Option-like Securities — Callable Bonds, Convertible Securities, and Warrants

Some securities have option-like qualities: callable bonds, convertible securities, and warrants. This similarity to options allows option-like securities to be priced or valued using the methods of valuing options.

Callable Bonds

Callable bonds are bonds that can be called by the issuer after a specified duration — the call protection period — at a specified price — the call price — which is usually higher than the bond's face value. The call price is highest in the 1st year when the bond can be called, and decreases as the time to maturity decreases. Bond issuers issue callable bonds to take advantage of possible decreases in future interest rates, but they must pay the bond buyer a higher coupon rate to compensate for the call risk to the bondholder that the bond may be called early. Bonds are called when interest rates decline, and, thus, the bondholder not only loses the interest that the bond was paying, but also the capital appreciation of increased bond prices, which are capped at the call price. Moreover, the bondholder will not be able to invest in another bond paying the same interest rate for the same credit risk — what is called reinvestment risk.

When interest rates decline, straight bond prices increase, but callable
bonds are capped at the call price, because the issuer will call the bond and issue new bonds with a lower coupon rate.
Graph of callable bond prices versus straight bond prices.

So how does a bond issuer price a callable bond? A callable bond is a straight bond with a call option from the bondholder. The call option has value to the issuer, and so, the issuer must compensate the bondholder for the call feature. Calculating the bond call option, however, is more complicated than with listed call options, because the call cannot be exercised until after the call protection period has ended, and the price paid diminishes as the time to maturity decreases.

Convertible Securities

Convertible bonds and convertible preferred stock allow the holders of these securities to convert the security into the common stock of the issuing company. Because the convertibility has value, the issuer receives a higher price for its bonds, allowing it to pay lower yields. Convertible securities are characterized by either specifying the conversion ratio explicitly or by specifying the conversion price in the bond indenture. The conversion ratio is the number of shares of stock that can be converted for each convertible security. As another way to calculate the conversion ratio, the conversion price is the specified stock price used in determining the conversion ratio.

Example: How to Determine the Number of Converted Shares of Stock Based on a Conversion Ratio or a Conversion Price

The conversion price is specified before the convertible security is issued, and is always higher than the market value of the stock on the date of issue; otherwise, bond buyers would immediately convert their bonds into stock, thereby defeating the purpose of issuing the security in the 1st place. The current stock price determines whether the convertible security will be converted or not. Most convertibles are issued deep out of the money, so the stock must appreciate considerably before it would be profitable to convert. The conversion value is the value received if the convertible was converted into stock.

The convertible bond is more valuable than a straight bond, because the convertible can be considered to consist of 2 securities — the straight bond and a call option to buy company stock for the conversion price. If the stock price is below the conversion price, then the option only has time value, making the convertible bond only a little more valuable than the straight bond. As the stock price increases, the call option becomes more valuable. As the stock price increases above the conversion price, the bond price moves proportionately higher. The convertible bond value always slightly exceeds the conversion value, because the bond provides some protection against a stock price decline. If the stock declines below the conversion value, then the bond still has worth as a straight bond. Thus, a convertible security is like owning the stock with a protective put that has a strike price of the straight bond. Note, also, that a stock price above the conversion price will be a major determinant of the bond's price, and will lower the yield-to-maturity rate on the bond as the bond's value increases with the stock price.

When the stock is near zero, its bonds are also near zero because of the danger that it will go bankrupt. As the stock price increases, the straight bond's price quickly reaches a peak, but the convertible bond price
continues to increase with the stock price.
Graph of convertible bond value compared to the stock price and a straight bond.

However, the value of the call feature of convertibles is difficult to calculate because the stock may have paid dividends during the life of the convertible, the conversion price might rise at specified times, and most convertibles are callable. A forced conversion occurs when the company issues a call on the convertible when the conversion price is below the stock price. The bondholders have about a month to convert, so if the current stock price is higher than the conversion price, the bondholder will convert the bond to stock for an immediate profit.


Warrants, also called subscription warrants or stock-purchase warrants, are call options written by a company to buy its common stock at a specified price, usually within a specified time, although perpetual warrants have no expiration date. The money paid by the initial warrant buyer goes directly to the company as well as the money paid to exercise the warrant to receive company stock. When the warrant is exercised, the company must issue new shares of stock, increasing the number of shares outstanding. These new shares are accounted for in financial reports as fully diluted earnings per share, which is what the earnings per share would be if all warrants were exercised and all convertible securities outstanding were converted.

The terms of the warrant are determined by the needs of the company, and, thus, are not standardized like listed options, but warrants are adjusted for stock splits and stock dividends. Warrants are frequently issued attached to bonds or preferred stock to reduce the interest or the dividends that must be paid to sell these securities. However, these warrants are detachable — thus, they are called detachable warrants — and can be traded independently of the attached security. Stock options issued by companies for employees are usually warrants.