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IRhunter
Topic Author
Posts: 42
Joined: October 26th, 2011, 4:07 pm

### Mid Curve Options VS Swaptions

I would like to compare the two following trades in terms of Delta and Vega exposure on the swap curve.

1.      6m20y swaption, ie an option on the 20y swap rate which expires in 6 months.
2.      6m10y10y mid curve option, ie an option on the 10y swap 10y forward which expires in 6 months.

Delta. With the first one I get a delta exposure at 20y swap rate. What about the second one. I believe that there we should have and some other exposures, at the 3 factor (curvature) of the curve at the 10y swap. Is this correct? Could someone please comment on that?

Vega. With the first one I get a vega exposure at the 20y swap rate. What about the second one? Where is my vega exposure?

Martinghoul
Posts: 3256
Joined: July 18th, 2006, 5:49 am

### Re: Mid Curve Options VS Swaptions

If the midcurve ends up ITM, what will be the delta of the resulting position?

As to the vega, it's similar to the delta, in a way.

IRhunter
Topic Author
Posts: 42
Joined: October 26th, 2011, 4:07 pm

### Re: Mid Curve Options VS Swaptions

Could you please be more specific? If you buy the vanilla swaption, your market view should be that the 20y swap rate will go up and its volatility will also go up.
What about the mid curve option. What market view should u have in order to enter to this trade.
Thank u.

Martinghoul
Posts: 3256
Joined: July 18th, 2006, 5:49 am

### Re: Mid Curve Options VS Swaptions

Could you please be more specific? If you buy the vanilla swaption, your market view should be that the 20y swap rate will go up and its volatility will also go up.
What about the mid curve option. What market view should u have in order to enter to this trade.
Thank u.
Well, I am sure you can answer this question yourself, hence my prodding.  The logic for the mid-curve option is exactly the same as for the vanilla.
If you buy a payer, you will make money if the underlying rate goes up.  You also make money if the vol of the underlying goes up, but let's get there when we get there.

IRhunter
Topic Author
Posts: 42
Joined: October 26th, 2011, 4:07 pm

### Re: Mid Curve Options VS Swaptions

Thank you for your answer Martinghoul. I know that my two examples have the same market view (underlying up, vol up). My question has to do with the delta of midcurve relatively to the vanilla one. Do i have the same DV01 exposure there? Same question to the vol exposure at the mid curve, what is it relatively to the vanilla one.

I believe that the difference between these two trades is that at the mid curve there is a "hidden" steepening position at 10s20s and DVO1 is lower than the vanilla. Is this correct?

Martinghoul
Posts: 3256
Joined: July 18th, 2006, 5:49 am

### Re: Mid Curve Options VS Swaptions

Well, your exposure with the mid-curve, at expiry, is going to be 10y10y.  Assuming the vanilla and the midcurve have the same underlying DV01 at expiry (say $100k/bp), you'll have$100k/bp of 20y swap from the vanilla vs $100k/bp of 10y10y swap from the midcurve. The interpretation of this will depend on how you prefer to think about your risk. Some people are happy to view exposures in "fwd-fwd" terms, while others prefer to convert everything to "par". If it's the latter, then very simplistically and broadly, you can convert$100k/bp of your 10y10y into 10y and 20y (very roughly and simplistically, $100k/bp of 10y10y is$100k/bp of 10y vs \$200k/bp of 20y).  How you then choose to interpret this is up to you.

You can think about the vega using very similar logic.

IRhunter
Topic Author
Posts: 42
Joined: October 26th, 2011, 4:07 pm

### Re: Mid Curve Options VS Swaptions

My next question would be about the pricing. Apparently, there are not implied volatility quotes for mid curve options. You have to infer them using the vols from vanilla swaptions. Do you have any paper to suggest me regarding the pricing of mid curve options?

Ps: I think that back in 2010 in another forum you had suggested one.

Thank you very much for your time.

Martinghoul
Posts: 3256
Joined: July 18th, 2006, 5:49 am

### Re: Mid Curve Options VS Swaptions

Well, as long as there are midcurve price quotes, you can imply the vols.

I have a paper which I posted on one of the old threads a long time ago, but it was more abt the pricing of fwd vol.  Might help you, regardless, so I can send it to you.  PM me if it's what you desire.

IRhunter
Topic Author
Posts: 42
Joined: October 26th, 2011, 4:07 pm

### Re: Mid Curve Options VS Swaptions

I got the paper. Thank you.

smackya2000
Posts: 1
Joined: September 24th, 2018, 8:06 pm

### Re: Mid Curve Options VS Swaptions

Well, as long as there are midcurve price quotes, you can imply the vols.

I have a paper which I posted on one of the old threads a long time ago, but it was more abt the pricing of fwd vol.  Might help you, regardless, so I can send it to you.  PM me if it's what you desire.
Can you send me the paper on fwd vol? I couldn't find in any of the archived messages. Thanks you.

wickedwit
Posts: 46
Joined: August 6th, 2011, 3:48 pm

### Re: Mid Curve Options VS Swaptions

so have a model calculate it! But that underlying forward swap is also easily calculated by a model but can visualize that duration as the duration of a 20yr swap minus a 10yr swap 1:1 as a long 10y10y is basically short 10yrs and long 20yrs. Mid curves are a bit strange as it's not a walking forward in that it's always an option on 10y10y in 6 months to 1 month. There is a duration adjustment for that too.

Martinghoul
Posts: 3256
Joined: July 18th, 2006, 5:49 am

### Re: Mid Curve Options VS Swaptions

Apols, it's been a long time since I was here...  But yes, there's all sorts of funky adjustments, for sure.