The LIX: A model-independent liquidity index

This paper provides a new model-free indicator of liquidity, the so-called LIX index. The computation of the LIX index combines the conic finance theory, which recognizes the two-price economy and is built upon the concept of indices of acceptability of Cherny and Madan (2010), with the option payoff spanning formula of Breeden and Litzenberger (1978). Matching the conic finance bid and ask prices of the stock with those observed in the market allows us to derive a model-free and unit-less indicator of spot liquidity. Just as the VIX and the SKEW index quantify the volatility and the tail risk perceived by today’s investors, the resulting LIX index measures, in a similar market-implied fashion, the liquidity risk. The maximum likelihood estimation of popular mean-reverting processes applied to model-free liquidity time series indicates that spot liquidity tends to dry up during distress periods whereas a global drying-up of liquidity could not be detected during turmoil periods in the option market.     

Option market making under inventory risk

We propose a mean-variance framework to analyze the optimal quoting policy of an option market maker. The market maker’s profits come from the bid-ask spreads received over the course of a trading day, while the risk comes from uncertainty in the value of his portfolio, or inventory. Within this framework, we study the impact of liquidity and market incompleteness on the optimal bid and ask prices of the option. First, we consider a market maker in a complete market, where continuous trading in a perfectly liquid underlying stock is allowed. In this setting, the market maker may remove all risk by Delta hedging, and the optimal quotes will depend on the option’s liquidity, but not on the inventory. Second, we model a market maker who may not trade continuously in the underlying stock, but rather sets bid and ask quotes in the option and this illiquid stock. We find that the optimal stock and option quotes depend on the relative liquidity of both instruments as well as on the net Delta of the inventory. Third, we consider an incomplete market with residual risks due to stochastic volatility and large overnight moves in the stock price. In this setting, the optimal quotes depend on the liquidity of the option and on the net Vega and Gamma of the inventory.      

Options markets, self-fulfilling prophecies, and implied volatilities

This paper answers the following often asked question in option pricing theory: if the underlying asset's price does not satisfy a lognormal distribution, can market prices satisfy the Black-Scholes formula just because market participants believe it should? In complete markets, if the underlying asset's objective distribution is not lognormal, then the answer is no. But, in an incomplete market, if the underlying asset's objective distribution is not lognormal and all traders believe it is, then the answer is yes! The Black-Scholes formula can be a self-fulfilling prophecy. The proof of this second assertion consists of generating an economy where self-confirming beliefs sustain the Black-Scholes formula as an equilibrium. An asymmetric information model is provided, where the underlying asset's price has stochastic volatility and drift. This model is distinct from the existing pricing models in the literature, and it provides new empirical implications concerning Black-Scholes implied volatilities and the bid/ask spread. Similar to stochastic volatility models, this model is consistent with the implied volatility “smile” pattern in strike prices. In addition, it is consistent with implied volatilities being biased predictors of future volatilities.     

Central limit theorem for the realized volatility based on tick time sampling

A central limit theorem for the realized volatility estimator of the integrated volatility based on a specific random sampling scheme is proved, where prices are sampled with every ‘continued price change’ in bid or ask quotation data. The estimator is shown to be robust to market microstructure noise induced by price discreteness and bid–ask spreads. More general sampling schemes also are treated in case that the price process is a diffusion.     

Valuación de opciones de tipo de cambio asumiendo distribuciones α-estables

This paper aims to present the valuation of options using the Black-Scholes method assuming α-stable distributions as an alternative option valuation in the Mexican market. The use of α-stable distributions for modelling financial series allows to overcome the classical valuation main weakness which assumes normality, by capturing the presence of heavy tails and asymmetry in financial time series. One of the main results is the price differential between the two models and the effect of alpha and beta parameters on prices; to show the difference valuation is made of a call option and a put option for the peso-dollar exchange rate. Likewise, basic sensitivity measurements of options (delta, gamma, and rho) were made and the effect of the stability parameter (α) was made on the implied volatility of options assuming the α-stable price as the market price.     

Option market liquidity: Commonality and other characteristics

This study examines option market liquidity using Ivy DB's OptionMetrics data. We establish convincing evidence of commonality for various liquidity measures based on the bid–ask spread, volumes, and price impact. The commonality remains strong even after controlling for the underlying stock market's liquidity and other liquidity determinants such as volatility. Smaller firms and firms with a higher volatility exhibit stronger commonalities in option liquidity. Aside from commonality, we also uncover several other important properties of the option market's liquidity. First, information asymmetry plays a much more dominant role than inventory risk as a fundamental driving force of liquidity. Second, the market-wide option liquidity is closely linked to the underlying stock market's movements. Specifically, the options liquidity responds asymmetrically to upward and downward market movements, with calls reacting more in up markets and puts reacting more in down markets.     

Intraday futures market behaviour around major scheduled macroeconomic announcements: Australian evidence

This paper examines intraday futures market behaviour around major scheduled macroeconomic information announcements on the Sydney Futures Exchange (SFE). Prior literature analysing intraday price behaviour around announcements is extended to trading volume and quoted bid–ask spreads. The analysis of price volatility, trading volume and quoted bid–ask spreads indicates that the majority of adjustment to new information occurs rapidly, within 240 seconds of the scheduled time for major announcements, with some evidence of abnormal activity prior to announcements. Analysis of quoted bid–ask spreads suggests that they significantly widen in the 20 seconds prior to announcements and remain significantly wider for 30 seconds following announcements. The increase in quoted spreads is related to both expected and unexpected volatility, implying that market participants increase quoted spreads around information announcements as a consequence of adverse selection costs.     

S&P 100 Index Option Volatility

Using transaction data on the S&P 100 index options, we study the effect of valuation simplifications that are commonplace in previous research on the timeseries properties of implied market volatility. Using an American-style algorithm that accounts for the discrete nature of the dividends on the S&P 100 index, we find that spurious negative serial correlation in implied volatility changes is induced by nonsimultaneously observing the option price and the index level. Negative serial correlation is also induced by a bid/ask price effect if a single option is used to estimate implied volatility. In addition, we find that these same effects induce spurious (and unreasonable) negative cross-correlations between the changes in call and put implied volatility.     

Transparency,Liquidity, and Valuation: International Evidence on When Transparency Matters Most

We examine the relation between firm‐level transparency, stock market liquidity, and valuation across countries, focusing on whether the relation varies with a firm's characteristics and economic environment. We document lower transaction costs and greater liquidity (as measured by lower bid‐ask spreads and fewer zero‐return days) for firms with greater transparency (as measured by less evidence of earnings management, better accounting standards, higher quality auditors, more analyst following, and more accurate analyst forecasts). The relation between transparency and liquidity is more pronounced in periods of high volatility, when investor protection, disclosure requirements, and media penetration are poor, and when ownership is more concentrated, suggesting that firm‐level transparency matters more when overall investor uncertainty is greater. Increased liquidity is associated with lower implied cost of capital and with higher valuation as measured by Tobin's Q. Finally, a mediation analysis suggests that liquidity is a significant channel through which transparency affects firm valuation and equity cost of capital.     

Short-term market reaction after extreme price changes of liquid stocks

In our empirical study we examine the dynamics of the price evolution of liquid stocks after experiencing a large intra-day price change, using data from the NYSE and the NASDAQ. We find a significant reversal for both intra-day price decreases and increases. Volatility, volume and, in the case of the NYSE, the bid–ask spread, which increase sharply at the event, stay significantly high days afterwards. The decay of the volatility follows a power law in accordance with the `Omori law'. While on the NYSE the large widening of the bid–ask spread eliminates most of the profits that can be achieved by an outside investor, on the NASDAQ the bid–ask spread stays almost constant, yielding significant short-term profits. The results thus give an insight into the size and speed of the realization of an excess return for providing liquidity in a turbulent market.     

The impact of aggressive orders in an order-driven market: a simulation approach

This article investigates resiliency in an order-driven market. On basis of a vector autoregressive model capturing various dimensions of liquidity and their interactions, I simulate the effect of a large liquidity shock, measured by a very aggressive market order. I show that, despite the absence of market makers, the market is resilient. All dimensions of liquidity (spread, depth at the best prices and order book imbalances) revert to their steady-state values within 15 orders after the shock. For prices, a long run effect is found. Furthermore, different dimensions of liquidity interact. Immediately after a liquidity shock, the spread becomes wider than in the steady state, implying that one dimension of liquidity deteriorates, while at the same time, depth at the best prices increases, meaning an improvement of another liquidity dimension. In subsequent periods, the spread reverts back to the steady-state level but also depth decreases. Also, I find evidence for asymmetries in the impact of shocks on the ask and bid side. Shocks on the ask side have a stronger impact than shocks on the bid side. Finally, resiliency is higher for less-frequently traded stocks and stocks with a larger relative tick size.     

Interim Reporting Frequency and Financial Analysts' Expenditures

This paper relates interim financial reporting frequency in a multiperiod Kyle framework to securities prices, trading volume, market liquidity, and analysts' information acquisition expenditures. The model supports conventional wisdom that more frequent interim reporting improves the information content of securities prices, reduces reporting day price volatility and trading volume, and enhances market liquidity. However , the model suggests that more frequent financial reporting induces analysts to increase their redundant information acquisition expenditures, which may be socially wasteful.     

Liquidity supply in electronic markets

We examine the supply of liquidity by proprietary trading desks and hedge funds (PTDH) versus mutual funds, index funds, and insurance companies (MII) across ten bid (ask) steps of the limit order book. We document that institutional investors simultaneously supply liquidity at multiple prices in the limit order book. We also find that PTDHs are more price aggressive liquidity suppliers than MIIs, consistent with hypothesized responses to observed changes in the cost and risk of non-execution. We investigate whether these findings are robust to fast versus slow markets, the volatility of daily returns, and aggregate depth relative to daily volume.     

On the Distribution of CBOE Option Trade Prices Occurring Between Consecutive Stock Trades

This paper examines the volume distribution of option trade prices that occurs when the underlying stock price remains constant. The width of these option trade price bands provides direct evidence on the law of one price and the redundancy of options assumed in many option models. We find that index option bands are narrower than equity option bands. Furthermore, for both equity and index options, puts have narrower bandwidths than calls. In general, option price bandwidth is narrow and can be explained by the minimum price movement allowed by the Chicago Board Options Exchanges (CBOE). This supports the single price law and the redundancy assumption. The existence of bid/ask quotes on the option does not materially affect the above results although it does alter the frequency of multiple option trade prices for a given underlying stock price. We note that over 53% of option trading volume occurs without bid/ask quotes on the CBOE compared to less than 15% a decade ago. Our results suggest that the effective bid/ask spread on options is probably no larger than the minimum price movements allowed by the CBOE. Furthermore, the need for the liquidity services of market makers may be declining if the decline in quoting activity stems from cross trading (i.e. trades not involving market makers).     

To Trade or Not to Trade: The Effect of Broker Search and Discretionary Trading on Securities Market Performance

In this article we examine the interaction of brokerage search with the Bayesian learning behavior of competitive dealers under asymmetric information. We particularly focus on the effects of price search and discretionary trading on the performance of a dealer market. A search process is incorporated into a model in which brokers determine their reservation price and whether to continue their trades. The model enables us to uncover the interrelationships among search cost, bid‐ask spread, and price volatility. We show that both spread revision and price volatility are dependent upon the optimal search process, inventory fluctuation, and search cost. Furthermore, our model predicts a negative relationship between price volatility and liquidity trading volume.     

Market Response to Liquidity Improvements: Evidence from Exchange Listings

The study examines a sample of 895 stocks that moved from Nasdaq to the New York Stock Exchange or to the American Stock Exchange (Amex) between 1971 and 1994. We show how various measures of liquidity such as the bid‐ask spread, trading volume, and stock price precision improve in somewhat different ways upon transfer to NYSE (Amex). We also find that reductions in trading costs (percentage spread) and in pricing error volatility (Hasbrouck's σ₅) can explain most of stock market's positive response to exchange listing. Thus, liquidity has many facets and cannot be represented by the bid‐ask spread alone.     

The relationship between bid–ask spreads and holding periods: The case of Chinese A and B shares

The Chinese stock markets for A (domestic) shares and B (foreign) shares were completely separated. This study examines the relationship between spreads and holding periods across these segmented markets on the same set of firms. Our major findings are as follows. (1) There is a positive relationship between holding periods and bid–ask spreads in the Chinese stock market. (2) Investors' sensitivity toward liquidity is approximately the same in the A and B share markets, even though bid–ask spreads are substantially different across the two markets. These results provide strong support for the theoretical argument of Amihud and Mendelson [Amihud, Y., & Mendelson, H. (1986). Asset pricing and the bid–ask spread. Journal of Financial Economics, 17, 223–249.] that stocks with higher spreads tend to be held by long-term investors. Evidence also suggests that liquidity has a role in explaining the B share discount, although the results are less than conclusive.     

The relationship between bid–ask spreads and holding periods: The case of Chinese A and B shares

The Chinese stock markets for A (domestic) shares and B (foreign) shares were completely separated. This study examines the relationship between spreads and holding periods across these segmented markets on the same set of firms. Our major findings are as follows. (1) There is a positive relationship between holding periods and bid–ask spreads in the Chinese stock market. (2) Investors' sensitivity toward liquidity is approximately the same in the A and B share markets, even though bid–ask spreads are substantially different across the two markets. These results provide strong support for the theoretical argument of Amihud and Mendelson [Amihud, Y., & Mendelson, H. (1986). Asset pricing and the bid–ask spread. Journal of Financial Economics, 17, 223–249.] that stocks with higher spreads tend to be held by long-term investors. Evidence also suggests that liquidity has a role in explaining the B share discount, although the results are less than conclusive.     

Oil prices implied volatility or direction: Which matters more to financial markets?

We examine the impact of oil price uncertainty on US stock returns by industry using the US Oil Fund options implied volatility OVX index and a GJR-GARCH model. We test the effect of the implied volatility of oil on a wide array of domestic industries’ returns using daily data from 2007 to 2016, controlling for a variety of variables such as aggregate market returns, market volatility, exchange rates, interest rates, and inflation expectations. Our main finding is that the implied volatility of oil prices has a consistent and statistically significant negative impact on nine out of the ten industries defined in the Fama and French (J Financ Econ 43:153–193, 1997) 10-industry classification. Oil prices, on the other hand, yield mixed results, with only three industries showing a positive and significant effect, and two industries exhibiting a negative and significant effect. These findings are an indication that the volatility of oil has now surpassed oil prices themselves in terms of influence on financial markets. Furthermore, we show that both oil prices and their volatility have a positive and significant effect on corporate bond credit spreads. Overall, our results indicate that oil price uncertainty increases the risk of future cash flows for goods and services, resulting in negative stock market returns and higher corporate bond credit spreads.     

Minimum Price Variations,Time Priority,and Quote Dynamics

We analyze price competition between dealers in a security market where the bidding process is sequential. The model provides an interpretation for the evolution of the best ask and bid prices, in between transactions. We find that convergence to the competitive ask and bid prices can take time. The speed of convergence is determined by the frequency with which dealers check their offers and by the tick size. This creates a relationship between the expected trading cost and the timing of offers posted by the dealers. We also find that a zero minimum price variation never minimizes the expected trading cost. Finally, we study the role of time priority. Journal of Economic Literature Classification Numbers: D43, G10.