I'm not sure what exactly "USD 1-year swap rate" means, what ticker did you use to obtain that in BBG? If it is USSW1, this is the fixed rate for a 1 year swap with semi-annual payments on the fixed leg, quarterly payment and reset frequency on the floating leg with 3M Libor. Right now this is @1.3673.

If you change the floating rate to 12M Libor, the fixed rate would go up to 1.83%, close to 12M Libor, as it should. You can see these in SWPM.Let me know if this helps.

Dear Rubesam

Attached files are screen shots of Bromberg.

Best regards

As I mentioned above, you're comparing the fixed rate for a 1-year swap with quarterly payments on 3month libor with the 12-month libor rate.

Also, in your arbitrage example, Bank A would pay or receive the net amount at each cash flow date. That is, the float amount "received" from Bank B can't be counted on to pay Bank C, because bank A needs to pay the net amount to bank B, and this may change if LIBOR changes for the next reset date. Additionally, Bank A would have to borrow with initial term of 6 months and also enter into a forward contract to borrow again for another 6 months after the initial 6 months. For this, Bank C will charge the forward 6-month, 6-month rate. For this to be an arbitrage, you would need to show that the NPV of all these cashflow is positive for Bank A in any state of the world, including default of one or more of the banks.

Dear, Rubesam

Thanks for your kind reply.

I would like to answer in turn.

First of all, the present value of the 1-year swap is not affected by whether the floating side is 3-month Libor payable every 3-month or 6-month Libor payable every 6-month because the present value of floating side is always par (of course, adding the fictitious final exchange of the notional amount). Therefore the present value is determined by the present value of fix side (of course, again adding the fictitious final exchange of the notional amount).

The present value of swap=the present value of fix side minus that of floating side(always equal to 1, assuming with no spread ),

and in the case of market rate swap, this should be 0, i.e. the present value of fix side should be 1.

My question is very simple. By the market rate on 23/2/2017, the present value of the fix side of 1-year swap does not equal to 1 and how should I interpret this.

The arbitrage scheme is for only demonstrating that we can construct bilateral transactions for the borrowing and deposit side.

Best regards

Dear Masahiro,

As a former arbitrage trader, who lived in Tokyo and was responsible for Yen/$ fixed income arbitrage for Salomon Brothers (1989-1991), I am surprised to observe that such significant mispricings still exist. 

Another way to express this mispricing is to look at the cash flows from paying fixed 1 year vs 6 month Libor, where up is receive and down is pay. 

                         1.36239/2                     6mo L - 6 mo forward 

                                  !                               !

___________________________________________________________________

0                             6Mo                        12Mo

                                 !                               !

                         1.2965/2                  1.2965/2

You can lock in the 6 mo Libor rate one year forward by borrowing for 6 mo (1.36239) and lending for one year (1.74428).

While your basic analysis is sound, these are counterparty trades and Bloomberg rates are not tradeable. In order to execute the arbitrage you will need to find an actual swap counterpart who will take your credit.  And then borrow at 6 month Libor and invest at 12 month Libor.  Aside from the challenge of obtaining a swap counterparty, my guess is that the actual borrowing rate will make this trade hard to do profitably. 

If you are part of a large bank that can trade at Libor, this may be doable. 

Good luck. 

Dear Fujimoto, after the 2008 crisis, the swap market moved away from using Libor to discount swap cash flows, as market participants realized it was not reasonable to expect to gain Libor as collateral. Nowadays cash flows are generally discounted using OIS or the swap curves, which uses cash, futures and swaps. These are bootstrapped to build a zero curve, which is then used to calculate the forwards as well as to discount the cash flows.

In SWPM, you can choose the curve in tab 3 under "Market". Swap curve is 23 and OIS curve is 42. If you then go to tan 6) Cashflow, you can see the discount and zero rates applied to the fixed leg and confirm that the cash flows sum to 1. If you go to tab 7) Resets, you can see the forward reset rates implied by the zero curve.

Dear Alexandre,

Thanks for your reply.

I understood the situation.

Please teach me what is SWPM and where can I use.

Dear Michael,

Thanks for your reply.

As Alexandre pointed out, what look to a misprice is due to usage of the wrong discount rate.

In terms of the forward rate, the explanations are as follows.

As you pointed out, we can lock forward 6-month Libor by borrowing 6-month Libor from Bank A and investing at 12-month Libor to Bank B.

If A and B are different banks, we are taking the credit risk of Bank B and what seemed to be an arbitrage opportunity is not a true arbitrage opportunity but just a return for taking the credit risk.

If A and B are the same bank, realised borrowing and lending rate should be less than Libor because bilateral transaction cancels out credit risk each other. This means implied forward rate would be lower than the original level and it leads the arbitrage opportunity to disappear.

Best regards

Let me weigh in on this.

This is a long post but I think there are four the issues and

they can be easily summarized:

1. Different quotation bases

2. Single vs dual (OIS) curve

3. Futures for building the curve and illiquidity of 1 year libor

4. 3-month vs 6-month libor basis

Issues (1) and (2) don't matter - they are small numerically

Issue (4) is not directly relevant to the USSW1 but should be

mentioned.

Issue (3) is the key issue. Eurodollar futures are the relevant

securities for pricing and hedging swaps. They are cheap and easy

to transact. The 12-month libor deposit is illiquid and expensive

and it is just not the relevant security. You might think you

could arbitrage 12-month libor deposits against swaps or futures

but as a practical matter it will be too expensive. The 6-month

and 12-month libor are not really relevant.

I have attached a .pdf that you can download and read if you want to dig into the details. 

Dear Thomas,

Thanks for your helpful comment.

1, We should not use the cash-Libor rates to get the forward Libor rates since cash-Libor rates are expensive and illiquid. They are not good data. We should Eurodollar futures and/or the FRA data.

2, We should not use the cash-Libor rates to get the default free discount rates since cash-Libor rates reflect the credit risk of the good bank. We should use the ois rates.

As for my original question, the first point is most relevant and this is a new issue I have not been aware fully so far.

I have another two question.

In USD case, there are the ois with long maturity( probably 10 years).

But in GBP case which my current project involves, for example, the longest maturity of ois is 2-year and not enough to get the default-free discount curve up to 10-year.

How to handle this problem?

Possible solution might be 

1, we get the spread between the implied forward Libor and implied SONIA at the longest end from Libor-fix swap rates and ois rates up to 2 -year maturity.

2, Then subtracting that spread from Libor-fix swap rates with the maturity longer than 2-year to get the synthetic ois rates.

Is this solution legitimate?Are the discount rate of USD/GBP forex  

The second question is do the discount rate of USD/GBP in the forex market reflect the difference of Libor(synthetic  Libor rates as "clean rates") or default-free rates derived from ois rates?

Best regards