Introduction
On August 13th, most mortgage credit institutions in Denmark announced the issuance of fixed rate callable bond series with some form of an interest-only option.
Among the institutions the specific details of the contracts differ. For example, for the case of Realkredit Danmark (RD), the borrower will be able to freely choose 40 terms for a 30 year bond in which no scheduled repayments take place. While for example Nykredit (NYK) will only allow a window of no repayments in the first 10 years of the bond.
It is, however, generally believed in the market that the discount of these bonds compared to similar fixed rate callable bonds will be substantial, as much as DKK 2 pr. 100 nominal. For mortgagor having to choose which type of loan to finance a purchase with, this discount is likely to ensure that any mortgagor choosing such a loan will use it in a prudent fashion. This will make it more likely that the interest-only period will be fixed for long periods of time in stead of being used sporadically.
In contrast to the preliminary market sentiments our theoretical calculations, see below, based on a schedule of interest-only for the first 10 years indicate that the bond should have a discount of only 0.70.
Valuation
Implementing a model, taking into account optimal use of the, effectively, 40 options of the RD version is a cumbersome task, mainly because a non trivial path dependency is introduced. Further, such flexibility has not yet been allowed by the authorities. Additionally, issuers such as NYK only allow the borrower to choose a fixed period of no repayments.
To test these new bonds ScanRate has implemented a simple and efficient method. On an aggregate level we allow the user to designate a bond to have an interest-only period and set a time frame of the interest-only period. For example, for the NYK bond issued in October this could be January 2004 to January 2014.
This setup is in line with the contract terms of the proposed NYK bonds and, currently, also for RD given that it has not yet been allowed to obtain a loan with a completely free choice of interest-only terms.
The chosen setup also has the benefit of reflecting the data which is believed to become available upon issuance of the bonds, namely an aggregate cash flow which reflects the amount of loans in the series where the interest-only period is in effect.
Examples
In the following we will discuss valuation results for interest-only bonds in the context of the valuation method discussed above.
We will focus on the advertised RD 5'35 bond on the trade date 18th of August 2003 which will be valued in a standard setup, relying on the DMBS model provided by Reuters and ScanRate. For ease of exposition we shall assume that a newly issued bond will have exactly the same debtor distributions as the standard RD 5'35 bond.
All valuations are done on the swap curve and the term structure model is a CIR, calibrated to caps and swaptions. For point of reference, the standard fixed rate callable 5'35 bond of RD was traded at 95.9 18th of August, corresponding to an option adjusted spread of 33 bps. This spread is applied to the interest-only bond as well.
We shall assume that the interest-only bond has no repayments in the first 10 years.
The chart below illustrates how the model price (option adjusted present value), OAPV, responds to parallel shifts in the yield curve.
The red line is that of the standard fixed rate callable RD 5'35 bond, the green line is the OAPV for the bond with interest-only (IO) for the first 10 years. Finally the orange line, right axis, illustrates the difference between the two sets of OAPV's.
As can be seen, in this case, the OAPV is consistently lower for the interest-only bond, the difference being 0.70 for the current yield curve, rising to 2.2 for a parallel shift upwards of 1.8%.
For high interest rates we have, as expected, the largest effect, caused by the fact that in an environment of high interest rates, the investor only receives the, relatively low, interest rates and no repayments. Further, for an RD bond, a rational mortgagor would put the interest-only period in the first 10 years, and therefore the value of the bond in such a case would be similar to that shown in the figure above.
For low interest rates we also have a lower theoretical value for the interest-only bond. To understand this, suppose that the prepayments for the IO bond were identical to that of the standard bond. Due to the interest-only period we would then have that the theoretical value would be higher, as the coupon of the loan is far above market rates.
However, the prolonged payments along with low interest rates cause prepayments to increase, reducing the theoretical value to under that of the standard bond.
This is the effect one would experience for a bond similar to those issued by NYK. However, for the RD type the rational mortgagor will choose not to use the interest-only period, paying down the loan as normal or simply prepaying. This will cause the theoretical value to be very close to that of the standard bond. Hence, the currently chosen method will, for low interest rates, give a conservative estimate of the value of the interest-only bond where the interest-only periods can be chosen freely.
The chart below illustrates how the option adjusted duration (OAD) responds to parallel changes in the yield curve. The green curves are for the interest-only case while the red curves are for the standard case.
For shifts in the yield curve between -0.5% and upwards we experience an increase in the OAD with the introduction of the interest-only period, while the difference is negligible for more negative shifts. Evidently, the increased interest sensitivity is caused by the fact that for high interest rates there are no prepayments and with no repayments either, the present value of the cash flow responds more drastically to shifts in the yield curve.
Conclusion
To conclude, the NYK type bond can easily be valued in a simple extension of the current valuation framework. For the RD type bond the currently chosen method is believed to yield a conservative price estimate.