of derivatives markets’ efficiency has been given a lot of attention in the academic literature. Nevertheless, young and emerging derivatives markets lack coverage in this regard. In particular, to the best knowledge of the author, little to no academic literature addresses the options market equilibrium relationship and the put-call-futures parity in Warsaw Stock Exchange, while WSE is considered to be the largest stock exchange in Central and Eastern Europe. It is believed to be the leading exchange in Central and Eastern Europe in terms of liquidity, and it also attracts a substantial quantity of retail investors, being at the same time the leader in derivatives trading (Vozianov, 2015). In addition, one of the most liquid and demanded derivatives in WSE, together with forex derivatives, are index derivatives. These securities’ popularity is based upon the fact that they allow to track and bet on the performance of the broad market with relatively low transaction cost. Instead of buying a basket of shares’ derivatives, one can bet on or against the market, or even structure sophisticated trading strategies with up to three securities: index put and call options and futures.
The aim of the research is articulated as follows: to research the cross-market efficiency of options-futures markets and intra-market efficiency of options markets in Warsaw Stock Exchange. The criterion of market efficiency is the existence of arbitrage opportunities. A clear picture of the efficiency of the WSE derivatives market is important in the understanding of the whole WSE financial market.
The paper aims to accomplish the following goals:
1) Provide an overview of academic literature in the field of market efficiency, derivative
securities and their role in financial markets, as well as cover the existing empirical
research in the field in developed and developing countries.
2) Summarize the existing approaches to options intra-market and options/futures cross-
market efficiency, outline the pros and cons of these approaches, choose and advocate
the methodology for further research.
3) Implement the chosen methodology to the data collected from WSE, and to
differentiate the results according to investor type, time to maturity and trader strategy, as well as option moneyness, from the standpoint of market efficiency and arbitrage profits.
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4) Draw conclusions on top of the conducted empirical research and give recommendations for agents that trade in derivatives markets of WSE, as well as for WSE.
The object of the research is options and futures with WIG20 index as the underlying asset. The time period covered in the research is from December 2017 till December 2019. This yields a full two-year sample of daily closing prices, which is in coherence with Ackert and Tian (2001), as well as Zhang and Watada (2019). Because the author aims to avoid the unfavorable effect of the global market turmoil starting in early 2020, data after December 2019 is not included in the collection. Data is cross-sectional, collected from the official website of Warsaw Stock Exchange. For the means of the research, the following databases are employed: JSTOR, EBSCO, Scopus, Science Direct and others. Microsoft Excel and Stata were used to conduct the calculations on the basis of the gathered data and to further conduct the statistical tests of hypotheses.
The results of the research are to be beneficial for two groups of stakeholders: derivative instruments traders in WSE and the WSE itself. The managerial implementation of research findings for traders is somewhat straightforward: if the markets are proven inefficient, then economic agents can make profits without having to bear any additional risks (execute arbitrage transactions, in other words). Among the users of such information may be investment banks, mutual funds and other agents.
The implications of the research for Warsaw Stock Exchange may seem vague at first sight. Let us elaborate on that shortly. If the markets are proven inefficient, WSE obtains a clear signal to increase market efficiency. The reasons for increasing it are clear: inefficient markets may spook away investors, because if the market does not reflect the available information in market prices, then investors are exposed to additional, non-diversifiable risks. The exchange may therefore try to increase the efficiency of the market in numerous ways, such as increasing the transparency of market data, changing the regulations regime, etc.
The paper is organized as follows: the first chapter provides a review of existing academic research in the field of derivatives markets efficiency. It sets the conceptual field for further research. The concept of market efficiency is given more detail. In the first chapter the role of derivative securities in financial markets is discussed. The chapter covers main approaches to examining market efficiency in derivatives markets. Those are divided from the standpoints of model-based approaches and model-free approaches. It also provides a review of existing empirical research in developing and developed countries.
The second chapter is devoted to conducting empirical research: data collection and description of data, methodology of research, hypotheses testing procedure and its results are described. The context of the research is discussed, as well as Warsaw Stock Exchange is
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characterized in terms of its brief history and current state of affairs in the derivatives markets. We look deeper into the details of contracts traded on the floor WSE. Financial calculations are described, and the approaches covered in the first chapter are supplemented with a realistic revision. Hypotheses of the research are stated and tested with the use of relevant statistic tests. The corollary to the conducted empiric research is drawn in the final section of the chapter. The second chapter is followed by the conclusion to the whole paper.