Many corporate bonds are issued with a call feature, meaning the issuer has the right to redeem the bond early, typically at a predefined price.

In effect, the issuer has a call option on the bond with the predefined call price as the strike price.

This early repayment option is advantageous for issuers, especially if interest rates fall, allowing them to refinance at a lower cost.

Since this call right has value for the issuer, the investor who is effectively selling the option to the issuer by buying the callable bond should be compensated if the call option is exercised.

When interest rates have fallen, the investor will be forced to reinvest the proceeds at a lower interest rate than they were getting on the bond to provide compensation for this callable bonds are generally priced lower than comparable non callable bonds and offer higher yields as investors demand additional returns for taking on the potential downside of the bond being called in early.

Let's examine the additional risks that callable bond investors face in addition to the reinvestment risk they face, there is also a limit on the price appreciation of the bon as interest rates fall. For an ordinary bond, as rates fall, the bond price goes up, but the price at which the bond can be called acts as an upper limit for a callable bond, since no one will buy a bond for more than it could be called that in the future.

In addition, from the investor's perspective, buying a callable bond means taking on a short position in the option embedded in the bond.

This short position contributes to what we call negative convexity.

As rates fall, the price of the callable bond rises less than a non callable bond would, and if rates rise, the callable bonds price will fall in line with irregular bond.

This negative convexity is one reason investors receive a higher return as they're compensated with regular coupon payments, plus the option income for effectively selling the call option to the issuer.

Callable bonds come with different types of call options, depending on how often the issuer is allowed to redeem the bond before its final maturity.

Broadly, we can categorize these into single callable and multi-callable bonds.

Starting with single callable bonds, these bonds can only be called at one specific point in time.

For instance, a 10 year bond that's single callable in five years means the issuer has just One opportunity at the five-year mark to redeem the bond early.

If they don't exercise this option, the bond continues to maturity and there won't be another opportunity to call it before the maturity date another five years later.

This setup is similar to a European style option where there is only one possible exercise date.

Multi callable bonds allow the issuer more flexibility.

These bonds can be called at a range of specific dates.

Typically, after an initial no call period, a no call period is a set time during which the issuer is prohibited from calling the bond.

For example, a 10 year bond might offer annual call rights after a five year no call period, allowing the issuer to redeem the bond on any of these predefined dates after the no call period ends.

This setup is comparable to a Bermudan-style option, which can be exercised on multiple dates for investors.

Multi callable bonds add additional uncertainty about the bond's life because the issuer has multiple opportunities to call it often, depending on interest rate movements.

This flexibility generally results in multi callable bonds, offering a higher yield or price discount compared to single callable bonds, to compensate investors for the increased call risk.