SERVING THE QUANTITATIVE FINANCE COMMUNITY

Jhammer
Topic Author
Posts: 37
Joined: February 24th, 2014, 8:05 pm

### Filling up swaption missing vols

Hi Wilmott'ers,My question might seem a bit trivial but I'll ask it anyway.What is the market practice for filling up the missing vol surface data of EUR ATM swaption (or swaption vols in general)? Is there any convention, i.e., priorities to fill up the holes?Any input is greatly appreciated!
Last edited by Jhammer on March 29th, 2015, 10:00 pm, edited 1 time in total.

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

### Filling up swaption missing vols

Just interpolate liberally, innit?

Jhammer
Topic Author
Posts: 37
Joined: February 24th, 2014, 8:05 pm

### Filling up swaption missing vols

Thanks for you response!My main concern with the interpolation of volatility is the implication of negative forward vol in some cases. Consider the following simple example:one-year vol $$\sigma_1 = 0.2$$tow-year vol $$\sigma_2 = 0.15$$Linear interpolation results in 17.5% vol for one-and-half-year vol. This implies a negative forward vol between t=1.5 and t=2.I have found some helpful results here: http://finance.business.queensu.ca/psfi ... sed.pdfNow, the question is: Are there any other alternatives to interpolation that market uses? (e.g. proxies or stale data) if yes, in what order of priority?

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

### Filling up swaption missing vols

Ah, when you're referring to EUR swaption vols, you're talking about the Black %-age numbers?

Jhammer
Topic Author
Posts: 37
Joined: February 24th, 2014, 8:05 pm

### Filling up swaption missing vols

I am referring to black implied vols for ATM swaptions. The surface is on maturity and term.

pcaspers
Posts: 701
Joined: June 6th, 2005, 9:49 am

### Filling up swaption missing vols

in general negative forward vols can be avoided by interpolating in $\sigma^2 T$ in option maturity direction.However the holes you are currently observing in EUR are due to premiums that are not attainable in the Black model or negative forward atm level.The shifted Black surface has no holes (nor has the normal surface).

Jhammer
Topic Author
Posts: 37
Joined: February 24th, 2014, 8:05 pm

### Filling up swaption missing vols

Thanks for your response!You are absolutely right! interpolation on total variance resolves the issue. May I ask you to elaborate on you last sentence (shifted black model)? Can you introduce me a resource I can read more about?cheers!

pcaspers
Posts: 701
Joined: June 6th, 2005, 9:49 am

### Filling up swaption missing vols

the shifted Black vols are on Reuters Page VCAP1A, the corresponding shifts on VCAP1B, I think. I wrote a bit about it here. In general you can look for references on displaced diffusion models.

Jhammer
Topic Author
Posts: 37
Joined: February 24th, 2014, 8:05 pm

### Filling up swaption missing vols

Thanks for your input, I will look into it