Amazing Sarbo, this is a gem of a video. Such a beatiful explanation, with a clear voice. Was surprised to see this was the only video in the playlist. Keep posting such gems. Looking forward to seeing more.
Confused about the point at 16:42, beta=0, normal model, should allow you to price negative strikes right of forward rate? - do you have it opposite here?
Yes, but why would you want to price options on negative forward rates in the swaptions market? That is precisely why traders set Beta -> 1 at the short end of the curve, to force more lognormally distributed rates. At the longer end of the curve, where rates are very unlikely to go negative in a random process, Beta -> 0 is fine.
That is basically the implied volatility of a forward-starting swap where the start date on the swap is after the expiration date of the option. There is no particularly good way to get that volatility from a market cube. You can try a number of different methods, none of which are particularly simple or easy, because of all of the ways in which correlation and skewness interact. The simplest and easiest is probably to interpolate between the volatilities in the cube of two spot-starting swaptions that correspond to the tenors of your midcurve. e.g. if you have a 3M option on a 10Y swap that starts in 6M, then you can get the implied volatility by using the 3M10Y and 6M10Y points and coming up with some "intelligent" way of interpolating between those two points, or weighing the volatilities based on the historical correlation between the two other implied vols.
That video was the culmination of a personal interest project, before I got busy with other things. There are plenty of other good videos on these models by people much smarter than me. If I ever get the time and/or interest to go back to those models, I might make a new video eventually. Respectfully, I strongly disagree with your characterisation of R as a dead language. It is nothing of the sort, and is in very active use in the banking and insurance industries right now.
If SABR is not good for CMS due to bad calibration on far strikes. How can we address this issue if we still need to hedge a portfolio of cms, swaptions and capfloor cap/floor with SABR parameters? Can we add another parameters for a better fit (and in the mean time avoiding over parameterization of ) what's the best practice?
In theory, you could use a full tree model, like an HJM framework, or a Hull-White two-factor model. However, in reality, this would not really help much, because no matter how good your model is, you are still calibrating it against active market data. And the problem is, really deep-OTM/ITM swaptions are very illiquid, so when you go to the market looking for quotes, you will often find huge spreads (relatively speaking) between what different brokers and sell-side banks will charge you. For example, if you want to price a 15% payer swaption in the US market, you could go to Deutsche and get a quote that is, say, 80% implied vol. You could then go to BNP and ask them for the same product - and they might quote you 95% implied vol. And you can repeat the process right down the line, only to find lots of different quotes that are way off from each other. The result is an inevitable and very difficult challenge in pricing those really illiquid options - which, by definition, are highly variable in price. There is no model that can overcome this calibration problem - it is a function of markets, not mathematics.
In theory, yes, if Rho = 1, then you get division by zero, followed by spontaneous combustion and appearance of black holes in the living room, etc. In practice, however, forward rates and volatilities are NEVER 100% positively or negatively correlated. That equation is an output of the Singular Perturbation Analysis technique, and as such is a very close analytical approximation of the behaviours of the underlying stochastic processes.
This is as good a SABR model and calibration explanation as one would ever see
Amazing Sarbo, this is a gem of a video. Such a beatiful explanation, with a clear voice. Was surprised to see this was the only video in the playlist. Keep posting such gems. Looking forward to seeing more.
What a chad, you should upload more vids
Thank you very much, the video is really clear I cannot tell you how much you help me understand all of this.
Ramanujan > Kamta
Thank you I really like the explanation of this model, would it be possible to do the same video but for LMM/FMM? Cheers
Very good perspective ! Thanks for this. Looking forward to more such videos. Cheers✌🏻
Confused about the point at 16:42, beta=0, normal model, should allow you to price negative strikes right of forward rate? - do you have it opposite here?
Yes, but why would you want to price options on negative forward rates in the swaptions market? That is precisely why traders set Beta -> 1 at the short end of the curve, to force more lognormally distributed rates. At the longer end of the curve, where rates are very unlikely to go negative in a random process, Beta -> 0 is fine.
Hey Sarbo thanks for the insightful video, given this do you know how one could calculate the volatility of a midcurve swaption?
That is basically the implied volatility of a forward-starting swap where the start date on the swap is after the expiration date of the option. There is no particularly good way to get that volatility from a market cube. You can try a number of different methods, none of which are particularly simple or easy, because of all of the ways in which correlation and skewness interact. The simplest and easiest is probably to interpolate between the volatilities in the cube of two spot-starting swaptions that correspond to the tenors of your midcurve.
e.g. if you have a 3M option on a 10Y swap that starts in 6M, then you can get the implied volatility by using the 3M10Y and 6M10Y points and coming up with some "intelligent" way of interpolating between those two points, or weighing the volatilities based on the historical correlation between the two other implied vols.
This was great! But it was 2 years ago. where are the next models in the series, especially hullwhite, karasinski etc. in python (R is dead)
That video was the culmination of a personal interest project, before I got busy with other things. There are plenty of other good videos on these models by people much smarter than me. If I ever get the time and/or interest to go back to those models, I might make a new video eventually.
Respectfully, I strongly disagree with your characterisation of R as a dead language. It is nothing of the sort, and is in very active use in the banking and insurance industries right now.
If SABR is not good for CMS due to bad calibration on far strikes. How can we address this issue if we still need to hedge a portfolio of cms, swaptions and capfloor cap/floor with SABR parameters? Can we add another parameters for a better fit (and in the mean time avoiding over parameterization of ) what's the best practice?
In theory, you could use a full tree model, like an HJM framework, or a Hull-White two-factor model. However, in reality, this would not really help much, because no matter how good your model is, you are still calibrating it against active market data. And the problem is, really deep-OTM/ITM swaptions are very illiquid, so when you go to the market looking for quotes, you will often find huge spreads (relatively speaking) between what different brokers and sell-side banks will charge you.
For example, if you want to price a 15% payer swaption in the US market, you could go to Deutsche and get a quote that is, say, 80% implied vol. You could then go to BNP and ask them for the same product - and they might quote you 95% implied vol. And you can repeat the process right down the line, only to find lots of different quotes that are way off from each other.
The result is an inevitable and very difficult challenge in pricing those really illiquid options - which, by definition, are highly variable in price. There is no model that can overcome this calibration problem - it is a function of markets, not mathematics.
If Rho is a correlation coefficient that can take on values between -1 and 1, how can x(z) have (1-Rho) as a divisor?
In theory, yes, if Rho = 1, then you get division by zero, followed by spontaneous combustion and appearance of black holes in the living room, etc. In practice, however, forward rates and volatilities are NEVER 100% positively or negatively correlated. That equation is an output of the Singular Perturbation Analysis technique, and as such is a very close analytical approximation of the behaviours of the underlying stochastic processes.
Also what’s your website! Great video btw thanks 😊
sarbosaha.com/
in 16:31 \beta=0 [\beta=1 ] gives you SDE that can be negative [only positive]. You changed this and said an opposite.