The Performance of Option Pricing Models Estimating the Marketability Discount in a Pre-IPO Real-World Data Setting: Evidence from Europe

Stefan O. Grbenic

doi:10.1515/jbvela-2021-0020

Published by De Gruyter February 28, 2022

The Performance of Option Pricing Models Estimating the Marketability Discount in a Pre-IPO Real-World Data Setting: Evidence from Europe

Stefan O. Grbenic

From the journal Journal of Business Valuation and Economic Loss Analysis

https://doi.org/10.1515/jbvela-2021-0020

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Abstract

Valuation analysts adjust prices of private firm’s stock downward from their fully marketable counterparts, reflecting the private firms’ lower level of marketability. This discount for lack of marketability can be substantial in magnitude. This study examines the performance (according to bias and accuracy employing estimation error methodology) of seven popular option pricing models in generating discount estimates to coincide with empirically observed discount benchmarks (based on the pre-IPO methodology) in European Union member countries over the period 2004 until 2018. The results allow for the general conclusion that some option pricing models are superior in most settings, coinciding with their individual benefits and deficiencies. The detailed analysis indicates that (i) the superiority of these option pricing models holds for a wide range of periods of assumed restricted marketability, (ii) segmenting discount benchmarks according to their size improves the performance of the option pricing models, (iii) segmenting discount benchmarks according to both, the underlying volatility of stock returns and dividend yields, does not improve the performance of the option pricing models, and (iv) IPO underperformance has no material impact on relative option pricing model’s performance.

Keywords: discount for lack of marketability; marketability discount; option pricing models; business valuation; private firms; valuation adjustments

Corresponding author: Stefan O. Grbenic, Graz University of Technology, Graz, Austria, E-mail: stefan.grbenic@tugraz.at

Appendix 1

Table 9:

DLOM expressed in terms of the underlying stock price of the put option.

OPM	Formula and notation
ATMEPOPM	Closed-form solution formula:
	D L O M i A T M E P O P M = 1 P i [ S i e − r i T N ( − φ i + σ i T ) − P i e − q i T N ( − φ i ) ]
	with φ i = l n ( P i S i ) + ( r i − q i + σ i 2 2 ) T σ i T
	where i is the index on the stocks related to DLOM observations, S_i is the strike (exercise) price of the put option, P_i is the current price of the underlying stock as on IPO date, r_i is the market interest rate as on IPO date, σ_i is the volatility of the underlying stock return, q_i is the dividend yield, T is the period of illiquidity indicating the period the stock is expected to remain non-marketable and, N() is the cumulative normal distribution function.

LPOPM	Closed-form solution formula:
	D L O M i L P O P M = 1 P i P i [ θ i ] with θ i = ( 2 + σ i 2 T 2 ) N ( σ i 2 T 2 ) + σ i 2 T 2 π e − σ i 2 T 8 − 1
	where i is the index on the stocks related to DLOM observations, P_i is the current price of the underlying stock as on IPO date, σ_i is the volatility of the underlying stock return, T is the period of illiquidity indicating the period the stock is expected to remain non-marketable and, N() is the cumulative normal distribution function.

ALPOPM	Closed-form solution formula:
	D L O M i A L P O P M = P i [ θ i ] 1 + P i [ θ i ] with θ i = ( 2 + σ i 2 T 2 ) N ( σ i 2 T 2 ) + σ i 2 T 2 π e − σ i 2 T 8 − 1
	where i is the index on the stocks related to DLOM observations, P_i is the current price of the underlying stock as on IPO date, σ_i is the volatility of the underlying stock return, T is the period of illiquidity indicating the period the stock is expected to remain non-marketable and, N() is the cumulative normal distribution function.

ASPOPM	Approximate closed-end analytical solution formula (since Asian put options have no closed-end solutions):
	D L O M i A S P O P M = 1 P i P i e − q i T [ N ( ϕ i ) − N ( − ϕ i ) ]
	with ϕ i = σ i 2 T + l n [ 2 ( e σ i 2 T − σ i 2 T − 1 ) ] − 2 l n ( e σ i 2 T − 1 ) 2
	where i is the index on the stocks related to DLOM observations, P_i is the current price of the underlying stock as on IPO date, q_i is the dividend yield of the underlying stock, σ_i is the volatility of the underlying stock return, T is the period of illiquidity indicating the period the stock is expected to remain non-marketable and, N() is the cumulative normal distribution function.

AAASPOPM	Approximate closed-end analytical solution formula (since Asian put options have no closed-end solutions):
	D L O M i A A A S P O P M = 1 P i P i e − q i T [ 2 N ( l n [ 2 ( e σ i 2 T − σ i 2 T − 1 ) ] − 2 l n ( e σ i 2 T ) 2 ) − 1 ]
	where i is the index on the stocks related to DLOM observations, P_i is the current price of the underlying stock as on IPO date, q_i is the dividend yield of the underlying stock, σ_i is the volatility of the underlying stock return, T is the period of illiquidity indicating the period the stock is expected to remain non-marketable and, N() is the cumulative normal distribution function.

FSPOPM	Closed-form solution formula:
	D L O M i F S P O P M = 1 P i e − q i T [ 2 N ( σ i T 2 ) − 1 ]
	where i is the index on the stocks related to DLOM observations, P_i is the current price of the underlying stock as on IPO date, q_i is the dividend yield of the underlying stock, σ_i is the volatility of the underlying stock return, T is the period of illiquidity indicating the period the stock is expected to remain non-marketable and, N() is the cumulative normal distribution function.

PEPOPM	Closed-form solution formula:
	D L O M i P E P O P M = 1 P i ( P i − ψ i − 1 2 ) ( − ψ i − 1 2 1 2 − ψ i ) ( 1 2 − ψ i ) with ψ i = 1 4 + 2 q i σ i 2
	where i is the index on the stocks related to DLOM observations, P_i is the current price of the underlying stock as on IPO date, q_i is the dividend yield of the underlying stock and, σ_i is the volatility of the underlying stock return.

Appendix 2

Table 10:

Performance of OPM estimating real-world DLOM benchmarks – test on statistical significance.

Panel A: test on bias
RAE:	ATMEPOPM	LPOPM	ALPOPM	ASPOPM	AAASPOPM	FSPOPM	PEPOPM
ATMEPOPM		–	–	−4.3226	−4.3226	−2.4827	–
				(0.0000)	(0.0000)	(0.0130)
LPOPM	−0.1975		−4.7292	−5.7493	−5.7493	−5.7493	−5.4948
	(0.8434)		(0.0000)	(0.0000)	(0.0000)	(0.0000)	(0.0000)
ALPOPM	−0.1975	–		−5.7493	−5.7493	−5.7493	–
	(0.8434)			(0.0000)	(0.0000)	(0.0000)
ASPOPM	–	–	–		–	−6.0053	–
						(0.0000)
AAASPOPM	–	–	–	−7.3151		−6.0053	–
				(0.0000)		(0.0000)
FSPOPM	–	–	–	–	–		–

PEPOPM	−2.4602	–	−1.2232	−1.6630	−1.6630	−1.6630
	(0.0139)		(0.2213)	(0.0963)	(0.0963)	(0.0963)

Panel B: test on accuracy
RLAE:	ATMEPOPM	LPOPM	ALPOPM	ASPOPM	AAASPOPM	FSPOPM	PEPOPM
ATMEPOPM		–	–	–	–	−0.5985	–
						(0.5495)
LPOPM	−0.6287		−4.7292	−6.0053	−6.0053	−8.3993	–
	(0.5295)		(0.0000)	(0.0000)	(0.0000)	(0.0000)
ALPOPM	−0.8403	–		−6.0053	−6.0053	−8.3993	–
	(0.4007)			(0.0000)	(0.0000)	(0.0000)
ASPOPM	−5.9186	–	–		–	−7.3151	–
	(0.0000)					(0.0000)
AAASPOPM	−5.9186	–	–	−7.3151		−7.3151	–
	(0.0000)			(0.0000)		(0.0000)
FSPOPM	–		–	–	–		–

PEPOPM	−2.4602	−0.6899	−0.6899	−4.0105	−4.0105	−5.0990
	(0.0139)	(0.4903)	(0.4903)	(0.0001)	(0.0001)	(0.0000)

RSE:	ATMEPOPM	LPOPM	ALPOPM	ASPOPM	AAASPOPM	FSPOPM	PEPOPM

ATMEPOPM		–	–	−4.3226	−4.3226	−2.4827	−4.6977
				(0.0000)	(0.0000)	(0.0130)	(0.0000)
LPOPM	−0.1975		−4.7292	−5.7493	−5.7493	−5.7493	−5.4948
	(0.8434)		(0.0000)	(0.0000)	(0.0000)	(0.0000)	(0.0000)
ALPOPM	−0.1975	–		−5.7493	−5.7493	−5.7493	−5.4948
	(0.8434)			(0.0000)	(0.0000)	(0.0000)	(0.0000)
ASPOPM	–	–	–		–	−6.0053	–
						(0.0000)
AAASPOPM	–	–	–	−7.3151		−6.0053	–
				(0.0000)		(0.0000)
FSPOPM	–	–	–	–	–		–

PEPOPM	–	–	–	−1.6630	−1.6630	−1.6630
				(0.0963)	(0.0963)	(0.0963)

RLPE:	ATMEPOPM	LPOPM	ALPOPM	ASPOPM	AAASPOPM	FSPOPM	PEPOPM

ATMEPOPM		–	−2.1004	−1.7529	−1.7529	−1.000	–
			(0.0357)	(0.0796)	(0.0796)	(0.3173)
LPOPM	−0.4201		−4.1973	−2.9341	−2.9341	−1.000	−2.8031
	(0.6744)		(0.0000)	(0.0033)	(0.0033)	(0.3173)	(0.0051)
ALPOPM	–	–		−2.9341	−2.9341	−1.000	–
				(0.0033)	(0.0033)	(0.3173)
ASPOPM	–	–	–		−2.9341	−1.000	–
					(0.0033)	(0.3173)
AAASPOPM	–	–	–	–		−1.000	–
						(0.3173)
FSPOPM	–	–	–	–	–		–

PEPOPM	−1.2741	–	−2.8031	−2.0226	−2.0226	−0.4472
	(0.2026)		(0.0051)	(0.0431)	(0.0431)	(0.6547)

Statistical significance is measured employing the two-tailed Wilcoxon signed rank test (using the normal approximation for large samples). Z-values are reported without brackets, p-values in brackets. Panel A reports the results on the test on bias, panel B on the test on accuracy.

References

Abbott, A. 2009. “Discount for Lack of Liquidity: Understanding and Interpreting Option Models.” Business Valuation Review 28 (3): 144–8, https://doi.org/10.5791/0882-2875-28.3.144.Search in Google Scholar

Akerlof, G. A. 1970. “The Market for “Lemons”: Quality Uncertainty and the Market Mechanism.” The Quarterly Journal of Economics 84 (3): 488–500, https://doi.org/10.2307/1879431.Search in Google Scholar

Bajaj, B., D. J. Denis, S. P. Ferris, and A. Sarin. 2001. “Firm Value and Marketability Discounts.” Journal of Corporation Law 27 (1): 89–115.10.2139/ssrn.262198Search in Google Scholar

Baker, M., and R. S. Ruback. 1999. “Estimating Industry Multiples.” In Harvard University Research Paper, 1–30. Cambridge, Massachusetts, USA.Search in Google Scholar

Barber, B. M., and T. Odean. 2000. “Trading is Hazardous to Your Wealth: The Common Stock Investment Performance of Individual Investors.” The Journal of Finance 55 (2): 773–806, https://doi.org/10.1111/0022-1082.00226.Search in Google Scholar

Bartholdy, J., D. Olson, and P. Peare. 2007. “Conducting Event Studies on a Small Stock Exchange.” The European Journal of Finance 13 (3): 227–52.10.1080/13518470600880176Search in Google Scholar

Beatty, R. P., S. M. Riffe, and R. Thompson. 1999. “The Method of Comparables and Tax Court Valuations of Private Firms: An Empirical Investigation.” Accounting Horizons 13 (2): 177–99, https://doi.org/10.2308/acch.1999.13.3.177.Search in Google Scholar

Bhojraj, S., and C. M. C. Lee. 2002. “Who is My Peer? A Valuation-Based Approach to the Selection of Comparable Firms.” Journal of Accounting Research 40 (2): 407–39.10.1111/1475-679X.00054Search in Google Scholar

Bowie, D. C., and D. J. Bradfield. 1993. “A Review of Systematic Risk Estimation on the JSE.” De Ratione 7 (1): 6–22, https://doi.org/10.1080/10108270.1993.11435038.Search in Google Scholar

Chaffee, D. B. H. 1993. “Option Pricing as a Proxy for Discount for Lack of Marketability in Private Company Valuation.” Business Valuation Review 12 (4): 182–8, https://doi.org/10.5791/0882-2875-12.4.182.Search in Google Scholar

Chen, L. H., E. A. Dyl, G. J. Jiang, and J. A. Juneja. 2015. “Risk, Illiquidity or Marketability: What Matters for Discounts on Private Equity Placements?” Journal of Banking and Finance 57: 41–50, https://doi.org/10.1016/j.jbankfin.2015.03.009.Search in Google Scholar

Chullen, A., H. Kaltenbrunner, and B. Schwetzler. 2015. “Does Consistency Improve Accuracy in Multiple-Based Valuation?” Journal of Business Economics 85: 635–62.10.1007/s11573-015-0768-2Search in Google Scholar

Clarke, J., C. Dunbar, and K. M. Kahle. 2001. “Long-Run Performance and Insider Trading in Completed and Canceled Seasoned Equity Offerings.” Journal of Financial and Quantitative Analysis 36 (4): 415–30, https://doi.org/10.2307/2676218.Search in Google Scholar

Cohen, L., C. Malloy, and L. Pomorski. 2012. “Decoding Inside Information.” The Journal of Finance 67 (3): 1009–43, https://doi.org/10.1111/j.1540-6261.2012.01740.x.Search in Google Scholar

Degryse, H., F. De Jong, and J. Lefebvre. 2009. “An Empirical Analysis of Legal Insider Trading in the Netherlands.” In Tilburg University CESIFO Working Paper No. 2687, 1–52. Tilbourg, Netherlands.10.2139/ssrn.1430283Search in Google Scholar

Del Brio, E. B., A. Miguel, and J. Perote. 2002. “An Investigation of Insider Trading Profits in the Spanish Stock Market.” The Quarterly Review of Economics and Finance 42 (1): 73–94, https://doi.org/10.1016/s1062-9769(01)00103-x.Search in Google Scholar

Dimson, E., and P. Marsh. 1983. “The Stability of UK Risk Measures and the Problem of Thin-Trading.” The Journal of Finance 38 (3): 753–83.10.1111/j.1540-6261.1983.tb02500.xSearch in Google Scholar

Dittmann, I., and E. Maug. 2008. “Biases and Error Measures: How to Compare Valuation Methods.” In Working Paper, 1–39. SSRN.947436.10.2139/ssrn.947436Search in Google Scholar

Duffy, R. 2011. “Why Finnerty’s Put Option Model is the DLOM Model of Choice.” Financial Valuation Litigation Expert 32: 40–1.Search in Google Scholar

Dymke, B. M., and A. Walter. 2008. “Insider Trading in Germany – Do Corporate Insiders Exploit inside Information?” Business Research 1 (2): 188–205.10.1007/BF03343533Search in Google Scholar

Finnerty, J. D. 2012. “An Average-Strike Put Option Model of the Marketability Discount.” The Journal of Derivatives 9 (24): 53–69, https://doi.org/10.3905/jod.2012.19.4.053.Search in Google Scholar

Finnerty, J. D. 2013. “Using Put Option-Based DLOM Models to Estimate Discounts for Lack of Marketability.” Business Valuation Review 32 (4): 165–70, https://doi.org/10.5791/13-00001.1.Search in Google Scholar

Finnerty, J. E. 1976. “Insiders and Market Efficiency.” The Journal of Finance 31 (4): 1141–8, https://doi.org/10.1111/j.1540-6261.1976.tb01965.x.Search in Google Scholar

Fishman, J. E., and L. Barenbaum. 2013. “Do Put Option Models Overstate Discounts for Lack of Marketability.” Financial Valuation and Litigation Expert 42: 9–11.Search in Google Scholar

Ghaidarov, S. 2009. “Analysis and Critique of the Average Strike Put Option Marketability Discount Model.” In White Paper, 1–15.10.2139/ssrn.1478266Search in Google Scholar

Ghaidarov, S. 2010. “The Cost of Illiquidity for Private Equity Investments.” In Working Paper, 1–28.10.2139/ssrn.1525666Search in Google Scholar

Ghaidarov, S. 2014. “Analytical Bound on the Cost of Illiquidity for Equity Securities Subject to Sale Restrictions.” The Journal of Derivatives 21 (4): 31–48.10.3905/jod.2014.21.4.031Search in Google Scholar

Gilson, S. C., E. S. Hotchkiss, and R. S. Ruback. 2000. “Valuation of Bankrupt Firms.” The Review of Financial Studies 13 (1): 43–74, https://doi.org/10.1093/rfs/13.1.43.Search in Google Scholar

Graham, J. R., and C. R. Harvey. 1996. “Market Timing Ability and Volatility Implied in Investment Newsletters’ Asset Allocation Recommendations.” Journal of Financial Economics 42 (3): 397–421, https://doi.org/10.1016/0304-405x(96)00878-1.Search in Google Scholar

Gregory, A., J. Matako, I. Tonks, and R. Purkis. 1994. “UK Directors’ Trading: The Impact of Dealings in Smaller Firms.” The Economic Journal 104 (422): 37–53.10.2307/2234673Search in Google Scholar

Henschke, S., and C. Homburg. 2009. “Equity Valuation Using Multiples: Controlling for Differences Amongst Peers.” In Working Paper, 1–38. Cologne, Germany.10.2139/ssrn.1270812Search in Google Scholar

Herrmann, V., and F. Richter. 2003. “Pricing with Performance-Controlled Multiples.” Schmalenbach Business Review 55: 194–219.10.1007/BF03396674Search in Google Scholar

Hertzel, M., and R. L. Smith. 1993. “Market Discounts and Shareholder Gains for Placing Equity Privately.” The Journal of Finance 48 (2): 459–69.10.1111/j.1540-6261.1993.tb04723.xSearch in Google Scholar

Jaffe, J. F. 1974. “Special Information and Insider Trading.” Journal of Business 47 (3): 410–28, https://doi.org/10.1086/295655.Search in Google Scholar

Kahl, M., J. Liu, and F. A. Longstaff. 2003. “Paper Millionaires: How Valuable is Stock to a Stockholder Who is Restricted from Selling it?” Journal of Financial Economics 67 (3): 385–410.10.3386/w8969Search in Google Scholar

Kahle, K. M. 2000. “Insider Trading and the Long-Run Performance of New Security Issues.” Journal of Corporate Finance 6 (1): 25–53, https://doi.org/10.1016/s0929-1199(99)00015-2.Search in Google Scholar

Kaplan, S. N., and R. S. Ruback. 1995. “The Valuation of Cash Flow Forecasts: An Empirical Analysis.” The Journal of Finance 50 (4): 1059–93, https://doi.org/10.1111/j.1540-6261.1995.tb04050.x.Search in Google Scholar

Kim, M., and J. R. Ritter. 1999. “Valuing IPOs.” Journal of Financial Economics 53 (3): 409–37, https://doi.org/10.1016/s0304-405x(99)00027-6.Search in Google Scholar

Kumar Garg, A., and K. Kumar. 2014. “Option Pricing Models of Private Equity Valuation: A Comparative Analysis.” The IUP Journal of Applied Finance 20 (3): 28–40.Search in Google Scholar

LeClair, M. S. 1990. “Valuing the Closely-Held Corporation: The Validity and Performance of Established Valuation Procedures.” Accounting Horizons 4 (3): 31–42.Search in Google Scholar

Lerch, M. A. 2000. “Measuring Lack of Marketability Discounts from IPO Pricing – The Graphic Approach. IPO Data: November 1995 – April 1997.” Business Valuation Review 19 (2): 70–9, https://doi.org/10.5791/0882-2875-19.2.70.Search in Google Scholar

Lerch, M. A. 2003. “The Graphic Measurement of Marketability Discounts from IPOs on Common Stocks – June 1997 Through March 2000.” Business Valuation Review 22 (2): 77–89, https://doi.org/10.5791/0882-2875-22.2.77.Search in Google Scholar

Lie, E., and H. J. Lie. 2002. “Multiples Used to Estimate Corporate Value.” Financial Analysts Journal 58 (2): 44–54.10.2469/faj.v58.n2.2522Search in Google Scholar

Liu, J., D. Nissim, and J. Thomas. 2002. “Equity Valuation Using Multiples.” Journal of Accounting Research 40 (1): 135–72, https://doi.org/10.1111/1475-679x.00042.Search in Google Scholar

Longstaff, F. A. 1995. “How Much Can Marketability Affect Security Values?” The Journal of Finance 50 (5): 1767–74, https://doi.org/10.1111/j.1540-6261.1995.tb05197.x.Search in Google Scholar

Loughran, T., and J. Ritter. 2004. “Why Has IPO Underpricing Changed Over Time?” Financial Management 33 (3): 5–35.10.2139/ssrn.331780Search in Google Scholar

Luoma, M., T. Martikainen, J. Perttunen, and S. Pynnonen. 1994. “Different Beta Estimation Techniques in Infrequently Traded and Inefficient Stock Markets.” Omega International Journal of Management Science 22 (5): 471–6.10.1016/0305-0483(94)90028-0Search in Google Scholar

Maynes, E., and J. Rumsey. 1993. “Conducting Event Studies with Thinly Traded Stocks.” Journal of Banking and Finance 17 (1): 145–57.10.1016/0378-4266(93)90085-RSearch in Google Scholar

McClelland, D. E., C. J. Auret, and T. K. Wright. 2014. “Thin-Trading and Beta Estimation: Results from a Simulated Environment.” Journal of Studies in Economics and Econometrics 38 (2): 19–31, https://doi.org/10.1080/10800379.2014.12097265.Search in Google Scholar

Myers, S. C., and N. S. Majluf. 1984. “Corporate Financing and Investment Decisions When Firms Have Information that Investors Do Not Have.” Journal of Financial Economics 13 (2): 187–221, https://doi.org/10.1016/0304-405x(84)90023-0.Search in Google Scholar

Paulsen, J. 1998. “More Evidence on IPO Marketability Discounts.” Business Valuation Review 17 (1): 10–2.10.5791/0882-2875-17.1.10Search in Google Scholar

Paulsen, J. 2001. “Marketability Discount Concerns.” Business Valuation Review 20 (1): 24–6.10.5791/0882-2875-20.1.24Search in Google Scholar

Reilly, R., and A. Rotkowski. 2007. “The Discount for Lack of Marketability: Update on Current Studies and Analysis of Current Controversies.” Tax Lawyer 61 (1): 241–86.Search in Google Scholar

Robak, E. 2007. “Lemons or Lemonade? A Fresh Look at Restricted Stock Discounts.” Valuation Strategies 13 (1): 5–15.Search in Google Scholar

Rotkowski, A. M., and M. A. Harter. 2013. “Current Controversies Regarding Option Pricing Models.” Insights: 25–34.Search in Google Scholar

Rozeff, M. S., and M. A. Zaman. 1988. “Market Efficiency and Insider Trading: New Evidence.” Journal of Business 61: 25–44, https://doi.org/10.1086/296418.Search in Google Scholar

Serra, R. G., and R. Martelanc. 2013. “Estimation of Betas of Stocks with Low Liquidity.” Brazilian Business Review 10 (1): 49–78, https://doi.org/10.15728/bbr.2013.10.1.3.Search in Google Scholar

Sommer, F., and A. Wöhrmann. 2011. “Triangulating the Accuracy of Comparable Company Valuations: A Multidimensional Analysis Considering Interaction Effects.” In Working Paper, 1–42. Muenster, Germany.10.2139/ssrn.2360077Search in Google Scholar

Sommer, F., C. Rose, and A. Wöhrmann. 2014. “Negative Value Indicators in Relative Valuation – An Empirical Perspective.” Journal of Business Valuation and Economic Loss Analysis 9 (1): 23–54.10.1515/jbvela-2013-0024Search in Google Scholar

Stockdale, J. J. 2008. “A Test of DLOM Computational Models.” Business Valuation Review 27 (3): 131–7, https://doi.org/10.5791/0882-2875-27.3.131.Search in Google Scholar

Von Helfenstein, S. 2017. “Option Pricing Models and the DLOM: Why OPMs are Not a Silver Bullet.” The Value Examiner 2017 (5): 18–23.Search in Google Scholar

Walling, J., and C. Moore. 2010. “Does Black Scholes Overvalue Early Stage Company Allocations?” Business Valuation Update 2000 (1): 1–6.Search in Google Scholar

Wisniewski, T. P., and M. T. Bohl. 2005. “The Information Content of Registered Insider Trading Under Lax Law Enforcement.” International Review of Law and Economics 25 (2): 169–85, https://doi.org/10.1016/j.irle.2005.06.002.Search in Google Scholar

Received: 2021-12-12

Accepted: 2022-02-02

Published Online: 2022-02-28

The Performance of Option Pricing Models Estimating the Marketability Discount in a Pre-IPO Real-World Data Setting: Evidence from Europe

Abstract

References

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