Pricing Foreign-Currency Bonds with Credit and FX Risk

# Pricing foreign currency bonds - which approach is more theoretically "sound"?


# Pricing foreign currency bonds - which approach is more theoretically "sound"?












You own a fixed rate corporate bond in foreign currency (let's say JPY). Your domestic currency is USD. Which of the these two approaches do you consider theoretically better?

- Discount JPY cash flows using a yield comprised of a) JPY risk free rate + b) CDS spread for corresponding WAL of the security. Convert JPY NPV to USD using spot.

- Convert JPY cash flows into USD using USDJPY fx forward rates. Discount using a USD yield for corresponding WAL and rating.

Each approach comes with a different value. Significantly enough that they cannot be considered equivalent. I believe the approach 1. is more sound. What are your thoughts? Any literature out there?

## Answer by Marcino (score 6, accepted)

https://quant.stackexchange.com/a/28356

In #2, you can use FX forwards to convert your JPY cashflows to USD but it is more common in practice to use a cross-currency swap for this purpose. Indeed, the advantage of the latter is that it allows you to keep the nominal of your synthetic USD bond constant because the final exchange in the swap is done at FX spot (not forward), and the difference is made up with higher or lower coupons. This way you can use simple yield calculation methods on the synthetic USD bond without issues.

However, the real issue with #2 is that the USDJPY FX Forwards you apply to the JPY cashflows should be defaultable in order to fairly price the equivalent USD amount; if the bond defaults, the remaining JPY cashflows will not be paid and therefore you want your USDJPY forwards you entered into on day 1 to be cancelled, otherwise you will be asked to deliver a JPY amount which you are not receiving from the bond anymore.

The pricing impact comes from the FX-credit correlation. If a Japanese corporate defaults, chances are the Japanese economy is in trouble which should devalue JPY vs USD. This correlation is priced in the quanto CDS market; how much cheaper is a credit protection which pays in the local currency of the entity whose default you are protecting against, compared to a protection which pays you in a hard currency like USD?

Using defaultable FX forwards is the only way this method could make sense.

However, let's take a step back and evaluate your main question: as a USD investor with JPY bonds on my broker account, the price of my bond fluctuates everyday and so does the USDJPY FX. My daily P&L in USD would depend on those two elements. This is what you describe in #1 and I don't see why you would need anything else.

If the question is, how do I protect myself against the USDJPY movement, or how do I replicate such a bond, then you can start exploring cross-currency swaps (defaultable for fair pricing) or look at the corporate CDS as a proxy for the bond's Z-spread. On the latter note, as others pointed out, the CDS-bond basis will have an impact.

## Answer by JoshK (score 0)

https://quant.stackexchange.com/a/25617

I think you have to remember that the value is where it's trading. I know that might not be as deep as what you are looking for. But when you start to get into CDS you are getting into what the right spread is.

You can trade forwards on every point on the curve with JPYUSD, so you can compare it pretty easily to a similar USD denominated bond. So I guess #2 is more accurate. Also, the forwards will essentially lock in the respective USD and JPY rates. That's something that is otherwise difficult to achieve.

## Answer by Ami44 (score 0)

https://quant.stackexchange.com/a/28247

For the value of the bond it can not matter what your domestic currency is. Thats why your first approach is correct.

If no market price is available you can value the bond usind DCF with JPY interest rates (plus spread), because it pays interest in JPY. If you convert this JPY Cashflows later in USD that is your private fun, and is not a feature of the bond. Imagine for every expected JPY Cashflow you make a forward FX contract to convert it to USD, than you can value the Bond and the forward contracts separatly.

A price you have determined that way is the price you can sell the bond for (theoretically). The money from the sales you would convert then with the spot rate.

## Answer by user24237 (score 0)

https://quant.stackexchange.com/a/29951

This is a very interesting topic, which I would like to comment. So, let's take the original problem. Suppose that we use a dcf model and the two possibilities are:

a) Discount JPY cash flows with JPY risk free rate + spread from issuer in JPY, convert this to USD with spot

b) convert the JPY cash flow to USD via FX Forwards and use a dcf model with USD risk free rate + spread from issuer in USD.

In my opinion, what is really decisive here is that we need a liquid spread from the same issuer in both JPY and USD. However, often we do not have these liquid spreads available. In your example, we would assume that we have a JPY spread from the Japanese issuer. What is a favorite workaround in the market is two convert to JPY spread into a USD spread by using the cross currency basis spread between USD and JPY.

But now let's have a look at your second possibility: When using FX Forwards in order to switch to USD we already make use of the cross currency basis (since these are containted in the quoted FX Forwards). But then again we also need this cross currency adjustment in the spread component, which cancels out with the basis from the FX Forwards.

Therefore I would conclude that both of your strategies will be more or less equivalent IF we can assume that the JPY spread and the USD spread from the same issuer differs by exactly the cross currency basis (for pure no arbitrage arguments, this should be true).

However, in the market you can observe that liquid spreads in different currencies from the same issuer may not be explained by the cross currency basis. One possible explanation for this phenomenon was already pointed out by Marcino above: FX-credit correlation. If your issuer is a large bank (being strategically important), a possible default of this bank would have a significant impact on the FX rate. In this case you would rather have your bond in the currency which will be stronger upon default (because your recovery payment will be more valuable). But this will potentially come with an additional spread on top of the cross currency basis (the latter one is not issuer dependent).