Stock price synchronicity and liquidity

We argue and provide evidence that stock price synchronicity affects stock liquidity. Under the relative synchronicity hypothesis, higher return co-movement (i.e., higher systematic volatility relative to total volatility) improves liquidity. Under the absolute synchronicity hypothesis, stocks with higher systematic volatility or beta are more liquid. Our results support both hypotheses. We find all three illiquidity measures (effective proportional bid-ask spread, price impact measure, and Amihud's illiquidity measure) are negatively related to stock return co-movement and systematic volatility. Our analysis also shows that larger industry-wide component in returns improves liquidity. We find that improvement in liquidity following additions to the S&P 500 Index is related to the stock's increase in return co-movement.     

Volume,volatility and information linkages in the stock and option markets

This paper examines the relationship between option trading activity and stock market volatility. Although the option market is uniquely suited for trading on volatility information, there is little analysis on how trading activity in this market is linked to stock price volatility. The bulk of the discussion tends to focus on whether trading activity in the stock market is informative about stock volatility. To analyze the information in option trading activity for stock market volatility, a sample of 15 stocks with the highest option trading volume is selected. For each stock, it is noted that the trading activities in the put and call option markets have significant explanatory power for stock market volatility. In addition, the results indicate that the call option trading activity has a stronger impact on stock volatility compared with that of the put options. Our results demonstrate that information and sentiment in the option market is useful for the estimation of stock market volatility. Also, the significance of the effects of option trading activity on stock price volatility is observed to be comparable to that of stock market trading activity. Furthermore, the persistence and asymmetric effects in the volatility of some stocks tend to disappear once option trading activity is taken into account.     

Option pricing model with sentiment

In this paper, we develop a closed-form option pricing model with the stock sentiment and option sentiment. First, the model shows that the price of call option is amplified by bullish stock sentiment, and is reduced by stock bearish sentiment, and the price of put option is in the opposite situation. Second, the price of call option is more sensitive to bullish stock sentiment; the price of put option is more sensitive to bearish stock sentiment. Third, the price of call option increases substantially with respect to the stock sentiment and the option sentiment. The price of put option decreases substantially with respect to the stock sentiment, increases substantially with respect to the option sentiment. Fourth, our models also reveal that the option volatility smile is steeper (flatter) when the stock sentiment becomes more bearish (bullish). Finally, stock sentiment and option sentiment lead to the option price deviating from the rational price. The model could offer a partial explanation of some option anomalies: option price bubbles and option volatility smile.     

A market-induced mechanism for stock pinning

Abstract

We propose a model to describe stock pinning on option expiration dates. We argue that if the open interest on a particular contract is unusually large, delta-hedging in aggregate by floor market-makers can impact the stock price and drive it to the strike price of the option. We derive a stochastic differential equation for the stock price which has a singular drift that accounts for the price-impact of delta-hedging. According to this model, the stock price has a finite probability of pinning at a strike. We calculate analytically and numerically this probability in terms of the volatility of the stock, the time-to-maturity, the open interest for the option under consideration and a ‘price elasticity’ constant that models price impact.     

The Volatility and Price Sensitivities of Managerial Stock Option Portfolios and Corporate Hedging

We use estimates of the Black–Scholes sensitivity of managers' stock option portfolios to stock return volatility and the sensitivity of managers' stock and stock option portfolios to stock price to test the relationship between managers' risk preferences and hedging activities. We find that as the sensitivity of managers' stock and stock option portfolios to stock price increases, firms tend to hedge more. However, as the sensitivity of managers' stock option portfolios to stock return volatility increases, firms tend to hedge less.     

Binomial option pricing with stochastic parameters: A beta distribution approach

This research extends the binomial option-pricing model of Cox, Ross, and Rubinstein (1979) and Rendleman and Barter (1979) to the case where the up and down percentage changes of stock prices are stochastic. Assuming stochastic parameters in the discrete-time binomial option pricing is analogous to assuming stochastic volatility in the continuous-time option pricing. By assuming that the up and down parameters are independent random variables following beta distributions, we are able to derive a closed-form solution to this stochastic discrete-time option pricing. We also derive an upper and a lower bounds of the option price.     

Stochastic Dominance Bounds on American Option Prices in Markets with Frictions

We derive equilibrium restrictions on the range of the transactionprices of American options on the stock market index and indexfutures. Trading over the lifetime of the options is accountedfor, in contrast to earlier single-period results. The boundson the reservation purchase price of American puts and the reservationwrite price of American calls are tight. We allow the marketto be incomplete and imperfect due to the presence of proportionaltransaction costs in trading the underlying security and dueto bid-ask spreads in option prices. The bounds may be derivedfor any given probability distribution of the return of theunderlying security and admit price jumps and stochastic volatility.We assume that at least some of the traders maximize a time-separable utility function. The bounds are derived by applyingthe weak notion of stochastic dominance and are independentof a trader's particular utility function and initial portfolioposition.     

Illiquidity,return and risk in G7 stock markets: Interdependencies and spillovers

Trading activity in G7 stock markets reflects not only the macroeconomic and financial impact of these G7 economies in international economic growth, but also their financial interdependence. While this nexus of major stock markets has been explored in terms of volatility and return spillovers, there has been no combined analysis of return, volatility and illiquidity spillovers. We study illiquidity spillovers because they are transmissions of trading activity and, thereof, transmissions of information and market sentiment. We find that the dynamics of international stock markets are characterized by persistent illiquidity and also that illiquidity shocks are significantly correlated across markets. Furthermore, we discover Granger causal associations between risk, return and illiquidity across G7 stock market and also within each stock market. Our findings bear significance for the regulation of international financial markets and also for international portfolio diversification.     

Option prices and stock market momentum: evidence from China

Option prices tend to be correlated to past stock market returns due to market imperfections. We unprecedentedly examine this issue on the SSE 50 ETF option in the Chinese derivatives market. To measure the price pressure in the options market, we construct an implied volatility spread based on pairs of the SSE 50 ETF option with identical expiration dates and strike prices. By regressing the implied volatility spread on past stock returns, we find that past stock returns exert a strong influence on the pricing of index options. Specifically, we find that SSE 50 ETF calls are significantly overvalued relative to SSE 50 ETF puts after stock price increases and the reverse is also true after the stock price decreases. Moreover, we validate the momentum effects in the underlying stock market to be responsible for the price pressure. These findings are both economically and statistically significant and have important implications.     

Estimation and pricing under long-memory stochastic volatility

We treat the problem of option pricing under a stochastic volatility model that exhibits long-range dependence. We model the price process as a Geometric Brownian Motion with volatility evolving as a fractional Ornstein–Uhlenbeck process. We assume that the model has long-memory, thus the memory parameter H in the volatility is greater than 0.5. Although the price process evolves in continuous time, the reality is that observations can only be collected in discrete time. Using historical stock price information we adapt an interacting particle stochastic filtering algorithm to estimate the stochastic volatility empirical distribution. In order to deal with the pricing problem we construct a multinomial recombining tree using sampled values of the volatility from the stochastic volatility empirical measure. Moreover, we describe how to estimate the parameters of our model, including the long-memory parameter of the fractional Brownian motion that drives the volatility process using an implied method. Finally, we compute option prices on the S&P 500 index and we compare our estimated prices with the market option prices.     

Does short selling improve stock price efficiency and liquidity? Evidence from a natural experiment in China

China introduced short selling for designated stocks in March 2010. Using this important policy change as a natural experiment, we examine the effect of short selling on stock price efficiency and liquidity. We show that the introduction of short selling significantly improves price efficiency, as measured by the differences in individual stock responses to market returns and the delay in price adjustments. Short selling also enhances stock liquidity, as measured by bid-ask spread and Amihud [2002. ‘Illiquidity and Stock Returns: Cross-section and Time-series Effects.’ Journal of Financial Markets 5: 31–56] illiquidity measure; and reduces stock volatility. Overall, our results suggest that short selling helps to stabilize asset prices, provides additional liquidity and improves market quality, even in an emerging economy with a less developed stock market than that in the US and Europe.     

The Pricing of Options on Assets with Stochastic Volatilities

One option-pricing problem that has hitherto been unsolved is the pricing of a European call on an asset that has a stochastic volatility. This paper examines this problem. The option price is determined in series form for the case in which the stochastic volatility is independent of the stock price. Numerical solutions are also produced for the case in which the volatility is correlated with the stock price. It is found that the Black-Scholes price frequently overprices options and that the degree of overpricing increases with the time to maturity.     

Volatility Information Trading in the Option Market

This paper investigates informed trading on stock volatility in the option market. We construct non-market maker net demand for volatility from the trading volume of individual equity options and find that this demand is informative about the future realized volatility of underlying stocks. We also find that the impact of volatility demand on option prices is positive. More importantly, the price impact increases by 40% as informational asymmetry about stock volatility intensifies in the days leading up to earnings announcements and diminishes to its normal level soon after the volatility uncertainty is resolved.     

Pricing and static hedging of European-style double barrier options under the jump to default extended CEV model

This paper develops two novel methodologies for pricing and hedging European-style barrier option contracts under the jump to default extended constant elasticity of variance (JDCEV) model, namely: a stopping time approach based on the first passage time densities of the underlying asset price process through the barrier levels; and a static hedging portfolio approach in which the barrier option is replicated by a portfolio of plain-vanilla and binary options. In doing so, both valuation methodologies are extended to a more general set-up accommodating endogenous bankruptcy, time-dependent barriers and the commonly observed stylized facts of a positive link between default and equity volatility and of a negative link between volatility and stock price. The two proposed numerical methods are shown to be accurate, easy to implement and efficient under both the JDCEV model and the nested constant elasticity of variance model.     

Implied integrated variance and hedging

If the volatility is stochastic, stock price returns and European option prices depend on the time average of the variance, i.e. the integrated variance, not on the path of the volatility. Applying a Bayesian statistical approach, we compute a forward-looking estimate of this variance, an option-implied integrated variance. Simultaneously, we obtain estimates of the correlation coefficient between stock price and volatility shocks, and of the parameters of the volatility process. Due to the convexity of the Black–Scholes formula with respect to the volatility, pricing and hedging with Black–Scholes-type formulas and the implied volatility often lead to inaccuracies if the volatility is stochastic. Theoretically, this problem can be avoided by using Hull–White-type option pricing and hedging formulas and the integrated variance. We use the implied integrated variance and Hull–White-type formulas to hedge European options and certain volatility derivatives.     

Informed Trading in Stock and Option Markets

We investigate the contribution of option markets to price discovery, using a modification of Hasbrouck's (1995) "information share" approach. Based on five years of stock and options data for 60 firms, we estimate the option market's contribution to price discovery to be about 17% on average. Option market price discovery is related to trading volume and spreads in both markets, and stock volatility. Price discovery across option strike prices is related to leverage, trading volume, and spreads. Our results are consistent with theoretical arguments that informed investors trade in both stock and option markets, suggesting an important informational role for options.     

A tale of idiosyncratic volatility and illiquidity shocks: Their correlation and effects on stock returns

This paper documents that the idiosyncratic volatility shock is not a stand-alone anomaly compared to the illiquidity shock. Our empirical evidence shows that the illiquidity shock Granger-causes idiosyncratic volatility shock and is statistically and economically significant in predicting stock returns. More importantly, it subsumes most of the predictive power of idiosyncratic volatility shock. In addition, we find that it is the illiquidity shock, not idiosyncratic shock, that is significantly affected by earnings surprise and is more consistently related to other information-signaling variables such as changes in analyst dispersion, number of sell-side analyst coverage, and institutional ownership.     

Stock market illiquidity,bargaining power and the cost of borrowing

We show that firms with illiquid stock have higher syndicated loan spreads. This result is invariant to measurement of stock illiquidity, and is robust to a wide set of cross-sectional loan and firm features, firm and time fixed effects. It also holds using a matched difference-in-differences estimator, at an exogenous reduction in the minimum tick size of major United States exchanges, and using a two-stage least squares estimator. Stock illiquidity is shown to increase spreads more when a lead lender has a high market share or a borrower has a low credit rating. It increases spreads less when a borrower has public rated debt and it diminishes the benefit to the loan recipient of a lending relationship. Measurements of stock price informativeness and firm-level governance do not affect the stock illiquidity and loan spread relation. A rationale for these findings is that stock illiquidity impairs the bargaining power of corporate borrowers, in negotiating a loan rate, as it raises the cost of alternatively raising funds by issuing equity.     

Risk sharing in a financial market with endogenous option prices

This article investigates a financial market in which investors may trade in risk-free bonds, stock and put options written on the stock. In each period, stock and option prices are simultaneously determined by market clearing. While the introduction of put options will decrease the systematic risk in the financial market, it will increase the price of risk. Investors with mean-variance preferences will generally hold portfolios containing the primary asset and the put option and may use the option to increase the risk in their wealth position in exchange for higher returns. Aggregate wealth is unaffected by an option market when there are no spillover effects on stock prices, and it is shown that short selling of options will increase the volatility of individual wealth positions. Investors with erroneous beliefs may on average be better off not trading in put options.     

Option Pricing Bounds in Discrete Time

Upper and lower bounds are derived for call options traded at discrete intervals. These bounds are independent of assumptions on the stock price distribution other than a restriction satisfied by the stock being “non-negative beta.” The development of the bounds relies on the single-price law and arbitrage arguments. Both single-period and multiperiod results are produced, and put option bounds follow by extension. The bounds exist as equilibrium values given a consensus on stock price distribution; they are also valid for empirical studies, being adjustable for dividends and commissions.