Option Market Makers Research Articles

Funding Illiquidity Implied by S&P 500 Derivatives

Based on the typical positions of S&P 500 option market makers, we derive a funding illiquidity measure from quoted prices of S&P 500 derivatives. Our measure significantly affects the returns of leveraged managed portfolios; hedge funds with negative exposure to changes in funding illiquidity earn high returns in normal times and low returns in crisis periods when funding liquidity deteriorates. The results are not driven by existing measures of funding illiquidity, market illiquidity, and proxies for tail risk. Our funding illiquidity measure also affects leveraged closed-end mutual funds and, to an extent, asset classes where leveraged investors are marginal investors.

COVID lockdown, Robinhood traders, and liquidity in stock and option markets

In this study, I investigate the impact of active option trading on stock market liquidity during the COVID-19 lockdown, particularly in connection with the rapidly growing retail trading activities during this period. I find that stocks with actively traded options, as well as those held by more Robinhood users, experience a lesser deterioration in liquidity during the US COVID-19 lockdown. However, a broader Robinhood user base appears to diminish the alleviation effect of actively traded options on the underlying stock's liquidity decline during the lockdown period. This observation is consistent with the postulation that informed traders shift away from option markets and towards stocks where the stock liquidity is improved. Further analysis suggests that, during the lockdown, a more extensive retail presence in the stock market is also associated with a narrower bid-ask spread in the option market. This finding supports the previous theories and empirical evidence suggesting that option market makers may offer tighter spreads when their hedging costs in the underlying market are reduced. Overall, this study presents novel evidence on the joint dynamics across stocks and options during the COVID-19 episode, and highlights the significant roles played by Robinhood traders in these dynamics.

VIX to S&P 500 Correlation Over the Weekend: Are Market Makers Using S&P 500 Weekend Returns to Price VIX on Monday Morning?

This paper studied the correlation between the S&P 500 ETF (SPY) weekend returns and the VIX changes. Two distinct patterns are found: (1) VIX is dropping intraday and rising overnight; (2) a negative SPY weekend return correlates with VIX weekend change. We found the negative correlation is statistically significant (P=0.000). This proves that option market makers are using SPY Friday overnight returns to adjust the implied volatility the next morning. This may lead to a profitable options model that sells high IV options closing on Friday and buys them back next Monday, especially before the earnings announcement.

Intraday momentum in the VIX futures market

This study examines intraday momentum in the unexplored VIX futures market and verifies its existence through various empirical tests. The intraday momentum of VIX futures appears to be robust across contracts with different expirations, intraday returns with different time intervals, different trading sessions, and multiple sub-periods. We propose that the hedging demand of VIX option market makers may contribute to the intraday momentum. Our empirical evidence shows that intraday momentum persists only when the net gamma exposure of VIX options is negative and the effect weakens when European investors are away from the market, supporting our proposed explanation. Strikingly, we also find that trading strategies based on intraday momentum can generate an average annualized return of up to nearly 18%.

Delta-hedging demand and intraday momentum: Evidence from China

This paper reveals that the rest-of-day return has positively significant prediction on the last 30-min return in the Chinese SSE 50 exchange-traded fund market. Its predictive power is economically significant and will decay in the next three days. Moreover, it reveals the relationship between intraday return prediction and short gamma hedging demand from option market makers, demonstrating that intraday hedging could be postponed till the end of a trading day. Intraday momentum caused by rebalancing traders and information investors cannot be completely offset by option market makers on days with positive net gamma exposure. Our results are robust to alternative exchange-traded fund index option and its underlying asset.

The impact of option hedging on the spot market volatility

We theoretically model and empirically quantify the feedback effect of delta hedging for the spot market volatility of the forex market. We start from an economy with two types of traders, an aggregated option market maker (OMM) and an aggregated option market taker (OMT), whose exposures reflect the total outstanding positions of all option traders in the market. A different hedge ratio of the OMM and OMT leads to a net delta hedge activity, which introduces market friction. We represent this friction by a simple linear permanent impact model. This approach allows us to derive the dependence of the spot market volatility on the gamma exposure of the traders. Our theoretical model shows that the spot market volatility is increased (decreased) by a negative (positive) gamma exposure of the OMM, whereby the amount of the increase depends on the net delta hedge amount executed in the spot market. To empirically test this model, we first reconstruct the aggregated OMM’s gamma exposure by using trade repository data and find that it is negative. The empirical analysis performed over the period from 21st October 2017 to 30th June 2018 using our reconstructed OMM data then strongly supports our theoretical model: The gamma exposure of the OMM turns out to be highly significant for the spot market volatility and, as expected, the spot market volatility is increased with the OMM’s short gamma exposure. Quantitatively, a negative gamma exposure of the OMM of approximately −1000 billion USD (which is around what we observe from our reconstructed OMM data) leads to an absolute increase in volatility of 0.7% in EURUSD and 0.9% in USDJPY.

Delta hedging bitcoin options with a smile

We analyse robust dynamic delta hedging of bitcoin options using a set of smile-implied and other smile-adjusted deltas that are either model-free, in the sense that they are the same for every scale-invariant stochastic and/or local volatility model, or they are based on simple regime-dependent parameterisations of local volatility. These deltas are popular with option market makers in traditional assets because they are very easy to implement. Previous empirical research on dynamic delta hedging is based solely on equity index options, but analysis of our unique data on hourly historical bitcoin option prices reveals that bitcoin implied volatility curves behave very differently from those of equity index options. For call and put options with a wide range of moneyness and with synthetic constant maturities of 10, 20 and 30 days, we compare the dynamic hedging performance of different smile-adjusted deltas over two one-year periods. We also examine the use of the perpetual contract rather than the standard futures as hedging instrument because the basis risk for the perpetual is very much smaller than it is for calendar futures. Results are presented as testable statistics of hedging error variance ratios. In certain periods the use of smile-implied hedge ratios can significantly out-perform the simple Black–Scholes delta hedge, especially when using the perpetual swap as hedging instrument, where efficiency gains can exceed 30% for out-of-the-money puts, and reach an average of 15% when hedging short-term out-of-the money calls during periods when the implied volatility curve slopes upwards. The advantage of using the perpetual contract is especially evident during 2021, for the longer-term contracts for which the basis is still rather large.

Algorithmic market making for options

In this article, we tackle the problem of a market maker in charge of a book of options on a single liquid underlying asset. By using an approximation of the portfolio in terms of its vega, we show that the seemingly high-dimensional stochastic optimal control problem of an option market maker is in fact tractable. More precisely, when volatility is modeled using a classical stochastic volatility model—e.g. the Heston model—the problem faced by an option market maker is characterized by a low-dimensional functional equation that can be solved numerically using a Euler scheme along with interpolation techniques, even for large portfolios. In order to illustrate our findings, numerical examples are provided.

Does Option Trading Have a Pervasive Impact on Underlying Stock Prices?

Abstract The question of whether and to what extent option trading affects underlying stock prices has been of interest to researchers since exchange-based options trading began in 1973. Recent research presents evidence of an informational channel through which option trading affects stock prices by showing that option market makers’ stock trades to hedge new options positions cause the information reflected in option trading to be impounded into underlying equity prices. This paper provides evidence of a noninformational channel through which option market maker hedge rebalancing affects stock return volatility and the probability of large stock price moves.

Option Market Making with Inventory Risk: The Effect on Information Diffusion

This paper develops a model to study how option market makers' inventory and capital influence the relative informativeness of the option and stock markets. The model suggests that the option market maker's capital defines a lower bound for the option market informativeness. In addition, when perfect hedging is impossible, a larger inventory of sold (bought) options diminishes the informativeness of changes in the option's ask (bid) quote and increases the informativeness of changes in the option's bid (ask) quote. Finally, the model implies that noisy information is more likely to enter through the option market than the stock market. My empirical analysis provides stylized facts consistent with the model's key implications.

Option Spreads and the Uncertain Cost of Equity Liquidity: Evidence from the Knight Capital Trading Glitch

Since the early 2000s liquidity in option markets has become less resilient, and our evidence suggests that it is so because of an increased vulnerability to liquidity shocks in the underlying. To demonstrate the causal impact, we consider an incident in which a large broker dealer erroneously executed millions of orders in the stock market. The computer glitch increased uninformed order flow resulting in liquidity-related uncertainty in the equity market. Option spreads of impacted stocks widened by as much as one-third while abnormal stock order flow was ongoing and remained wide until uncertainty about the glitch was resolved. The evidence is consistent with a mechanism whereby option market makers face risk of being picked off with every revised quote in the underlying. Option market participants bear higher adverse selection costs than equity market participants, making the derivative markets fragile.

A Tractable Framework for Option Pricing with Dynamic Market Maker Inventory and Wealth

We develop a tractable dynamic model of an index option market maker with limited capital. We solve for the variance risk premium and option prices as a function of the asset dynamics and market maker option holdings and wealth. The market maker absorbs end users’ positive demand and requires a more negative variance risk premium when she incurs losses. We estimate the model using returns, options, and inventory and find that it performs well, especially during the financial crisis. The restrictions imposed by nested existing reduced-form stochastic-volatility models are strongly rejected in favor of the model with a market maker.

Option prices and costly short-selling

Much empirical evidence shows that stock short-selling costs and bans have significant effects on option prices. We reconcile these findings by providing a dynamic analysis of option prices with costly short-selling and option market makers. We obtain simple, closed-form, unique option bid and ask prices that represent option market makers’ expected hedging costs, and are weighted averages of well-known benchmark prices (Black–Scholes, Heston). Our analysis delivers rich implications that support the empirical evidence on the effects of short-selling costs and bans on option prices, as well as uncovering several novel predictions. We also apply our methodology to corporate bonds, which have option-like payoffs.

Option Returns and Conditional Serial Correlation in Currency Markets

Weekly option writing returns in currency markets are (volatility-) regime dependent: they are low when implied volatility is low, and high when implied volatility is high. However, a time-varying volatility risk premium (ex-post) might only be part of the explanation. Daily exchange rate returns show (volatility-)regime dependent departures from normality and (volatility-)regime dependent serial correlation. This leads to weekly absolute movements that differ from a reasonable expectation under normality and iid. In particular, I document positive daily autocorrelation in low implied volatility quantiles, which might arise from actions of either speculators or option market makers who trade urgently in a relatively less resilient/liquid market.

Stock Options, Stock Loans, and the Law of One Price

Historically, option market makers were exempt from borrowing shares when short selling which allowed them to hedge their exposure in hard-to-borrow stocks. As a result, options were not redundant securities -- they allowed traders to circumvent short-sale constraints. Regulators removed this exemption in 2008 and in 2013 they prohibited a workaround using 'reverse conversions'. These regulatory changes eliminated the shadow supply of hard-to-borrow shares provided by options; we find that these changes increased the redundancy of option securities and caused a significant increase in equity loan fees. Consequently, market quality has deteriorated: price efficiency is lower and stocks are more overpriced.

Volatility Uncertainty, Time Decay, and Option Bid-Ask Spreads in an Incomplete Market

This paper documents the fact that in options markets, the (percentage) implied volatility bid-ask spread increases at an increasing rate as the option’s maturity date approaches. To explain this stylized fact, this paper provides a market microstructure model for the bid-ask spread in options markets. We first construct a static equilibrium model to illustrate the aforementioned phenomenon where risk averse and competitive option market makers quote bid and ask prices to minimize their inventory risk in an incomplete market with both directional and volatility risk. We extend this model to multiperiods and show that the same phenomenon occurs there as well. Two new implications are generated: a volatility level effect and a volatility variance effect. These implications are empirically tested, and the empirical results confirm the model’s validity. Finally, we document the importance of detrending the maturity effect by showing that the detrended percentage volatility spread explains future jump intensities better than the original percentage volatility spread. The online appendix is available at https://doi.org/10.1287/mnsc.2017.2867 . This paper was accepted by Neng Wang, finance.

Why Do Option Returns Change Sign from Day to Night?

Returns for S&P 500 index options are negative and large: -0.7% per day. Strikingly, when we decompose these delta-hedged option returns into intraday (open-to-close) and overnight (close-to-open) components, we find that average overnight returns are -1% while intraday returns are actually positive, 0.3% per day. A similar return pattern holds for all maturity and moneyness categories, equity and ETF options, and VIX futures. Rational theories struggle to explain positive intraday returns. We show that returns change sign and become positive because option prices fail to account for the well-known fact that stock volatility is substantially higher intraday than overnight. Thus, option market-makers, some of the most sophisticated investors, appear to completely ignore one of the strongest volatility seasonalities, which can be easily added to option pricing models. Finally, other option investors also appear unaware of this anomaly, which may explain its persistence.

Understanding Bona Fide Option Market Makers

This paper builds a uni ed theoretical framework under which the quoting and hedging strategies of a competitive option market maker are analyzed. I show that the option market maker trades fewer shares of the underlying stock and widens the bid-ask spread as trading the underlying stock becomes more costly. Then I model the option market maker as being involved in more than one market within the same option chain. The market maker adjusts bid and ask quotes in multiple markets simultaneously to encourage transactions that help him/her easily hedge the inventory. This paper has potential implications in the recent debate over structural banking reform.

Fails-to-Deliver after the Implementation of Rule 203 and Rule 204T

We study the determinants of fails‐to‐deliver in the period before and after the implementation of Rule 203 (elimination of option market maker exception from the locate and close‐out requirement) and Rule 204 (t+3 close‐out rule) in September 2008. We find a positive relation between short selling and fails‐to‐deliver that weakens after the implementation of these rules. Fails‐to‐deliver are higher for stocks with low institutional ownership, low book‐to‐market, small market capitalization, high turnover, and put option availability. The relation between short selling and these measures of borrowing costs is also weaker after the implementation of these rules.

Fails-to-Deliver before and after the Implementation of Rule 203 and Rule 204

AbstractWe study the determinants of fails‐to‐deliver in the period before and after the implementation of Rule 203 (elimination of option market maker exception from the locate and close‐out requirement) and Rule 204 (t+3 close‐out rule) in September 2008. We find a positive relation between short selling and fails‐to‐deliver that weakens after the implementation of these rules. Fails‐to‐deliver are higher for stocks with low institutional ownership, low book‐to‐market, small market capitalization, high turnover, and put option availability. The relation between short selling and these measures of borrowing costs is also weaker after the implementation of these rules.