Bond instrument accrued interest

Convertible instruments are usually issued with attached call or put options. Such features can be implemented into the valuation model. If a soft call feature has been implemented, it enables the issuer to force the conversion when the share price overcomes a percentage or trigger level above the conversion price. However, this option cannot be called in the first years hard call . Differently, after the protection period, the issuer can exercise the option. This second time is referred to soft call . Using the same example shown in Section 9.3.1, we assume that the bond may be redeemed in whole but not in part at their principal amount plus accrued interest on the last 2 years, in which the maturity date is at 20 February 2019. On and after this call date , if the share price exceeds 130% of the conversion price the issuer can force the conversion. Figure 9.23 shows the stock price tree in which at years 4 and 5 the stock price is above the threshold. 

The reverse convertible bonds have increased popularity in Europe and United States. This type of instrument gives to the issuer (not the bondholder) at maturity the right to exchange the bond into shares or to redeem it at par value plus accrued interests. In the first case, the bond is exchanged if the share price is less than conversion price, or if the conversion value is less than par value. Conversely, the issuer can redeem the bond. They typically have a domestic stock as underlying security, but they can also include foreign shares and indexes. 

In the event of a default, there will be no payment of accrued interest by the issuer since generally coupons are not recoverable, so we can ignore that aspect of the valnation. The only component left to the bond is its value upon a default or its recovery value. If a default occurs, the bondholder will lose all future cash flows of the instrument (i.e., they are at risk), but will be left with a nonperforming asset worth R. The same technique is used here as in the default swap—except this time the payout is R rather than 1 - R upon default. Conveniently, this formula is identical to equation (22.11), except that the term (1 - R) is replaced by R. 

The left side of equation (16.6) is the bond s market price broken into clean price plus accrued interest, as it was in (16.4). In fact, it can be shown that rmu is identical to the initial yield in (16.4), mt. The value of % that results in a stable future bond value is the Macaulay duration. At this point, assuming the existence of only one, parallel yield shift, a change in yield will not impact the future value of the bond. The bond s cash flows are immunized, and the instrument can be used to match a liability existing on that date. 

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See also in sourсe #XX -- [ , ]

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