The data that support the findings of this study are available from OptionMetrics, Markit, Trade Alert, NYSE, and CRSP. Restrictions apply to the availability of these data, which were used under license for this study. Data are available from the author with the permission of OptionMetrics, Markit, Trade Alert, NYSE, and CRSP.
Reference
Atmaz, A., Basak, S., 2019. Option prices and costly short-selling. Journal of Financial Economics 134, 1-28.
Barraclough, K., Whaley, R., 2012. Early exercise of put options on stocks. Journal of Finance 67, 14231456.
Battalio, R., Shultz, P., 2006. Options and the Bubble. Journal of Finance 61, 2071-2102.
Battalio, R., Shultz, P., 2011. Regulatory Uncertainty and Market Liquidity: The 2008 Short Sale Ban’s Impact on Equity Option Markets. Journal of Finance 66, 2013-2053.
Black, F., Scholes, M., 1973. The pricing of options and corporate liabilities. Journal of Political Economy 81, 637654.
Black, F., 1975. Fact and fantasy in the use of options. Financial Analyst Journal 31, 3672.
Boguth, O., Simutin, M., 2018. Leverage constraints and asset prices: Insights from mutual fund risk taking.
Journal of Financial Economics 127, 325-341.
Brunnermeier, M., Pedersen, L.H., 2009. Market liquidity and funding liquidity. Review of Financial Studies 22, 2201-2238.
D’Avolio, G., 2002. The market for borrowing stock. Journal of Financial Economics 66, 271306.
Easley, D., Engle, R., OHara, M., Wu, L., 2008. Time-Varying Arrival Rates of Informed and Uninformed Trades. Journal of Financial Econometrics 6, 171207.
Easley, D., O’Hara, M., 1987. Price, trade size, and information in securities markets. Journal of Financial Economics 19, 69-90.
Easley, D., OHara, M., Srinivas, P. S., 1998. Option volume and stock prices: Evidence on where informed traders trade. Journal of Finance 53, 431465.
Fama, E.F., MacBeth, J.D., 1973. Risk, return, and equilibrium: empirical tests. Journal of Political Economy 81, 607636.
Fostel A., and Geanakoplos J., 2008. Leverage Cycles and the Anxious Economy. American Economic Review 98, 1211-44.
Frazzini, A., Pedersen, L. H., 2014. Betting against beta. Journal of Financial Economics 111, 1-25.
Garleanu, N., Pedersen, L. H., 2011. Margin based asset pricing and deviations from the law of one price.
Review of Financial Studies 24, 19802022.
Garleanu, N., Pedersen, L. H., Poteshman, A. M., 2009. Demand-based option pricing. Review of Financial Studies 22, 4259-4299.
Ge, L., Lin, T., Pearson, N., 2016. Why does the option to stock volume ratio predict stock returns? Journal of Financial Economics 120, 601-622.
Glosten, L.R., Milgrom, P.R., 1985. Bid, ask and transaction prices in a specialist market with heterogeneously
informed traders. Journal of Financial Economics 14, 71-100.
Gromb, D., Vayanos, D., 2002. Equilibrium and Welfare in Markets with Financially Constrained Arbitrageurs.
Journal of Financial Economics 66, 361-407.
Gromb, D., Vayanos, D., 2018. The Dynamics of Financially Constrained Arbitrage. Journal of Finance 73, 1713-1750.
Goncalves-Pinto, L., Grundy, B.D., Hameed, A., van der Heijden, T. and Zhu, Y., 2020. Why do option prices predict stock returns? The role of price pressure in the stock market. Management Science, forthcoming.
Gould, J. P., Galai, D., 1974. Transactions costs and the relationship between put and call prices. Journal of Financial Economics 1, 105-129.
Goyenko, R., Ornthanalai, C. and Tang, S., 2015. Options illiquidity: Determinants and implications for stock returns. Working Paper, Rotman School of Management.
Grundy, B., Lim, B., Verwijmeren, P., 2012. Do option markets undo restrictions on short sales? Evidence from the 2008 short-sale ban. Journal of Financial Economics 106, 331-348.
Hu, J., 2014. Does option trading convey stock price information?. Journal of Financial Economics 111, 625645.
Hu, J., 2018. Option listing and information asymmetry. Review of Finance 22, 1153-1194.
Hu, J., Kirilova, A., Park, G., Ryu, D., 2020. Who profits from trading options? Working paper, Singapore Management University.
Hu, X., Pan, J., Wang, J., 2013. Noise as information for illiquidity. Journal of Finance 68, 2341-2382.
Jiang, W., 2018. Leveraged Speculators and Asset Prices. Working Paper, Chinese University of Hong Kong.
Kalay, A., Karakas, O., Pant, S., 2014. The market value of corporate votes: Theory and evidence from option prices. Journal of Finance 69, 12351271.
Kamara, A., Miller, T.W., 1995. Daily and intradaily tests of European put-call parity. Journal of Financial and Quantitative Analysis 30, 519-539.
Klemkosky, R., Resnick, B., 1979. Put-call parity and market efficiency. Journal of Finance 34, 1141-1155.
Klemkosky, R., Resnick, B., 1980. An ex ante analysis of put-call parity. Journal of Financial Economics 8, 363-378.
Lamont, O., Thaler, R., 2003. Can the Market Add and Subtract? Mispricing in Tech Stock Carve-outs.
Journal of Political Economy 111, 227-268.
Merton, R. C., 1973. The Relationship Between Put and Call Option Prices: Comment. Journal of Finance 28, 183-184.
Mitchell, M., and Pulvino, T., 2012. Arbitrage crashes and the speed of capital. Journal of Financial Economics 104, 469-490.
Muravyev, D., Pearson, N. D., Broussard, J. P., 2013. Is there price discovery in equity options? Journal of Financial Economics 107(2), 259283.
Muravyev, D., Pearson, N. D., Pollet, J., 2018. Understanding Returns to Short Selling Using Option-Implied Stock Borrowing Fees. Working paper, Michigan State University.
Muravyev, D., Pearson, N. D., 2020. Options Trading Costs Are Lower than You Think, Review of Financial Studies, forthcoming.
Newey, W.K., West, K.D., 1987. A simple, positive semi-definite, heteroskedasticity, and autocorrelation consistent covariance matrix. Econometrica 55, 703708.
Odean, T., 1998. Are Investors Reluctant to Realize their Losses? Journal of Finance 53, 1775-1798.
Ofek, E., Richardson, M., Whitelaw, R., 2004. Limited arbitrage and short sale constraints: Evidence from the options market. Journal of Financial Economics 74, 305342.
Pan, J., Poteshman, A., 2006. The Information in Option Volume for Future Stock Prices. Review of Financial Studies 19, 871-908.
Phillips, S.M., Smith, C.W., 1980. Trading costs for listed options the implications for market efficiency.
Journal of Financial Economics 8, 179-201.
Ross, S. A., 1976. The arbitrage theory of capital asset pricing. Journal of Economic Theory 13, 341360.
Rytchkov, O., 2014. Asset pricing with dynamic margin constraints. Journal of Finance 69, 405-452.
Stoll, H., 1969. The relationship between call and put option prices. Journal of Finance 24, 801-824.
[Dataset] Center for Research in Security Prices, Daily Close Stock Bid and Ask Prices 2007-2012 [Dataset] Option Metrics, Daily Close Stock Bid and Ask Option Prices 2007-2012
[Dataset] Markit, Security Lending Fee, Total Loanable Shares and Outstanding Shares on Loan 2007-2012 [Dataset] Trade Alert, Options Tick Data 2007-2012
[Dataset] New York Stock Exchange, Trade and Quote Data 2007-2012
Table 1
Sample description
This table describes the sample in the study from 2007 to 2012. To be included, a common stock (CRSP code 10 and 11) must have options prices available in Option Metrics and short selling data from Markit with its stock price above $5. Stock-day observations with non-dividend stock distributions, loanable shares more than number of shares outstanding, negative stock borrowing fees, crossed or locked close bid and ask prices in either the stock or options market are excluded.
Reported for each year as well as the full sample are the total number of stock-day observations, number of unique stocks in the year, average daily stock and options trading volumes and options open interest per stock. Stock trading volume is in number of shares. Options trading volume and open interest are counted in option lots with one lot equivalent to one hundred shares of stocks.
Year N of ob N of stocks Stock volume Option volume Open interests
2007 346,723 2,351 2,150,539 3,883 99,157
2008 305,790 2,308 3,060,339 4,669 105,045
2009 278,344 2,160 3,115,314 4,676 91,966
2010 326,319 2,247 2,832,596 4,471 92,019
2011 338,198 2,341 2,726,529 5,091 98,037
2012 319,427 2,295 2,472,760 5,366 96,468
Total 1,914,801 3,330 2,707,798 4,685 97,189
Table 2
Mid quote locations in the two markets
This table compares the synthetic mid quote price with the borrowing-cost adjusted mid quote price in the stock market in the sample described in Table 1. The synthetic bid and ask prices are constructed using a pair of closest-to-the-money call and options as follows:
bidi= (Bid Call− EEP Call) − (Ask Put − EEP Put) + PV (K) + PV (Div), aski= (Ask Call − EEP Call) − (Bid Put − EEP Put) + PV (K) + PV (Div),
where PV (K) is the present value of the strike price, EEP is the early exercise premium calculated as the difference between the actual midpoint of the option bid-ask prices and the Black-Scholes (1973) European option price, and Div is the present value of the announced dividends before the options maturity. For each underlying stock, only the closest-to-the-money option pair expiring in 10 to 40 days is chosen to calculate the synthetic stock prices every day. The borrowing-cost adjusted bid and ask prices are:
bida= bid ∗ (1 − lending f ee ∗ t0∗ exp(−r ∗ t)),
aska= ask ∗ (1 − utilization ∗ lending f ee ∗ t ∗ exp(−r ∗ t)),
where bid and ask are the close bid and ask prices in CRSP, utilization is the percentage of shares on loan relative to the total number of shares available for lending, lending f ee is the net stock borrowing cost in percentage, t is the time to expiration of the synthetic stock, t0 is t minus three days assuming short sellers deliver stocks three days after the transaction, and r is the risk-free rate of return. The mid quote prices are the average of bid and ask prices labeled as midifor the synthetic stock, mid for the actual stock without security lending costs, and mida for the actual stock with security lending costs. Panel A reports the descriptive statistics of the ratio and difference between the two mid quote prices of synthetic and actual stocks. Panel B reports the percentage of observations in each category.
Panel A: Descriptive statistics
Variable N Mean Std Min Max
midi/mid 1,914,801 99.975 0.473 75.291 153.886
midi/mida 1,914,801 100.001 0.464 75.321 153.895
midi- mid 1,914,801 -0.664 14.455 -886.266 1763.82
midi- mida 1,914,801 -0.046 14.23 -874.539 1764.22
Panel B: Mid quote comparison
Table 3
Comparing actual and synthetic bid prices
This table compares the synthetic bid price with the borrowing-cost adjusted bid price in the stock market in the sample described in Table 1. The synthetic bid (bidi), borrowing-cost adjusted actual bid (bida) and unadjusted actual bid (bid) are the same as defined in Table 2. Panel Panel A reports the descriptive statistics of the ratio and difference between the two bid prices. Panel B reports the percentage of observations in each category.
Panel A: Descriptive statistics
Variable N Mean Std Min Max
bidi/bid 1,914,801 98.946 1.32 38.793 153.142
bidi/bida 1,914,801 98.973 1.309 38.797 153.158
bidi- bid 1,914,801 -26.396 36.756 -3353.7 3765.88
bidi- bida 1,914,801 -25.717 36.531 -3344.07 3770
Panel B: Bid prices comparison
year N bidi≥bid bidi<bid bidi≥bida bidi<bida
2007 346,723 1.53 98.47 1.94 98.06
2008 305,790 1.07 98.93 1.39 98.61
2009 278,344 1.12 98.88 1.33 98.67
2010 326,319 1.66 98.34 2.12 97.88
2011 338,198 1.94 98.06 2.30 97.70
2012 319,427 2.70 97.30 3.42 96.58
Total 1,914,801 1.69 98.31 2.10 97.90
Table 4
Comparing actual and synthetic ask prices
This table compares the synthetic ask price with the borrowing-cost adjusted ask price in the stock market in the sample described in Table 1. The synthetic ask (aski), borrowing-cost adjusted actual ask (aska) and unadjusted actual ask (ask) are the same as defined in Table 2. Panel A reports the descriptive statistics of the ratio and difference between the two ask prices. Panel B reports the percentage of observations in each category.
Panel A: Descriptive statistics
Variable N Mean Std Min Max
aski/ask 1,914,801 101.003 1.284 76.677 161.473
aski/aska 1,914,801 101.023 1.287 76.688 161.477
aski- ask 1,914,801 25.068 36.68 -1934.12 3492.82
aski- aska 1,914,801 25.53 36.654 -1934.03 3492.82
Panel B: Ask prices comparison
year N aski≥ask aski<ask aski≥aska aski<aska
2007 346,723 97.45 2.55 97.79 2.21
2008 305,790 97.39 2.61 97.95 2.05
2009 278,344 97.72 2.28 98.23 1.77
2010 326,319 97.13 2.87 97.63 2.37
2011 338,198 96.98 3.02 97.54 2.46
2012 319,427 95.96 4.04 96.94 3.06
Total 1,914,801 97.09 2.91 97.67 2.33
Table 5
Locations of actual and synthetic quotes and arbitrage opportunities
This table reports the percentage of stock-day observations for six types of quote locations as described in Figure 1 for individual years as well as the full sample. Synthetic ask (aski) and bid (bidi) are calculated as in Tables 2. Actual ask and bid prices are adjusted for security lending costs in Panel A and unadjusted in Panel B. Type A is when the synthetic ask is above the actual ask and the synthetic bid is below the actual bid. Type B is when the synthetic ask is above the actual ask and the synthetic bid is above the actual bid but below the actual ask. Type C is when the synthetic ask is below the actual ask but above the actual bid and the synthetic bid is below the actual bid.
Type D is when the synthetic ask is below the actual ask and the synthetic bid is above the actual bid. Type E is an arbitrage opportunity when both the synthetic ask and bid are above the actual ask. Type F is an arbitrage opportunity when both the synthetic ask and bid are below the actual bid.
Panel A: With lending fees
year Type A Type B Type C Type D Type E Type F
2007 96.16 1.30 1.59 0.30 0.34 0.31
2008 96.73 0.95 1.51 0.17 0.27 0.37
2009 97.00 0.77 1.17 0.10 0.46 0.51
2010 95.52 1.17 1.38 0.01 0.94 0.98
2011 95.25 1.03 1.23 0.02 1.26 1.22
2012 93.51 1.42 1.58 0.01 2.00 1.48
Total 95.66 1.12 1.41 0.10 0.89 0.82
Panel B: Without lending fees
year Type A Type B Type C Type D Type E Type F
2007 96.22 0.99 1.75 0.29 0.24 0.51
2008 96.48 0.71 1.71 0.16 0.20 0.74
2009 96.69 0.66 1.31 0.09 0.37 0.88
2010 95.48 0.85 1.47 0.01 0.80 1.39
2011 95.05 0.82 1.26 0.01 1.11 1.76
2012 93.26 0.98 1.67 0.00 1.72 2.36
Total 95.50 0.84 1.53 0.09 0.75 1.28
Table 6
Transition matrix for different quote types
This table reports the estimated Markov chain transition matrix for the six types of synthetic and actual quote locations as described in Figure 1 in the full sample of 2007 to 2012. Synthetic ask (aski) and bid (bidi) are calculated as in Tables 2. Actual ask and bid prices are adjusted for security lending costs. Type A is when the synthetic ask is above the actual ask and the synthetic bid is below the actual bid. Type B is when the synthetic ask is above the actual ask and the synthetic bid is above the actual bid but below the actual ask. Type C is when the synthetic ask is below the actual ask but above the actual bid and the synthetic bid is below the actual bid. Type D is when the synthetic ask is below the actual ask and the synthetic bid is above the actual bid. Type E is an arbitrage opportunity when both the synthetic ask and bid are above the actual ask. Type F is an arbitrage opportunity when both the synthetic ask and bid are below the actual bid. The transition probabilities are estimated from day t − 1 to t.
t-1/t Type A Type B Type C Type D Type E Type F
Type A 97.22 0.80 1.04 0.08 0.39 0.47
Type B 68.52 11.56 7.68 0.59 6.85 4.79
Type C 70.49 6.14 12.23 0.50 3.56 7.08
Type D 79.18 5.33 8.51 3.79 1.03 2.15
Type E 41.11 8.93 5.62 0.15 37.98 6.21
Type F 54.73 6.34 12.50 0.30 6.57 19.56
Table 7
Arbitrage profits
This table reports the number of arbitrage opportunities and average arbitrage profit per share for Type E (when the synthetic bid is above the actual ask) in Panel A and for Type F (when the synthetic ask is below the actual bid) in Panel B for individual years as well as the full sample. The synthetic bid (bidi) and ask (aski) prices and the borrowing-cost adjusted bid (bida) and ask (aska) prices for arbitragers are calculated as in Tables 2. Columns (3) and (4) considers the commission the arbitrager pays to trade 10 lots of stocks and synthetic stocks. Columns (5) and (6) considers the commission the arbitrager pays to trade 1 lot only.
(1) (2) (3) (4) (5) (6)
Panel A: Type E arbitrage
Fee for 10 lots Fee for 1 lot
year N mean N mean N mean
2007 1,175 0.800 706 1.279 390 2.017
2008 840 0.267 452 0.440 160 0.859
2009 1,294 0.355 636 0.665 291 1.123
2010 3,062 0.311 1,188 0.740 479 1.483
2011 4,252 0.094 1,577 0.186 317 0.384
2012 6,384 0.330 2,898 0.667 1,147 1.332
Total 17,007 0.299 7,457 0.621 2,784 1.297
Panel B: Type F arbitrage
Fee for 10 lots Fee for 1 lot
year N mean N mean N mean
2007 1,070 0.123 557 0.180 113 0.331
2008 1,126 0.087 459 0.150 72 0.330
2009 1,408 0.043 298 0.112 32 0.318
2010 3,208 0.030 511 0.081 42 0.224
2011 4,138 0.040 926 0.089 74 0.326
2012 4,727 0.045 818 0.157 100 0.733
Total 15,677 0.049 3,569 0.128 433 0.411
Table 8
Determinants of the relative ask price
This table examines determinants of the relative ask price in the cross-section. The synthetic ask (aski) and borrowing-cost adjusted ask (aska) are the same as in Table 2. Reported are the coefficient estimates from daily Fama-MacBeth (1973) regressions of the relative ask defined as PD ask = aski/aska− 1 with t-statistics calculated using Newey-West (1980) standard errors. Spread is the percentage bid-ask spread of the underlying stock. Volatility is the standard deviation of daily stock returns in the past 21 trading days.
Vol ivol is the standard deviation of the average implied volatility of the at-the-money call and put option pair with 30 days to maturity using the past 21 trading days. Ownership is the institutional holding at the end of the previous quarter. OOI and SOI are the option delta imbalance and net stock order imbalance calculated as in Hu (2014). All variables are calculated on the same day except Ownership. All coefficients are multiplied by 100. ***,**, and * indicate statistical significance at the 1, 5, and 10% level, respectively.
variable (1) (2) (3) (4)
N per day 1305 1312 1312 1305
Table 9
Determinants of the relative bid price
This table examines determinants of the relative bid in the cross-section. The synthetic bid (bidi) and borrowing-cost adjusted bid (bida) are the same as in Table 2. Reported are the coefficient estimates from daily Fama-MacBeth (1973) regressions of the relative bid defined as PD bid = bidi/bida− 1 with t-statistics calculated using Newey-West (1980) standard errors. Spread is the percentage bid-ask spread of the underlying stock. Volatility is the standard deviation of daily stock returns in the past 21 trading days.
Vol ivol is the standard deviation of the average implied volatility of the at-the-money call and put option pair with 30 days to maturity using the past 21 trading days. Ownership is the institutional holding at the end of the previous quarter. OOI and SOI are the option delta imbalance and net stock order imbalance calculated as in Hu (2014). All variables are calculated on the same day except Ownership. All coefficients are multiplied by 100. ***,**, and * indicate statistical significance at the 1, 5, and 10% level, respectively.
variable (1) (2) (3) (4)
N per day 1305 1312 1312 1305
Figure 1
Types of actual and synthetic quote locations
This figure shows the six types of actual and synthetic quote locations. The synthetic bid and ask prices are constructed using a pair of closest-to-the-money call and options as follows:
bidi= (Bid Call − EEP Call) − (Ask Put − EEP Put) + PV (K) + PV (Div), aski= (Ask Call − EEP Call) − (Bid Put − EEP Put) + PV (K) + PV (Div),
where PV (K) is the present value of the strike price, EEP is the early exercise premium calculated as the difference between the actual midpoint of the option bid-ask prices and the Black-Scholes (1973) European option price, and Div is the present value of the announced dividends before the options maturity. For each underlying stock, only the closest-to-the-money option pair expiring in 10 to 40 days is chosen to calculate the synthetic stock prices every day. The borrowing-cost adjusted bid and ask prices are:
bida= bid ∗ (1 − lending f ee ∗ t0∗ exp(−r ∗ t)),
aska= ask ∗ (1 − utilization ∗ lending f ee ∗ t ∗ exp(−r ∗ t)),
where bid and ask are the close bid and ask prices in CRSP, utilization is the percentage of shares on loan relative to the total number of shares available for lending, lending f ee is the net stock borrowing cost in percentage, t is the time to expiration of the synthetic stock, t0 is t minus three days assuming short sellers deliver stocks three days after the transaction, and r is the risk-free rate of return.
Type A Type B
Type D Type E
Type C
Type F
Synthetic Ask Synthetic Bid Cash Ask Cash Bid