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atulnahar21
Topic Author
Posts: 15
Joined: January 13th, 2014, 3:41 pm

### Average/asian swap

Lets say we have average/asian swap whose floating leg payoff is dependent on the arithmatic average of the forward rates. Would these forward rates require convexity/timing adjustments? How would these adjuatments look like in a negative rate environment. Lets say this is a EUR swap.

Any reference to a paper/book would be very helpful. Thanks in advance for your help.

list1
Posts: 1696
Joined: July 22nd, 2015, 2:12 pm

### Re: Average/asian swap

I understand that it might be well known fact but usually duration and convexity are associated with bond valuations but I did not read about forward rates convexity adjustments including swap too. Though I think that it makes sense.

bearish
Posts: 5980
Joined: February 3rd, 2011, 2:19 pm

### Re: Average/asian swap

Lets say we have average/asian swap whose floating leg payoff is dependent on the arithmatic average of the forward rates. Would these forward rates require convexity/timing adjustments? How would these adjuatments look like in a negative rate environment. Lets say this is a EUR swap.

Any reference to a paper/book would be very helpful. Thanks in advance for your help.
Assuming it is a straight up swap with no optionality involved, you can decompose the floating leg into a sum of the reset rates, each of which will (at least in principle) require a convexity adjustment to the extent that the actual payment period is different from the natural one that the reset refers to. Rates being negative doesn't particularly change anything, although it obviously makes a mockery of any model that can only handle positive rates, e.g. a lognormal rate model. By far the simplest approach, especially in the presence of negative rates, would be a Gaussian model, where the convexity adjustment is analytical.

list1
Posts: 1696
Joined: July 22nd, 2015, 2:12 pm

### Re: Average/asian swap

Lets say we have average/asian swap whose floating leg payoff is dependent on the arithmatic average of the forward rates. Would these forward rates require convexity/timing adjustments? How would these adjuatments look like in a negative rate environment. Lets say this is a EUR swap.

Any reference to a paper/book would be very helpful. Thanks in advance for your help.
Assuming it is a straight up swap with no optionality involved, you can decompose the floating leg into a sum of the reset rates, each of which will (at least in principle) require a convexity adjustment to the extent that the actual payment period is different from the natural one that the reset refers to. Rates being negative doesn't particularly change anything, although it obviously makes a mockery of any model that can only handle positive rates, e.g. a lognormal rate model. By far the simplest approach, especially in the presence of negative rates, would be a Gaussian model, where the convexity adjustment is analytical.
I am wondering why one is obliged to invest or deposit money at negative rate, ie loose money over the time if he can keep them inside of the company at zero rate?

outrun
Posts: 4573
Joined: April 29th, 2016, 1:40 pm

What we need is $1bln bills, just like in WWII, these bills would make it very easy to store lots of cash, ...except that you need a lot of protection. Doing a trade that generates cash flows would require moving that paper money around physically. You can't email each other "I owe you"s because those have credit risk. list1 Posts: 1696 Joined: July 22nd, 2015, 2:12 pm ### Re: Average/asian swap What we need is$1bln bills, just like in WWII, these bills would make it very easy to store lots of cash, ...except that you need a lot of protection. Doing a trade that generates cash flows would require moving that paper money around physically. You can't email each other "I owe you"s because those have credit risk.
I am talking about discount factor used for valuation of a particular swap or option. For a large principal which has effect on discount factor it might have sense to discuss adjustment on a model pricing and we can leave this for a while for other discussions.

atulnahar21
Topic Author
Posts: 15
Joined: January 13th, 2014, 3:41 pm

### Re: Average/asian swap

Lets say we have average/asian swap whose floating leg payoff is dependent on the arithmatic average of the forward rates. Would these forward rates require convexity/timing adjustments? How would these adjuatments look like in a negative rate environment. Lets say this is a EUR swap.

Any reference to a paper/book would be very helpful. Thanks in advance for your help.
Assuming it is a straight up swap with no optionality involved, you can decompose the floating leg into a sum of the reset rates, each of which will (at least in principle) require a convexity adjustment to the extent that the actual payment period is different from the natural one that the reset refers to. Rates being negative doesn't particularly change anything, although it obviously makes a mockery of any model that can only handle positive rates, e.g. a lognormal rate model. By far the simplest approach, especially in the presence of negative rates, would be a Gaussian model, where the convexity adjustment is analytical.
Thanks Bearish. I am able to find papers on gaussian convexity adjustments for CMS swaps . Can that be tweaked around for average/asian swaps. Not able to find good reference material for this. Again, thanks for your help.

tglauner
Posts: 16
Joined: December 27th, 2002, 7:44 pm

### Re: Average/asian swap

I would be interested in this topic as soon you will have averaging SOFR swaps possibly that will be very long dated. The reason is that Libor loans may get converted to SOFR loans that are not compounding like OIS swaps but averaged becuase of loan system limitations. The swap to hedge will then be an average 1D SOFR rate swaps. The paper 'Valuation of Arithmetic Average of Fed Funds Rates and Construction of the US dollar Swap Yield Curve Katsumi Takada, September 30, 2011' talks about a convexity adjustment but I do not know how accurate the paper is.
If there is any update please let me know.

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