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Key words: bond, pricing, eurobond, yield, foreign currency, cash flow conversion, curves, FX, forwards, swap, interest rate, fixed income
Pricing domestic & eurobond issues using bond, swap & FX curves

A typical objective in Debt Capital Markets (DCM) is to identify the cost of borrowings (i.e. coupon level) for corporate clients or oneself in multiple geographies.
This article describes a straightforward approach to deriving indicative coupon rates of bonds denominated in domestic and foreign currencies.
Over the past couple of decades Emerging Markets (EM) have played a large role in DCM due to strong interest in high yields.
Why are these yields higher? Well, there can be several factors: political risk, credit risk, inflation expectations etc.
Let’s have a look at a step-by-step derivation of the yield equivalents.

First we require the borrower’s domestic yield curve.
This can be achieved if the entity has enough issues at different tenors.
If the entity has only 2 – 3 actively traded bonds, then we should look for more peer companies with the same credit rating and from the same industry and make all necessary considerations when selecting the bonds and fitting the curve (see article on yield curve construction).
After the curve is ready, we can extrapolate it to whichever tenor we are interested in.
Our next step is to generate a table with yields at standardized tenors (1Y, 2Y, 5Y, etc.) – these are the indicative offering rates at which the borrowing entity can issue debt denominated in its native currency.
With an issue price of 100 the obtained rates can be used for further book building and price guidance stages in the origination process.
But if you are interested in identifying the equivalent yields in foreign currency, the following steps are required.

Our next objective is to choose the currency of the prospective eurobond issue and obtain a forward curve so that the projected cash flows could be converted from the domestic currency.
But there can be 2 problems at this stage:
1) the domestic market (especially EM) can have short forward curves;
2) absence of cross currency swaps (CCS) or forwards for most FX pairs. Dealing with these issues is quite simple.

For problem 1 let’s look at the example of the Russian USD/RUB forward curve, which has tenors up to 1 year.
We can derive implied forwards from the bootstrapped swap (IRS) curve by using the following formula:

In the equation above rRUB and rUSD are the interpolated swap rates at time t and Δt represents the tenor in years (for details on FX quotations please see our previous article).
As a result we can get an extrapolated FX forward curve that reflects the implied market expectations.

Problem 2 is solved by using USD as a proxy for converting into other currencies.
Thus we obtain the forward FX rates, and can now use them to convert bond cash flows from one currency into another.
As we have discussed that the bond curve rates can be treated as indicative coupons at various tenors, generating the cash flows should not be a problem.
In the case of a RUB denominated bond, we divide each payment by the respective interpolated forward FX rate.
As soon as the conversion is complete, the cash flows should be discounted conventionally using a new YTM.
Note that if coupons are paid semiannually, we will get a semi-bond interest rate (S/B).
It can be easily converted into an annualized yield (annual money or A/M), which are widely compared in DCM practice. Just apply the following formula:

The annualized and semi-bond yields will provide the borrowers with the indication of what they should expect from issuing bonds both locally and globally in the eurobond market.
Below is a screenshot of a typical DCM pricing sheet.

Data source: Thomson Reuters, calculations done by author.

The initial yield curve above was created from domestic government bonds denominated in RUB, and since the majority of bonds have semi-annual coupons, the original output rates are given as S/B.
For demonstration purposes I have added adjustment spreads (in basis points) at tenors 2 – 10.
It is a common practice for DCM analysts to tweak the curve data this way.
This can happen, for example, when there is a need to invoke a premium or a discount.
The annual money equivalent is provided in order to stress the return investors would be making provided there is no reinvestment of the coupon payment, and it makes our calculations comparable with annualized deposit rates (remember that the borrower has a choice of FI/MM instruments, which is not limited to bonds). It is also a common practice to calculate swap spreads (to IRS curves) when pricing bonds. The swap spreads given above were calculated to IRS for respective currencies. The reason for this calculation is that the swaps are heavily traded by banks, thus the provided spread in b.p. supplies the indicative credit risk over the interbank market. The current example would be even more interesting, if the domestic bond yield curve would be fitted to a portfolio of risky bonds representing the banking or corporate sector with a lower rating. If we look at pricing prospectuses published by deal managers or such services like the IFR Markets (International Finance Review), we will normally see a reference spread to mid swaps (which represents the average value of bid and ask rates of the swap curve) in b.p. And since the pricing is not firm we state that the swap spread is in the ### b.p. area.

If you have a closer look at the table above, the far end of the EUR curve approaches zero even despite the spread adjustments.
This can be explained by the implied RUB inflation expectations of the market that are present in the forward rates.

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