How Do Options Add Value? Evidence from the Convertible Bond Market

January 23, 2023

How Do Options Add Value? Evidence from the Convertible Bond Market
Inmoo Lee, Rex Wang Renjie, Patrick Verwijmeren
Review of Finance, Volume 27, Issue 1, February 2023, Pages 189–222,

In this paper, we study whether options add value to issuers of underlying stocks in the context of convertible bond issues. Convertible bonds provide an interesting empirical setting to study the role of options because pricing convertibles requires essentially the same set of information necessary to price options. If the options market provides additional information that is useful in pricing convertibles (e.g., implied volatilities) and convertible bond issuers and investors actively utilize it, the availability of listed options will reduce adverse selection problems and affect convertible bond valuation.

We collect a sample of 1,357 convertible bond offerings issued by 815 unique U.S. public firms. Consistent with prior studies, convertible bonds in our sample are offered at significant discounts. We find that the offering discount from issues with listed options is about 26% smaller relative to issues without options. Of course, option exchanges do not randomly select underlying stocks for individual stock option listing. The smaller discount for issues with listed options could be due to unobserved factors that simultaneously influence the availability of options and the pricing of convertible bonds. To address this concern, our main conclusions are based on analyses that exploit the Securities and Exchange Commission’s minimum stock price requirement for option listing. This ad hoc price cutoff creates a discontinuity in the likelihood of option listing.

Using the distance between an issuer’s average stock price and the cutoff price as the forcing variable, we employ a fuzzy regression discontinuity design. We find that the likelihood of option listing increases from below 30% to above 50% as soon as the forcing variable passes the threshold. We then use this listing eligibility as an instrumental variable for the availability of options and estimate two-stage least squares (2SLS) regressions controlling for the forcing variable and other firm characteristics. The 2SLS results indicate that the availability of listed options significantly reduces convertible bond underpricing after addressing concerns regarding the endogeneity of option listing decisions.

We further investigate through which channels options affect the convertible market and find evidence of both information- and hedging-related channels. The relation between the availability of options and offering discounts is stronger when the information environment of issuers is poor. Transaction prices of convertible bonds with listed options also converge more quickly to their theoretical prices in the years after issuance, which is in line with a continuing provision of implied volatility estimates through option prices. Moreover, the availability of options significantly increases the number of convertible bond buyers. The increase in demand comes from both hedge funds who can use options to implement convertible arbitrage strategies and long-only institutional investors who benefit from the information provided by options.

Overall, our findings accord with the notion that individual stock options enable issuers of underlying stocks to attract more capital suppliers when they issue convertible bonds through both an improved information environment and a facilitation of arbitrage strategies.