Options Embedded in Convertible Bonds versus Exchange Traded Options: Do their Implied Volatilities Differ?

Abstract

A convertible bond consists of a straight bond and an underlying stock option. Conventionally, its value is measured by adding up the values of these two components. The option value is calculated using the Black-Scholes-Merton model with an assumption that stock volatility is of the same level as the one used to price the exchange traded option. However, this paper aims to ascertain that the volatility between the two models could in fact be different since the perceptions of firm agents and market participants toward the option differ. The paper concludes that in the United States, the volatility of embedded options is significantly lower than the volatility of Exchange Traded Options. Additionally, using growth perspective, size, maturity, default probability, cost of debt, coupon rates, and financial health as control variables, abnormal volatilities are observed with statistical significance. This observation shows that institutional investors could seize arbitrage profits from this imparity.