how does volatility surface work in market practice

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PatrickYu

Lots options strategies focus on the volatility. E.g. Long a straddle to gain from volatility rallying, or short a straddle to gain when volatility falls.
So the key is if the implied volatility (for the listed options) is underestimated or not, comparing it to the historical volatility, using tools like volatility cone or something else.

And we also found lots models (papers) of constructing implied volatility surface, local valatility surface, stochastic volatility and etc. How was these volatilities used in market practice?
In OTC market, the sell side (market makers) may need them to pricing their own options (usually exotic options) to sell?
But if a buy side speculator who just trade exchange listed options, how could these volatility models could be used?

Thanks in advance.
 
In practice, the SABR volatility model is often used in the interest rate derivatives market. (swaptions / caplets / floorlets)

The SABR model is a stochastic volatility model that attempts to model the volatility surface and to capture the empirically observed dynamic behavior of the volatility smile.

The SABR parameters can be determined by calibration to market data. Specifically, the model is calibrated to a set of option prices for a given expiration.

While the SABR model is not often used for equity derivatives, recently it has been paired with several short rate models to price long maturity equity derivatives, particularly exotic options.


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PatrickYu said:
(a) In OTC market, the sell side (market makers) may need them to pricing their own options (usually exotic options) to sell?
(b) But if a buy side speculator who just trade exchange listed options, how could these volatility models could be used?
More...
(a) Market makers (OTC and listed) use various models of volatility dynamics for both pricing and hedging. LV/SLV are accepted in the FX/EQD community, SABR is more or less standard in the rates world. More exotic models are used for various properly exotic products, though these days there is less and less trading in that world.

The idea there is that a model that approximates dynamics will allow you to better hedge (delta, foremost, and gamma/vega secondarily) by including varius cross-effects into the primary greeks. MMs are also able to actively play the vol surface shape or dynamics, though most of the time it's not model-driven.

(b) Most of the time, a buy-side trader should not be trying to build perfect no-arb models but rather concentrate more on bigger-margin/higher-risk trades. A retail trader should avoid delta-hedging all together, you just can't get the same leverage.

-- Just my .25 vega.
 
sle said:
(a) Market makers (OTC and listed) use various models of volatility dynamics for both pricing and hedging. LV/SLV are accepted in the FX/EQD community, SABR is more or less standard in the rates world. More exotic models are used for various properly exotic products, though these days there is less and less trading in that world.

The idea there is that a model that approximates dynamics will allow you to better hedge (delta, foremost, and gamma/vega secondarily) by including varius cross-effects into the primary greeks. MMs are also able to actively play the vol surface shape or dynamics, though most of the time it's not model-driven.

(b) Most of the time, a buy-side trader should not be trying to build perfect no-arb models but rather concentrate more on bigger-margin/higher-risk trades. A retail trader should avoid delta-hedging all together, you just can't get the same leverage.

-- Just my .25 vega.
More...
Thanks for the replies. sle, then how about risk management for the option tradings.
e.g. we usually calcualte var against price for the cash equity / FX. Now for options trading, shall we take both underlying price and volatility (and the greeks of option) account into var calculation?

And the scenario analysis and stress test are commonly used in risk management. Is there any special when they used for options?

I searched but did not find the ways for option risk management especially.
 
What kind of model is used to price SPX options, their volatilities and skew?
Is there a model that calculates the change of IV over time (IV surface)?

Thanks
 
PatrickYu said:
And the scenario analysis and stress test are commonly used in risk management. Is there any special when they used for options?
More...

For book management, you mostly want your regular Greeks and some sort of spot slides per underlying. If you have a large enough book, you also want all sorts of operational gimmics like roll/expiration delta report, early excersize reports etc. In some specific cases you actually want a complex model/scenario system - e.g. for my VIX mm book, I use a pretty complex methodology that includes PCA etc. At some point, the general practice becomes a personal know-how that gets the trader paid the big bucks.

Benthecat said:
What kind of model is used to price SPX options, their volatilities and skew?
Is there a model that calculates the change of IV over time (IV surface)?
More...
Yes, a good desk would use some sort of smart dynamics model for risk management. Usually, it's something done in-house, the general thought is to have a skew+smile component that fits every volatility slice and then use a backbone for the evolution of vol as a function of spot. In terms of time evolution, you rarely do anything beyond keeping a term structure of skew, e.g. in form of sk10 per expiration.
 
This is a very interesting topic. As sle says, most of the tools of the trade are highly proprietary, and its unlikely anybody wants to give away their secret sauce. Still, I'm sure many (myself included) would find it helpful if a few furtive hints could be cast as to what kind of tricks others have up their sleeve.

I'll get the ball rolling a bit with a few meager offerings of my own. As sle mentioned, one of the main aims is to approximate the vol dynamics for inclusion in your greeks (namely delta). From Bergomi's excellent Smile Dynamics series of papers, one has the result of ATM vol moving ~1.5x the move priced into the Skew [ie ATMvol(t) -ATMvol(t-1) = 1.5xSkew1%x(S(t)/S(t-1)-1)] - so there, you've got yourself some very simple ATM vol dynamics (not just an empirical result either, but has theoretical justification - the multiplier should be 2-SkewDecayPower, which is usually 0.5 ie everyone's beloved root time law). From there, you probably want to build a factor model for the skew's evolution (ie skew tends to flatten with spot lower, steepen with spot higher - add as many bells and whistles as you see fit). With just these two simple tweaks, one is likely to find their deltas much more reliable - especially for skew sensitive positions like callspreads or riskys.
 
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