Callable bond

A callable bond , also called a bond at notice , is a bond in which either the issuer or the creditor is granted the right to terminate .

Issuer termination right

If the bond has a debtor termination right, the issuer is entitled to redeem the bond early; in economic terms, this right corresponds to a purchase option .

The right of termination is usually only granted for certain points in time - for example for all coupon dates.

Termination decision

Early termination of the bond is attractive for the issuer if the issuer can refinance more cheaply on the market - essentially when the market interest rate for the remaining term is lower than the bond yield.

Duplication

To this end, two bonds with the same coupon as the callable bond are considered.

Worst case return

A calculation of the effective interest rate is not possible due to the case distinction. Therefore, one avails oneself with the key figure yield in the worst case (English yield to worst case ).

To determine the return (from the perspective of the creditor) one starts with the consideration of when the issuer would terminate if he had to make a decision today. The prerequisite for the invoice is that a market price for the callable bond is known. The possible returns for all possible scenarios are then calculated and sorted. The lowest value is the worst case return.

Two cases can be distinguished for the sake of simplicity. The amount of the return is determined by two factors:

coupon
Discount or premium , spread over the term.

A discount increases the returns and a premium reduces them. This second component becomes smaller and smaller as the remaining term increases. Thus, with a discount (rate <100) the return in the worst case corresponds to the return without termination and with a premium (rate> 100) the return on termination at the next possible date.

The yield in the worst case , the effective interest rate, assuming a termination in : : If the price of the callable bond under par is : ${\ displaystyle T_ {i}}$ ${\ displaystyle y (T-1), y (T_ {2}), ..., y (T_ {n})}$ ${\ displaystyle (K <100)}$

${\ displaystyle \ y (T-1)> y (T_ {2})> ...> y (T_ {n})}$

Right to give notice of creditors

If the bond has a creditor's right of termination, the creditor is entitled to redeem the bond early. Such a right of termination is usually only granted for certain points in time - for example for all coupon dates.

The price is above the law of the two reference bonds. It is exactly the reverse case of the issuer's right of termination.

Duration of a callable bond

The duration of a callable bond can be calculated by specifying the likelihood of termination. In the simplest case, when only a single termination date has been agreed, the duration can be calculated as (1 probability of termination) * remaining term .

interpretation

A two-year termination bond, which is equipped with an issuer call rights after one year, can be used both as a coupon bond with put option (put) as well as a coupon bond with purchase option interpret (call).

The right of termination is:

Firstly, the right to buy the underlying coupon bond at the base price after one year . This short right together with a two-year coupon bond results in the termination bond.
On the other hand, the right to sell a coupon bond with a term of t = 2 for 100 after one year. This is a put option. This short right together with a one-year coupon bond results in the termination bond. If the option right is not exercised, the coupon bond runs for one year. When exercising the put option, however, there is a two-year term.