# STIR Topics: XCCY pricing and trilemma between SOFR, FF & FRA

Question on STIR.

Suppose we sell a 3m JPY swap with spot start date, and we are able to back out the 3m implied JPY forward points (hence swap points), using 3m JPY OIS (3m TONA) and 3m USD OIS (3m Fed Fund rate), using covered interest parity formula.

1. What does it mean to sell 3m JPY swap? Do we buy USD, sell JPY in the near leg, and in the far leg (i.e. 3m), we sell USD, buy JPY?
2. How will we make profit? Should the swap points be more negative or positive?
3. Where does the XCCY basis come into play?
4. What is FX-OIS?
5. What is the trilemma between SOFR, FF and FRA, or even XCCY basis for that matter? And why should we care about them when pricing FX Forwards or Swaps?
6. What's straight and split?
7. How can you hedge a FX swap without doing the exact reverse? For example, how to hedge 3m JPY swap sell?
8. Slightly unrelated, but related: if our portfolio is +ve DV01, are we paid (or are we a payer)? And why?
• There are too many questions in my humble opinion.
– dm63
Jul 12, 2022 at 22:32
• Would you reckon splitting up the post helps? @dm63 Jul 13, 2022 at 4:03
• That would be better, also share some of your own thoughts. Jul 13, 2022 at 6:07
• I will try to answer all 8 at the weekend. Keep it here for now. Jul 13, 2022 at 8:52
• thanks @JanStuller! Much appreciated! Jul 13, 2022 at 11:45

## 1 Answer

1. The USD/JPY FX Swaps are quoted the same "way" as the spot, i.e. today's quote for a 3-month forward is:
• Bid 138.310, Offer 138.317, Mid 138.313. The spot FX rate is 138.325, so the mid 3-month forward is also quoted as -120 FX Points: $$(138.313 - 138.325)*10,000 = -120$$
• The direction depends on whether you are "buying" or "selling" the FX Swap: if you are the market maker, and someone hits your "Bid", you buy at 138.310, so you pay this rate in the future, so you buy JPY and sell USD at spot and buy USD and sell JPY in the future. If someone hits your "Offer", it means you will be paid the "higher" price in the future, so it's vice versa.
1. You can make a profit in two different ways: if you are a market maker and people come to you for quotes, you sell at Offer and buy at Bid, capturing the spread. Another way to make profit is if your funding rate for one of the currencies is lower than the implied OIS rate from the FX points. Then, even if you trade at mid, you can make a profit via cheaper funding.

2. There are 4 unknowns in FX swap equation: Spot, Forward, USD rate and JPY rate. If you take the most liquid 3 variables (Spot, Forward and the USD 3-month OIS rate), you can back out the implied JPY rate from the FX Swap. This rate will be different to the actual 3-month JPY OIS rate. The difference between the implied FX Swap JPY rate and the actual JPY OIS rate is the XCCY basis and reflects the momentary supply and demand for funding in one currency via the other currency (if many more people wanna sell USD to get JPY, the XCCY basis will be positive, if many more people wanna sell JPY to get funding in USD, the XCCY basis on the Japanese leg will be negative).

3. FX OIS would be the implied rate from the FX Swap: as said above, there are 4 unknowns. Spot, Forward and the two rates. If you fix the Spot, Forward and plug in an OIS 3-month rate for one of the two currencies, you can solve for the implied FX OIS rate for the other currency.

4. This is only my guess: but the "trilemma" would come from choosing which of the three rates (FRA, SOFR or FF) to plug in for the USD leg to compute the implied FX JPY rate. The answer is simple: it should be the rate closest to the funding rate of your desk.

5. Don't know this one, I let someone else answer.

6. When you execute the swap, you don't run an FX risk, but you run a funding risk. If you sold USD and bought JPY and fixed the rates for 3 months via the swap, you are sitting on JPY whilst being short USD. One way to hedge this is that you keep entering into overnight (or weekly) FX swaps whereby you sell JPY and get USD (but here, if the short term USD funding explodes, you can lose a lot of money, so it's not really a hedge). If USD is your natural funding currency, you don't need to hedge it: as said, you could just fund it via Fed-Funds or SOFR for 3 months and then lend it out via the FX Swap. But if you are a European bank with no direct access to USD funding, and you are short the USD, you run the risk that the short-term USD funding will explode: the only way to hedge it properly is to get the USD funding fixed for 3-months.

7. DV01 positive means that if the quantity you are "DV01 positive" goes up, you make money. So if you are DV01 positive the FX Points, it means you pay JPY in the future (because if the FX points go up, you had fixed them at a lower value, so you make money): so that means you "bought" the FX Swap (you hit market-maker's offer or if you are the market maker someone hit your bid).

• Thanks for this, this is super informative! I have some insights for q5, q6 and q7, which I will share over the weekend. One other question, Jan- if you know the step AUD OIS (using AU bank bill futures) for 19 Jul 2022 meeting, 23 Aug 2022 meeting, and so on, how will you calculate the 1w AUD OIS rate? Jul 18, 2022 at 15:11
• Not sure about the AUD OIS, I have very little experience with AUD (I only ever traded AUD spot FX). Ask a new question on the AUD OIS from AU bank bill futures...I'd be interested in the answer myself. Jul 18, 2022 at 15:38