mtsm


Total Posts: 232 
Joined: Dec 2010 


how would you compute realized volatility for a european swaption?
the more I think about it, the more I wonder what it actually means?
thanks! 




EGH


Total Posts: 59 
Joined: Nov 2014 


do you mean for the swaption itself, or for the underlying? the swaption itself you need a good price database for swaptions. When it comes to volatility in option prices there is a lot of interesting effects, some party deterministic. For example the vol tend to increase as you get closer to maturity (very logical if you think about it, except if so far otm or itm as no change in price for change in underlying), also the vol is patly deterministic with respect to atm, otm. etc.
I traded a few options on swaptions (an interesting variant of compound options) (but only a few OTC) and yes then I looked somewhat into this, but not in as great detail as one ideally should do, as it only was a couple of trades in a market with very wide bid ask spreads.
Alternatively you could try to model the swaption volatility indirectly from the underlying (the swap), but this will at best be a rough approximation at least if based on models based on dynamic delta hedging to remove all risk all the time. Even stochastic vol models will give you unrealistic dynamic here in my view, but can still give you some insight.
A very interesting topic, but yes you need good database for many strikes, preferably intraday, and good knowledge of options. (but I do not really know what or why you are interested in this of course, I am mainly interested in theory that are useful in practice)
By sorting out different strikes etc and doing a lot of comparisons you should be able to see that some of the dynamic is actually deterministic, also models and higher order greeks (read my know your weapon even if only for standard options not for compounds) will help you too understand the dynamic of the volatility in the swaption itself.
If from a pure theoretical point of view under highly unrealistic assumptions of geometric brownian motion you could simply take the vol of underlying (swap) and multiply by the absolute value of the elasticity. Then you have a approximation of the vol of the swaption. From my memory it is something about this approximation method in Bensoussan, A., M. Crouhy, And D. Galai (1995):“BlackScholes Approximation of Warrant Prices,” Advances in Futures and Options Research, 8, 1–14. Not very useful in practice of course, but still it gives a little insight in my view.
Espen 



mtsm


Total Posts: 232 
Joined: Dec 2010 


no, sorry, I meant a measure of realized that is representative for the underlying swap of some swaption.
yes, you need a good db to do what you did and at a market maker you have such data available (for one source, ie the maker's source itself). at a maker you also realize what a joke that market is on so many days and for so many grid points. so that mitigates the quality of the data somewhat in a quite intrinsic way. 




EGH


Total Posts: 59 
Joined: Nov 2014 


"no, sorry, I meant a measure of realized that is representative for the underlying swap of some swaption. "
This is much easier than vol of swaption itself, but of course it depends on how detailed analysis you want. From the little I remember from my several years as market maker in swaptions (in several fixed income markets, mostly USD (very liquid) as well as NOK (very illiquid) (and to some degree I was also involved in market making of SEK and DKK swaption) was simply to look at realized from the underlying swap yields, daily of course, and if you also have intraday that is great in addition. The underlying swap is directly given from the swap yield, or other way around. Underlying swaps "volatility analyzing tools" is almost like any other market, naturally you need to check specification in the currency you are working in very well, as I am sure you have done..
Naturally some interesting effects to study also here, as a 5 year plain vanilla swap no longer is 5 year tomorrow. Also the underlying realized vol naturally tend to increase the shorter (tome to maturity) it is. Also you can do more advanced studies comparing vol on various days and hours and see if correlated to economic event calendar, mostly important for swaptions with short time to maturity.
Also I paid attention to overnight vol...close price to open price...the o/n vol is quite high in scandinavian currencies (I am talking about interest rate swaps in these currencies), as small open economies much dependent on also US, and swaption and swaps market in scandinavian at least back then where closed long before US closed....so you had gap risk o/n in particular, and this gap risk is partly reflected in o/n. vol. and hard to hedge with delta.
Check o/n vol + weekend vol as minimum in addition to basic analysis, then next you can do things on hourly basis etc. Well of course it all depends what you need it for. Just a few basic tips from previous swaption market maker....




Jurassic


Total Posts: 199 
Joined: Mar 2018 


> Also the underlying realized vol naturally tend to increase the shorter (tome to maturity) it is.
How do you normally deal with this (any asset)? 




Alpine


Total Posts: 60 
Joined: Mar 2007 


You'll want to look at the volatility of the underlying swap  i.e. the volatility of the forward swap rate (starting at option expiry). The instantaneous vol of the forward swap generally increases as the time to the forward start decreases.
For every day of yield curve movements you'll have a vector of realized changes for different forward starts of the same underlying swap. So instead of the simple time series analysis used for equities, you'll have paneltype data.
HtH. 



Jurassic


Total Posts: 199 
Joined: Mar 2018 


Im still a bit confused about the term structure effects 




manndeo


Total Posts: 1 
Joined: Oct 2018 


hi. im abit confused about how you would go about doing this too.
If we were looking for the realized volatility for the spot price of a currency pair for example we would first obtain a time series or the daily returns in spot of the currency pair and then we would obtain the stdev of this vector. This is pretty straightforward.
But in the case of a swaption we have different forward starts of the same underlying swaps. This would mean we would have multiple vectors of daily returns for a specific period for each of these vectors. If i take the stdev of these vectors then i will have a series of volatilities. How then would i put this all together to get one realized volatility figure for the whole swaption? This is the part i find confusing. 



Strange


Total Posts: 1532 
Joined: Jun 2004 


You have to take the term structure effect into account when comparing implied vs realized. It's not something specific to swaptions  you get the same problem (with an opposite sign) in options on commodity futures. Many ways to skin this cat, for example using an average of constant maturity forwards. 
I don't interest myself in 'why?'. I think more often in terms of 'when?'...sometimes 'where?'. And always how much?' 



mtsm


Total Posts: 232 
Joined: Dec 2010 


Look for the old ML article, it discusses this. 


