Estimating Cross-Currency Swap Rates from Bond Yields and Peer Markets

# Cross Currency Swap -- Unobservable bid/ask


# Cross Currency Swap -- Unobservable bid/ask












So in the place I work, one of the traders is dealing with a cross-currency swap within a country that has really no market for that kind of product.

He wants to estimate a theoretical bid/ask, and thought perhaps of using proxys (some options were): a) looking at ccy swaps in other countries b) looking perhaps at bonds in that country's market

So I was wondering... what characteristics should the ideal proxy have for cross currency swaps? How do people deal with this kind of situations in general where a product lacks liquidity?

Edit: There are bonds issue in that country for the same ccy swap maturity, that perhaps could be used as part of a multiplier

## Answer by Dimitri Vulis (score 5, accepted)

https://quant.stackexchange.com/a/55204

(Edited: sorry, I totally mis-understood the question initially.)

For concreteness, let us look at markets like Bolivia and Paraguay, where the market observables are spot FX and government bonds. There are no observable interest rate swaps or FX forwards. The yield of a government bond is your best information of what the exchange rate will be in the future.

Countries with more developed capital markets typically have at least these 3 curves:

1 nominal (not inflation-linked) government bonds

2 some swap curve (for interest rate swaps in local currency - fixed leg v floating linked to some index, like CAMARA in Chile or DTF in Colombia)

3 the cross-currency curve that you're looking for. When swap curve 2 exists, most people prefer to split #3 into #2 and a cross-currency basis.

In a few countries, e.g. Argentina, there really is no observable swap curve, so people look at #3 directly.

In your case, all you have is #1. I suggest you don't look for 2, but look for proxies for the 3-1 spread directly.

I suggest you look at all the 3-1 spreads in the markets where it observable (especially in the ones where the interest rate levels and other economic conditions are similar to your market; and the bid-ask spreads are wide, indicating illiquidity); pick the highest and lowest; take their midpoint as your mid; then, to be conservative, double the bid-ask spread.

Edit: I'm making up some numbers for a numerical example.

Suppose that in country X, the 5 year local-currency, non-inflation-linked government bond yield is 15%. Suppose that I want to price an FX forward where in 5 years I pay some USD and receive some fixed amount of local currency. What rate would I use to discount the local currency leg? It might be the sum of the local currency swap rate (say 16%) and the cross-currency basis (say 0.8%) if these were obserable, but none of these numbers are observable, so we look for proxies.

I look (on Bloomberg hopefully) for some markets where

- both the government bond yield and the cross-currency rate are observable.

- the 5 year goventment bond yield is not very different from X's 15%. I might assume that if this number is below 3% or above 30%, then this is not a good proxy. (thinking of Argentina and Venezuela).

- I'd manually reject any countries that are too different from my X because of civil wars, capital controls, etc. (For example, if I think there are many market participants in X who get revenue in local currency, but must repay debts in hard currenct - I'd want to look at similar emerging markets and would not want a country with different flows.)

- I'd make a histogram of the spread between government bond yields and the cross-currency rates in the countries that I picked. I'd look again at the outliers, consider why they differ from the rest of the sample, and might reject them as well. Hopefully the remaining data is close to being normally distributed.

Suppose (totally making up the numbers below!!) I'm left with something like

Mexico 100 bps

Uganda 100 bps

India 110 bps

Indonesia 120 bps

Sri Lanka 100 bps

South Africa 100 bps

Turkey 110 bps

Egypt 120 bps

I would then take the median (i.e. 110 bps), rather than the mean. (If the data is close to normally distributed, it makes little difference.)

I might then repeat this exercise and see how the result changes if I change which countries I reject as proxies (e.g., what if we include Zambia or Vietnam).

I would add this spread to X's bond yield and call the result 15% + 1.1% = 16.1% the mid for X's cross-currency rate.

Finally, I would look at the bid-ask spread on the cross-currency rates in my sample (this might be harder to find), take the maximum, double it to be conservative, and use it with the mid.

## Answer by user35980 (score 1)

https://quant.stackexchange.com/a/55316

This is an interesting question. Leaving aside the question of liquidity and the technicalities for now i.e. bid/ask spread etc (addressed to some extent by Dimitri Vulis's answer), the first question would be whether the basis is positive or negative. This will depend on whether there is more demand for the foreign ccy (say USD) over the domestic ccy. This is purely determined by the economics of the local market you're referring to. For instance while in Europe and Japan say the xccy basis to USD is usually negative (part of the reason being an excess of domestic corporate liabilities with settlement in USD within those countries), this is not the case say in Australia (where liabilities are generally settled in AUD). As a result the USD/AUD basis is generally positive. With regards to liquidity, as you indicate liquidity could be proxied to a similar economy where such products are already quoted. However the quoting rule would very much be 'wide and wonderful' until actual transactions establish the demand/supply levels and lead to more reliable price discovery.