Suppose that the term structure of interest rates is flat in the United States and Australia. The USD interest rate is 7% per annum and AUD rate is 9% per annum. The current exchange rate is 0.62USD/AUD. In a swap agreement, a financial institution pays 8% per annum in AUD and receives 4% per annum is USD. The principles in the two currencies are $12 million USD and $20 AUD. Payments are exchanged every year, with one exchange having just taken place. The swap will last two more years. Assume all interest rates are continuously compounded. What is the today's value of swap to the financial institution (in millions of dollars)? The answer is 0.795. I want to know the process.

OneClass: Suppose that the term structure of interest rates is flat in the United States and Australi...

Please read the article and answer these questions. Thanks.

Article:

TESTING THE GLOBAL CENTRAL BANK SWAP NETWORK

In the last few weeks, the ECB has been drawing on its liquidity swap line with the Fed, first $308 million for a week, then $658 million for a week, and last week back down to $358 million. Whatâs that about?

Itâs not such a large amount. Bank of Japan borrowed more in the past, $810 million in March and $1528 million in January. But the question then repeats, what was that about?

Both of these drawings are part of the new set of central bank swap lines linking what I call the C6: the Fed, ECB, Bank of Japan, Bank of England, Swiss National Bank, and Bank of Canada. On October 31, 2013these lines were made permanent and unlimited; contract details may be found here. Ever since then I have had a slide in my powerpoints saying âForget the G7, Watch the C6.â

So now weâre watching. What are we seeing?

Central bank swaps are in some ways quite similar to a standard commercial FX swap, but the differences are important and significant.

A standard swap involves exchange of two currencies today at the spot exchange rate prevailing today, plus a promise to reverse the transaction at maturity using the forward exchange rate prevailing today. Suppose that forward rate is calculated using covered interest parity as

F = S(1+r)/(1+r*)

where r and r* are respectively the dollar and foreign interest rate for a given term T, s is the spot exchange rate and f is the forward exchange rate for date T.

In this case, the exposure of the standard swap contract is identical to a swap of IOUs between the contracting parties at the prevailing interest rates in their respective currencies. One party borrows dollars at rate r and the other party borrows euros at the rate r*.

Central bank swaps are different. First, the forward rate in the contract is usually exactly the same as the current spot exchange rate. This means that central banks are never in the position of realizing profits or losses from the swap (although of course there will be implicit profits and losses), that come from deviation between the agreed forward rate and the spot rate at expiry.

Second, the interest rate on the contract is negotiated rather than calculated from market prices. But, given the choice of forward rate, the analogous commercial contract would call for payment of the interest differential, so anything different from that is significant. Significantly, the documentation of the current C6 swap line leaves open the question of who pays interest to who, and how much.

Usual practice has been for the party who draws on the line to pay interest on the line at some penalty rate. Thus the May 9, 2010 swap agreement between the Fed and ECB called for the ECB to pay the USD Overnight Index Swap Rate plus 100 basis points on its dollar borrowing, and the Fed to pay nothing on its euro borrowing. In effect, the ECB was simply borrowing dollars at the discount window, like any other bank, but with its own monetary liability serving as collateral instead of some financial asset.

This kind of arrangement is still in effect a swap of IOUs but at a price that is away from the market. Central bank swap lines thus in effect operate as a kind of outside spread providing bounds within which normal commercial dealing takes place. So long as prices stay at or near CIP, private agents prefer to do business directly with each other. But when CIP comes under pressure, because of one-sided liquidity flows, the central bank moves from backstop to market-maker and the outside price becomes the market price.

The ECB is borrowing dollars from the Fed and lending them on to banks in Europe who have dollar liquidity needs. Here is the tender documentation. Presumably it is doing this for banks who are unable, for whatever reason, to access dollar funding in the open market, or only at a premium that is higher than the ECB charges.

During the financial crisis, dollar funding needs like this got met by central bank liquidity swaps that rose almost to $600 billion, raising questions in Congress. Now, in normal times, smaller sums are becoming a routine way of handling the normal stresses and strains of world funding flows.

For lack of a world central bank, we have a network of central bank liquidity swaps.

(Council on Foreign Relations has a fun interactive app that shows the rest of the emerging swap network as well.)

Questions:

2. Forward rates in standard swaps are set relative to spot rates to eliminate arbitrage opportunities. Using a numerical example, demonstrate that an arbitrage opportunity would exist if a forward exchange rate quote differed from the formula given in Mehrlingâs article.

3. How do swap lines between central banks differ from standard foreign exchange swap contracts? How are forward rates set? How are interest rates determined?