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.      

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).     

Is there price discovery in equity options?

We use tick-by-tick quote data for 39 liquid US stocks and options on them, and we focus on events when the two markets disagree about the stock price in the sense that the option-implied stock price obtained from the put-call parity relation is inconsistent with the actual stock price. Option market quotes adjust to eliminate the disagreement, while the stock market quotes behave normally, as if there were no disagreement. The disagreement events are typically precipitated by stock price movements and display signed option volume in the direction that tends to eliminate the disagreements. These results show that option price quotes do not contain economically significant information about future stock prices beyond what is already reflected in current stock prices, i.e., no economically significant price discovery occurs in the option market. We also find no option market price discovery using a much larger sample of disagreement events based on a weaker definition of a disagreement, which verifies that the findings for the primary sample are not due to unusual or unrepresentative market behavior during the put-call parity violations.     

Pricing options on scenario trees

We examine valuation procedures that can be applied to incorporate options in scenario-based portfolio optimization models. Stochastic programming models use discrete scenarios to represent the stochastic evolution of asset prices. At issue is the adoption of suitable procedures to price options on the basis of the postulated discrete distributions of asset prices so as to ensure internally consistent portfolio optimization models. We adapt and implement two methods to price European options in accordance with discrete distributions represented by scenario trees and assess their performance with numerical tests. We consider features of option prices that are observed in practice. We find that asymmetries and/or leptokurtic features in the distribution of the underlying materially affect option prices; we quantify the impact of higher moments (skewness and excess kurtosis) on option prices. We demonstrate through empirical tests using market prices of the S&P500 stock index and options on the index that the proposed procedures consistently approximate the observed prices of options under different market regimes, especially for deep out-of-the-money options.     

The effects of newly listed derivatives in a thin stock market

This study examines the informational feedback effects associated to the listing and trading of derivatives in Switzerland. The observed changes in the price and higher moments of stock returns are representative of a thin stock market. The listing of stock options and index futures generated positive abnormal returns for large stocks and for the index while small stocks essentially benefited from the launching of index options. While reducing the variance of blue chips and of the index, their variance's stochasticity increased (decreased) at index options' (futures) listings. Finally, we detect significant stock and index derivatives' price leads which do not however generate arbitrage opportunities.     

Incentives of Stock Option Based Compensation

We introduce explicitly the effort as a choice variable in a continuous time utility maximisation framework of an executive who is partly compensated with stock options. We solve the model in the case where the executive is not allowed to trade in the company’s stock but is able to achieve a partial insurance through trading in a correlated market portfolio. We define the executive’s value of the options through a certainty equivalence approach both in the case of European call options and non-standard capped stock options and study the behaviour of the reservation price as relevant parameters change.JEL Classification: G13, G30, G32, J33, M12     

An empirical examination of the impact of market microstructure changes on the determinants of option bid-ask spreads

This paper examines the determinants of bid-ask spreads in the Australian Options Market before and after it switched from a quote-driven floor-traded market to an order-driven screen-traded market. This study reports that both put and call option bid-ask spreads are positively related to the option's value, its remaining term-to-maturity, its absolute hedge ratio and the volatility of returns from the underlying asset and negatively related to the level of trading activity in that option series. The study also reports that spreads are generally less when market makers are obliged to maintain continuous quotes in the market. The paper also finds that following the change in trading regime, both call and put option spreads became more sensitive to the absolute value of the option's delta. This finding is consistent with previous theoretical and empirical work from equities markets that has suggested that a switch to an electronic trading regime results in an increase in the adverse selection component of the bid-ask spread. There is also some limited evidence that suggests that the switch to electronic trading resulted in call option spreads being less sensitive to the return volatility of the underlying asset but more sensitive to the option's price.     

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.     

Options trading volume and stock price response to earnings announcements

We examine the effect of options trading volume on the stock price response to earnings announcements over the period 1996–2007. Contrary to previous studies, we find no significant difference in the immediate stock price response to earnings information announcements in samples split between firms with listed options and firms without listed options. However, within the sample of firms with listed options stratified by options volume, we find that higher options trading volume reduces the immediate stock price response to earnings announcements. This conforms with evidence that stock prices of high options trading volume firms have anticipated and pre-empted some earnings information in the pre-announcement period. We also find that higher abnormal options trading volume around earnings announcements hastens the stock price adjustment to earnings news and reduces post-earnings announcement drift.     

Single-stock futures: Evidence from the Indian securities market

Although single-stock futures (SSFs) are useful multi-purpose stock derivatives, they have not received much attention in developed markets. We analyze SSFs in the Indian market to understand their contribution in price leadership. The findings indicate that trades in the stock market contribute more to price discovery than trades in the SSF market (72% and 28%, respectively), while quotes in the SSF market are more price innovative than quotes in the stock market (39% and 61%, respectively). Our analysis suggests that while stock and SSF trade returns have predictive ability for each other, in the case of quotes, only SSF quotes have predictive ability for stock and SSF returns.     

Information-based stock trading and managerial incentives: evidence from China's stock market

This paper uses stock price informativeness, or information-based stock trading, to help explain the pay–performance sensitivity (PPS) of chief executive officer (CEO) compensation in China's listed firms. We argue that higher stock price informativeness, which we measure by the probability of informed trading, helps and encourages shareholders to incentivize the top management team based on stock market performance. The regression results support our argument and show that a higher level of stock price informativeness is associated with higher CEO PPSs. Moreover, the impact of stock price informativeness on CEO incentives is stronger for privately controlled listed firms than it is for state-controlled listed firms. The results also hold when information asymmetry is approximated by the accuracy and dispersion of the earnings forecasts made by financial analysts.     

Adverse selection costs,trading activity and price discovery in the NYSE: An empirical analysis

This paper studies the role that trading activity plays in the price discovery process of a NYSE-listed stock. We measure the expected information content of each trade by estimating its permanent price impact. It depends on observable trade features and market conditions. We also estimate the time required for quotes to incorporate all the information content of a particular trade. Our results show that price discovery is faster after risky trades and also at the extreme intervals of the session. The quote adjustment to trade-related shocks is progressive and this causes risk persistency and unusual short-term market conditions.     

Internationally cross-listed stock prices during overlapping trading hours: price discovery and exchange rate effects

We analyze exchange rates along with equity quotes for 3 German firms from New York (NYSE) and Frankfurt (XETRA) during overlapping trading hours to see where price discovery occurs and how stock prices adjust to an exchange rate shock. Findings include: (a) the exchange rate is exogenous with respect to the stock prices; (b) exchange rate innovations are more important in understanding the evolution of NYSE prices than XETRA prices; and (c) most (but not all) of the fundamental or random walk component of firm value is determined in Frankfurt.     

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.     

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.     

The liquidity effects associated with addition of a stock to the S&P 500 index: evidence from bid/ask spreads

This study examines changes in stock liquidity, as measured by the bid/ask spread, when a stock is added to the S&P 500 Index. The paper presents evidence of a significant decrease in the bid/ask spread upon S&P 500 addition, however, this effect is limited to only those stocks that were not trading listed options. Further, the decrease in the bid/ask spread for nonoptioned stocks is accompanied by a significant and permanent increase in share price and trading volume. While optioned stocks experience a permanent increase in trading volume, they experience only a temporary increase in share price. The findings for optioned stocks support the hypothesis that the price and volume effects associated with S&P 500 addition derive from temporary price pressure. Findings pertaining to the nonoptioned stocks indicate that the price and volume effects associated with S&P addition reflect enhanced stock liquidity. The decrease in the bid/ask spread for nonoptioned stocks is attributed to informational efficiencies achieved via index arbitrage trading, and it is argued that this effect is mitigated for optioned stocks due to the pre-existence of arbitrage trading between the option and the underlying stock.     

Stock price decreases prior to executive stock option grants

This study examines abnormal stock price changes prior to executive stock option grants. Executives have the incentive and opportunity to manage the timing of their communications of inside information to the market during the period just prior to the date of their stock-option grant so as to reduce the exercise price of their options. Executives benefit from temporary stock price decreases before the grant date and by stock price increases after the grant date. Executive stock option grants create a unique opportunity for insiders to profit by manipulating the timing of information flowing to the market without engaging in insider trading. Using data on 783 stock-option grants to chief executive officers, we find a statistically significant abnormal decrease in stock prices during the 10-day period immediately preceding the grant date.     

Modeling stock pinning

This paper investigates the effect of hedging strategies on the so-called pinning effect, i.e. the tendency of stock's prices to close near the strike price of heavily traded options as the expiration date nears. In the paper we extend the analysis of Avellaneda and Lipkin, who propose an explanation of stock pinning in terms of delta hedging strategies for long option positions. We adopt a model introduced by Frey and Stremme and show that, under the original assumptions of the model, pinning is driven by two effects: a hedging-dependent drift term that pushes the stock price toward the strike price and a hedging-dependent volatility term that constrains the stock price near the strike as it approaches it. Finally, we show that pinning can be generated by simulating trading in a double auction market. Pinning in the microstructure model is consistent with the Frey and Stremme model when both discrete hedging and stochastic impact are taken into account.     

Price distortion induced by a flawed stock market index

Despite the introduction of sophisticated stock market indices, investors often trade portfolios of the flawed indices to change their exposure to the market. In this study, we show that these transactions cause significant mispricing in individual stocks, especially during periods of significant market movement. As an influential, albeit flawed, stock index, we focus on the Nikkei 225. We find index constituents that are excessively weighted on the index, experience buying (selling) pressure when the stock market surges (falls), and experience price corrections after such periods of change. In contrast, non-constituent stocks do not experience such trading pressure.     

The information content of ETF options

We examine the information content of China's Shanghai Stock Exchange (SSE) 50 ETF options introduced in 2015. Trading volume and implied volatilities of calls versus puts differ markedly: trading volume is consistently higher for calls, and implied volatility is higher for puts. Put-call volume and implied volatility ratios are not good predictors of future SSE 50 returns. Implied volatility follows a right-skewed smirk across strike prices, indicating a tendency among option traders to turn bullish and expect the stock market to recover from the June 2015 market crash. The options market dominates the price discovery process, with an average information leadership share of 67%. Our price discovery results persist during the COVID outbreak.