International Finance: Putting Theory Into Practice

3.3. THE LAW OF ONE PRICE FOR SPOT EXCHANGE QUOTES 101

Figure 3.13:Triangular Arbitrage and Shopping-around

139.48 139.78-

X

140.20 140.50-

Z

139.68 139.98-

X’

140.00 140.30-

Z’

139.88 140.16-

Synth

DoItYourself problem 3.1
Thejpy/gbpsynthetic bid and ask rates, if the quotes are
jpy/usd101.07 - 101.20 and
gbp/usd0.72202 - .72254,
are

Synth St,bidjpy/gbp=

Sjpyt,bid/usd

Sgbpt,ask/usd

= 139. 88 , Synth St,askjpy/gbp=

Sjpyt,ask/usd

Sgbpt,bid/usd

= 140. 16.

(3.8)

• Derive this solution from the previous one, invoking our earlier results on inverse
  rates, equations (3.3) and (3.4).


• Verify that you get the above answer also if you first think of the dimensions
  and then apply the Law of the Worst Possible Combination.

Triangular Arbitrage with Transactions Costs

Now that we understand synthetic quotes, we can derive bounds imposed by
arbitrage and shopping around on quotes in the wholesale market. Just think of the
direct quotes as the quotes from bank X, and think of the synthetic quotes as the
quotes from bank Y.

• Arbitragethen says that the two bid-ask quotes should overlap by at least one
  point; otherwise, you can buy cheap in the direct market and sell at a profit
  in the synthetic market or vice versa.


• Shopping around implies that if a bank skews its quotes so as to be (very)
  attractive at (only) one side, then it will attract a lot of business very fast;
  thus, this skewing cannot be persistent. But when we talk about market