I need to price a USD bond using yield-to-maturity from the yield curve (YC). The bond is issued by a German company.
My question is what yield curve should I use: the US Treasury YC or the EUR YC of Germany?
If this German company already has other similar debts denominated in USD, and you are able to observe the yields at which they trade, then you can just interpolate their yields to the maturity of this bond, and you should get an acceptable answer without looking at any risk-free yield. If you can only observe other tiers of debt, e.g. first lien USD loans, but you need to price a bond, you can try to guess a further correction for that.
If the company has no USD debt, but has some EUR-denominated debt with observable yields, then you calculate the extra yield that the company's debt EUR-denominated pays on top of the risk-free EUR yield, and add this extra yield to the risk-free USD yield. For most other countries, you would need to add some additional yield for country risk, but for Germany, this model should be close enough.
If the company has no observable debts at all yet, then any answer will be pretty meaningless. If the company has an agency rating (like Moody/S&P/Fitch), then you can try to use as proxy the debts of other companies in the same country, industry, and ratings, but this is a very rough guess.
You should use the US Treasury yields but this is probably not the only thing you should take into account in pricing that bond.
I don't know if the bond you are trying to price would strictly qualify given a typical definition of a eurobond such as the following but it quite sounds like one:
A eurobond is an international bond that is denominated in a currency not native to the country where it is issued ... eurobonds have grown to be a more general way to perform financial operations in a currency while using the regulatory framework of a separate country.
The applicable regulatory framework and the venue are the reasons I say yours may or may not qualify in a strict sense but I don't think this matters hugely in relation your question.
In general, a eurobond is priced based on the reference yield at a similar maturity in the denomination currency (in your case the US Treasury yield at the same maturity if it is a discount bond, for example) with a spread being added to the reference yield according to the creditworthiness of the borrower relative to the issuer of the bonds used in determining the reference yield. However, there might be other considerations affecting the pricing.
According to Choudhry in "The Bond and Money Markets Strategy, Trading, Analysis" (2001, page 386), these other considerations could include:
Eurobonds are perhaps more heavily influenced by the target market’s ability to absorb the issue, and this is gauged by the lead manager in its preliminary offering discussions with investors. The credit rating of a borrower is often similar to that granted to it for borrowings in its domestic market, although in many cases a corporate will have a different rating for its foreign currency debt compared to its domestic currency debt.
The Turkish government, for example, is a heavy issuer of eurobonds (both in USD and EUR) and its eurobond yields are highly correlated with the government bond yields in similar maturities in the respective geographies (the USA and Eurozone) plus the corresponding Turkish eurobond credit default swaps (CDS’s). The Turkish USD eurobond CDS's, for example, approximately measure the relative creditworthiness of the Turkish government with respect to the US government at the corresponding maturities.