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Theoretical studies (Brunnermeier and Pedersen, 2009; Vayanos and Wang, 2013; Foucault et al., 2013) suggest that tight funding conditions impact on market liq- uidity and asset prices as traders become unable to raise funds, and subsequently face forced liquidation of their investments at depressed prices. Option markets are important as they are liquid, facilitate high leverage (Black, 1972; Easley et al., 1998), and because option prices have predictive power for returns (Cremers and Weinbaum, 2010; An et al., 2014). In such markets, we focus on Put-Call parity. This is a no-arbitrage relation, relating the European call and put option prices of the same underlying security with the same strike price and maturity date.

Sharpe et al. (1998) show that arbitrage is the process of earning a positive profit without risk by taking advantage of an asset’s pricing spreads. Wealth could be obtained by arbitrage as no money is required in the beginning. Occasionally, arbitrage opportunities may exist, but they do not last in the long run, because trading will quickly remove any arbitrage opportunity. Moreover, not all arbitrage opportunities have practical value, because trading influences the market. Further- more, trading costs, bid-ask spreads, and illiquidity also tend to quickly remove these chances.

Easley et al. (1998) show that buying a call or selling a put option includes a positive signal about future stock prices in normal time, because investors earn a profit from an increase in the stock price. In contrast, a negative signal about future prices is sent out with selling a call or buying a put option, because there is an expectation of decrease in the price of the underlying stock. Due to the pri- vate information problems, prices are not fully efficient as regards information. Hence, options may contain information about future prices of the underlying as- set. Easley et al. (1998) found that, if investors with private information trade in the option market, the option prices may include information about the underlying assets, which is useful for forecasting future price changes of the underlying as- set. That is, in the short run, if informed investors are present in the markets, the movement of option prices could deviate from the put-call parity and if so, option prices are no longer fully efficient. However, Baltussen et al. (2012) show that the diffusion of information from the option market into the underlying stock market is gradual, because exploitable signals are included in public option market infor- mation.

Furthermore, Cao and Wei (2010) argue that there is a strong relationship be- tween market-wide option liquidity and the underlying stock market’s movements, and information asymmetry is a critical basic driving force of liquidity. Theoret- ically, in the long run, the prices of call and put options will be in line with Put- Call parity because of arbitrage in the stock and option markets, which means that the price of the underlying stock will soon incorporate private information. How- ever, regarding to the limitation of transactions costs, such as the difference in lending and borrowing rates, taxes, and margin requirements, option prices may deviate form put-call parity without an arbitrage opportunity (Cao and Wei, 2010). In particular, Cao and Wei (2010) used Ivy DB’s OptionMetrics data to exam- ine option market liquidity, and they found that there is a relationship between market-wide option liquidity and the underlying stock market’s movements. They

provide evidence of commonality for several liquidity measures, and that the com- monality still exists after controlling for the underlying stock market’s liquidity and volatility. They show that the influence is stronger on liquidity than inventory risk due to information asymmetry, and that market-wide option liquidity corre- lates with the underlying stock market’s movements. In particular, the responds of option liquidity to upward and downward market movements is asymmetrical: calls react more in upward markets, while puts respond more in downward mar- kets.

Bali and Hovakimian (2009) show a significantly positive relationship be- tween the volatility spreads of call-put options and future returns by means of portfolio-level analyses and firm-level cross-sectional regressions. Moreover, they show that significant information flow from individual equity options to the under- lying stock is observed, indicating informed trading in the market by traders with inside information; for options or stocks with higher volatility spreads, this infor- mation spillover is even more significantly stronger. Ofek et al. (2004) examine the put-call parity relation to the restriction of short sales, and show that Put-Call parity violations are asymmetrical in the direction of short sales constraints, and that the influence is associated with the cost and ease of short sales. After consid- ering shorting costs and extreme assumptions of transaction costs, violations do not disappear. Moreover, violations may also be influenced by the option maturity and the stock market’s valuations; this is consistent with the behaviour of over- optimistic stock investors and market segmentation theory in behavioural finance. In addition, Grundy et al. (2012) examined the relationship between bearish option strategies and short sales during the short-sale ban in the USA in the September

2008, and found that there is an option bid-ask spread increase and a decrease of

option volumes for banned stocks compared to unbanned ones. Furthermore, a significant violation of the Put-Call parity boundary is seen during the ban period. Nonetheless, Battalio and Schultz (2006) found almost no evidence of violations of Put-Call parity using intraday options data in the presence of the short restric- tions at the peak of the Internet bubble.

Bali and Hovakimian (2009) found that there is a relationship between the trading volume of options, the future volume, and the underlying stock’s volatil- ity; this suggests that the option’s liquidity is associated with the stock market’s liquidity and risk. Using the difference in implied volatility of paired call and put options for same underlying assets as a measure of the violations of the put-call parity, Cremers and Weinbaum (2010) show that stocks with relatively expensive

calls are more profitable than stocks with relatively expensive puts. Specifically, high call-put volatility of stocks suggests more trading activities in the future, re- sulting in an increase of the liquidity of the stock. Hence, the spreads of the call and put implied volatilities could be used to forecast the drying up of market liq- uidity. Cremers and Weinbaum (2010) provide evidence that there is a strong re- lationship between deviations in the option price relative to Put-Call parity and the expected underlying stock returns. In addition, they obtained a smaller sam- ple with rebate rates, a measure of the ease of short-selling in the equity lending market, and found that short-sales restrictions do not drive the deviations. Further- more, this predictability reflects informed trading that first occurs in the options market, as suggested with by findings of Bali and Hovakimian (2009). The degree of predictability decreases in the long run.

However, Doran et al. (2013) found no significant relationship between the spreads of the implied volatility and the expected returns for at-the-money call options or put options. Using unique data on option volumes, they found that com- plicated company investors’ option demand contributes to positive equity return predictability, while individual investors’ demand drives negative call option re- turn predictability. That is, the spreads of the implied volatilities carry information about both company fundamentals and option mispricing. What is more, using in-

traday data on39liquid American stocks and their corresponding options and con-

centrating on events when the two markets do not move together, Muravyev et al. (2013) found that the option prices do not carry extra economically significant in- formation about expected stock returns beyond the information already reflected in the current prices of the underlying stocks.

An et al. (2014) argue that if there had been a large increase of call implied volatilities in the previous month, the underlying stock will earn high expected re- turns; in contrast, if a large increase of put implied volatility was observed in the prior month, the underlying asset will have low expected returns. However, Cre- mers and Weinbaum (2010) show that if the distribution of the underlying asset is skewed, which means that the call and put implied volatilities’ deviations are noisy proxies of pressure, the deviations might not be zero. However, with regards to the relation between skewness and expected returns, different studies have dif- ferent conclusions. For example, Xing et al. (2010) and Cremers and Weinbaum (2010) show that skewness is positively correlated with future returns, while Bali et al. (2011) and Conrad et al. (2013) found that there is a negative relationship be- tween skewness and expected returns. Bali and Murray (2013) constructed skew-

ness assets with a long option, a short option, and a long position of the underlying stock, and they found a strong negative relationship between risk-neutral skewness and the skewness of asset returns. The relationship holds after controlling for the market, size, book-to-market ratios, momentum, short-term reversal, spreads of the put-call implied volatility, and other option market factors.