Pricing Uneven FX Swaps

Question

I'm trying to figure out how to price uneven FX swaps. I just started on a FX trading desk and have been told that the all-in rate for a 2-legged FX swap is equal to:

1) Quote for market side of net spot impact + pts. on far leg's side

I've also been told:

2) The rate of an uneven swap is equal to the sum of its two parts: the cost of the near and far legs summed.

Point 2 makes sense to me, but I cannot get the math to balance out to prove point 1 simultaneously. Is there a quoting convention for uneven FX swaps?

E.g.

EURUSD spot = 1.1530/1.1535 (bid/ask)

EURUSD 6mo. points = .0183/.0185 (bid/ask)

Spread spot 30bps, spread pts. 10 bps

Client sells 10mm EUR near leg, buys 5mm EUR far leg.

1) By #1, 5mm * (LHS spot + RHS points)

Net spot impact (-10mm + 5mm) = -5mm EUR

-5mm *[(1.153 * 0.997) + ((1.153 + 0.0185)*0.001 + 0.00185)] = -5mm * 1.1525625 = -5,762,812.5 USD

2) By #2, -10mm * LHS spot + 5mm * (RHS spot + RHS pts)

Near leg cost = 1.153*(1 - 0.003)10mm = 1.149541-10mm = -11,495,410 USD

Far leg cost = [(1.1535 + 0.0185)0.001 + 0.0185 + 1.1535(1 + 0.003)]*5mm = 1.1766325 * 5mm = 5,883,162.5 USD Near leg + Far leg = -11,495,410 + 5,883,162.5 = -5,612,247.5 USD

The results of 1 & 2 do not match. Are points 1 & 2 both accurate? Am I miscalculating? Is there a way to quantify a single all-in rate for an uneven currency swap using the net spot impact?

Answer 1

I'm not sure what you are trying to calculate there. Those amounts you are calculating seem to be the dollar amounts, but you are saying they are EUR.

I think the point is that if the client wants to sell 10mm EUR spot versus buying 5mm EUR forward , you break it down into two trades : 1. Client buys 5mm forward versus X mm spot, where X is the present value of the 5mm for 6months. This trade is priced at the offered side forward points (.0185). The forward trader will not care what spot rate is referenced , since the trade is neutral to the spot setting.
2. Let's say X =4.9mm (I wasn't sure how to derive that from your data). Then the client needs to sell another 5.1mm spot. The rate for this is the bid side 1.1530. That rate will also be used as the spot ref for transaction 1.

Thus, client sells 10mm spot for 1.153 and buys 5mm forward for (1.153+.0185).