Since no-arbitrage tests only use the observed daily market prices, these tests can be considered tests of the weak form of market efficiency (Capelle-Blancard and Chaudhury, 2001). The purpose of the study is formulated as follows: to examine the cross-market efficiency of option-futures markets and the intra-market efficiency of options markets on the Warsaw Stock Exchange. A clear picture of the efficiency of the WSE derivatives market is important for the understanding of the entire WSE financial market.
The implications of the research for the Warsaw Stock Exchange may seem vague at first glance. The outcome of the empirical research that was carried out is drawn in the last section of the chapter.
MARKET EFFICIENCY AND APPROACHES TO EFFICIENCY
- M ARKET EFFICIENCY
- D ERIVATIVE SECURITIES IN FINANCIAL MARKETS
- M ODEL - BASED APPROACHES TO TESTING MARKET EFFICIENCY
- M ODEL - FREE APPROACHES TO TESTING MARKET EFFICIENCY
- Put-call-parity
- Put-call-futures parity
- Box spread
- R EVIEW OF EMPIRICAL RESEARCH IN DEVELOPED AND DEVELOPING COUNTRIES 16
So for the sake of a realistic review of the model, transaction costs must be taken into account. In this regard, futures contracts add liquidity to the spot market of the underlying instrument. Vipul (2008) studies put-call parity and put-call-future parity of the Indian Nifty index and finds that parity is frequently violated.
The main model-based approach is the Black-Scholes model, which can be complex to implement in practice, as described in the relevant section of the chapter. Further research is based on relevant existing empirical research in this area, which is extensively covered in the Literature Review section of the article.
DATA DESCRIPTION AND EMPIRICAL RESEARCH RESULTS
W ARSAW S TOCK E XCHANGE , DERIVATIVES AND WIG20 INDEX
The WIG20 index was calculated for the first time on 16 April 1994 by the Warsaw Stock Exchange and has been calculated ever since. It is composed of the 20 largest and most liquid companies traded on the floor of WSE. Considering only 20 blue-chip companies for index calculation is not a common practice worldwide, but the traded volume of these stocks accounts for 80% of the total stock market trading volume, as stated in Marcinkiewicz (2016, 3).
Graph 3 below also shows that the majority of derivatives traded on the WSE are index derivatives. WIG20 futures were the first derivatives introduced on the WSE (in 1998) and are also one of the most traded derivatives on the WSE.
D ATA COLLECTION
- Contract specification
- Data collection procedure, market conventions
The three-month maturity also corresponds to the maturity of the futures contracts, since the nearest WIG20 futures contract is used in the model as the most liquid and they are quarterly. It is also important to mention that the index calculation is designed in such a way that it does not account for dividends. Therefore, the dividend yield must be combined with the risk-free rate in order to compensate for this.
The sample reveals multiple violations of the put-call-future parity and the box spread conditions (assuming a frictionless market initially). Namely, without adding transaction costs to the equations, it is found that in 100% of the put-call-future parity triples the equation does not hold, so they are all mispriced. For the box spread, the same trend exists: 100% of put and call option pairs are mispriced.
Nevertheless, investors must encounter transaction costs in order to trade, so it would be incomplete to try to assess the space for arbitrage without considering the transaction costs. The next section sheds some light on transaction costs that investors encounter when trading on the WSE floor.
T RANSACTION COSTS
The study assumes the same cost of funds for all market participants, in line with Wang et al (2018) and others. Białkowski and Jakubowski propose a setup fee of 0.9% of the transaction value for retail investors on the WSE derivatives market. Therefore, a charge of 0.9% is additionally added to indirect trading costs and transfer costs to arrive at the total transaction costs for retail investors.
Carrying costs are essentially the opportunity cost of the capital allocated for contract provision to maintain the position. This includes the initial margin (applicable to short option positions and retail long-term futures positions, because according to WSE rules, WSE members pass the margin to their clients themselves, and do not provide a margin for real estate trading futures). The carrying cost is determined by the following three factors: the initial margin, the opportunity cost of capital (which is assumed to be the risk-free rate of return for the period to maturity) and transaction value.
The initial margin on short option positions in WSE is determined by KDPW_CCP, a central clearinghouse for trades in Poland. According to the KDPW_CCP calculator, the initial margin on short option positions is equal to 100% of the option value. These fees are calculated based on the value of the futures contract and the respective period until maturity of the funds (which, as mentioned above, is assumed to be the same annual interest rate for all market participants).
Nevertheless, indirect costs must be accounted for, as it is crucial to include all possible costs in the investigation of arbitrage in a market. It is important to note that the main concern of the research in this paper is not the exact amount of arbitrage profits, but the general efficiency of derivatives markets. Thus, the formula in (9) is used for the calculation of indirect trade costs and is further incorporated into the total setup costs.
R EALISTIC REVISION OF EQUATIONS
Since the research is based on daily closing data, which does not include bid/ask spreads, indirect trading costs cannot be directly calculated. Different option strike prices will most likely imply different bid/ask spreads, consistent with their liquidity. Ackert and Tian (2001) suggest assuming a 'common cut' of prices and using it to derive bid and ask prices from daily closing prices.
Therefore, in accordance with this logic, in this paper the 'ordinary spread' is calculated based on the current bid and ask prices of futures and options that are currently traded on the WSE. In the absence of other reliable sources of information, this would be the best approximation to adopt. This figure must be adjusted for dividend tax, which is equal to 19% in Poland.
A relevant comment would be to note that the dividend yield effect is somewhat marginal for arbitrage calculations. The contracts that we examine in this paper regarding arbitrage opportunities are mostly considered in a time horizon of up to 3 months (as the most liquid), so the effect of the discount rate is almost zero compared to the transaction costs. Nevertheless, it is important to include the dividend yield in the formulas due to the comprehensiveness of the factors in the research.
D ATA ANALYSIS AND HYPOTHESES TESTING
- Hypothesis 1
- Hypothesis 2
- Hypothesis 3
- Hypothesis 4
- Hypothesis 5
- Hypothesis 6
- Hypothesis 7
The descriptive statistics for put-call futures parity retail investor arbitrage profits are presented below in Table 2. The descriptive statistics for box spread member investor arbitrage profits are presented below in Table 3. The descriptive statistics for box spread small investors arbitrage profits are presented below in Table 4.
The average profits of short arbitrages and long arbitrages in put-call-futures parity are the same. The average profit from short arbitrage and long arbitrage in put-buy-futures parity is significantly different. 6 Do member investors' arbitrage profits under box spreads differ significantly by time to maturity.
7 Do the arbitrage profits of member investors differ significantly when accounted for in the money of the option. Descriptive statistics of arbitrage profits in the short arbitrage subsample are presented below in Table 6. Descriptive statistics of arbitrage profits in the long arbitrage subsample are presented below in Table 7.
The average member box spread arbitrage profits do not differ significantly for contracts with a maturity of up to 10 days (group 2) and for contracts with a maturity of more than 10 days (group 1). The summary of a Kruskal-Wallis test performed in Stata on contract subsamples of member box spread arbitrage winnings is shown in Figure 6 below. This means that there is a statistically significant difference in the average box spread arbitrage profits for contracts with different maturities.
The average membership box arbitrage profits do not differ significantly for at-the-money (ATM) and for in- or out-of-the-money (non-ATM) contracts. This means that there is a statistically significant difference in the average box spread arbitrage profits for different money contracts.
C OROLLARY
As already mentioned in the paper, the study of arbitrage opportunities in a given market is feasible and realistic only in the context of transaction costs. The results of the study are compared with other studies on the efficiency of derivatives markets in Poland and other emerging markets in Table 12 below. Later in the paper, we examine the significance of the difference in the average of short and long arbitrage strategies in put-call-futures parity and find that long futures arbitrage has different average arbitrage profits than short futures arbitrage.
The significance of the difference in average arbitrage profits for contracts with different maturities within box-spread strategies is tested. The paper covered a theoretical framework for research in the field of market efficiency and arbitrage opportunities. The form of market efficiency further tested in the article corresponds to the weak form of market efficiency.
As we go further, we found that there is a statistically significant difference in the mean of different arbitrage strategies within put-call-futures parity. This result may seem interesting given the fact that a general level of indirect transaction costs is assumed in the research, and contracts with longer durations usually show a higher level of indirect transaction costs, because they are less liquid (nearby contracts are the most traded contracts ). ). Incorporating an even higher level of indirect transaction costs for contracts with longer maturities would imply an even further reduction in the room for arbitrage in these contracts.
It is now relevant to consider how the results of the study are useful to the stakeholders mentioned in the introduction. For example, according to Marcinkiewicz (2016), the lifting of the short-selling restriction on the Warsaw Stock Exchange led to an increase in the efficiency of the respective WIG20 futures markets. Determinants of violations in SET50 index option price relationships, put-call futures parity, and box spread tests.
