Sticky strike/Delta vs skew

[ducatista]

Im having some trouble relating these terms to vol surface. I understand their basic definitions (sticky strike = vol & PX are inversely related, sticky Delta = they move together), and I do understand the market conditions under which we might expect to see one vs the other.

But are these terms also a proxy for skew? For example, does sticky strike = negative skew (equity indices *most* of the time) and sticky delta = positive skew (commodities etc)? Are they independent of each other and I’m missing something? Some clarification would be appreciated

Does this also mean that equity/index short vol would not work under sticky Delta? (Or rather, you’d have to flip your expectations of when you’d want to be short vol if you were planning to still do it nonetheless). Thanks

 

[isabellavillareal]

Hello,
By delta means the forward vol surface conditional on a future spot has the same shape so the vol of a fixed strike moves around as it's delta changes. By strike means a given strike keeps the same vol so the shape of the smile evolves.
This effect is about the evolution of the vol surface in time: E(v(S(T),T,k)|S(t)). If we assume the volatility is deterministic the shape of the forward surface is completely determined by the marginal distributions of the inital forward variance. The initial smile and skew decreases as you move further out in expiry and you observe a much flatter forward smile and skew with a higher at the money. There is still a spot vol correlation and vol of vol but it is completely determined by the spot process given the initial surface. This regime is most similar to the sticky strike case. If instead you allow the variance to have a random component, which they call stochastic vol and is described by the sde:

Here theta is the speed of the mean reversion, omega the average instantaneous variance, epsilon the vol of vol and B(t) a brownian motion with [dB,dB*](t)=pdt the covariance process of the brownian spot and vol processes. Spot is assumed to be, as in BS, an inhomogenous lognormal diffusion with sqrt(v) the volatility. The initial surfaces must match the local vol so the expected value of the forward variance integrated across all strikes is still fixed but with epsilon very big the second moment of the distribution increases so you get a higher forward smile, lower at the money. The third moment, so how uneven the wings are which determines the dynamics of the risk reversal at a given forward spot is determined by the correlation between the spot and vol processes p so with p close to -1 more of the forward variance is in the left tail of the distribution so you maintain the downside skew as in the initial surface. These conditions then are much closer to the by delta case and are what you observe in practice. In path dependent options like barriers vol swaps and other exotics this more realistic model is used in pricing usually with an extra parametre in front of the epsilon representing a blending parametre (note with a zero in front it reduces trivially to the local vol case). There are many problems with the approach.

 

[xandman]

Im having some trouble relating these terms to vol surface. I understand their basic definitions (sticky strike = vol & PX are inversely related, sticky Delta = they move together), and I do understand the market conditions under which we might expect to see one vs the other.

But are these terms also a proxy for skew? For example, does sticky strike = negative skew (equity indices *most* of the time) and sticky delta = positive skew (commodities etc)? Are they independent of each other and I’m missing something? Some clarification would be appreciated

Does this also mean that equity/index short vol would not work under sticky Delta? (Or rather, you’d have to flip your expectations of when you’d want to be short vol if you were planning to still do it nonetheless). Thanks

I am not sure what model you are building or where you are in trading on this. For me, these terms just describe describe generally observable behavioral differences between Equity and Commodity skews. One can normalize the options chain to whatever dimension they want.

If we believe that skewness reflects directional expectations in the market, then:

1) (ss) sticky strike means that the market IV levels are just bobbing up and down in unison. No change in long run expectations.
2) (sd) sticky delta means there is a shift in directional expectations

Why is ss ascribed more to equities?

The long term direction of equities is up with short term mean reversion. IV will always be higher on the OTM puts. It is ingrained to expectations.

Why is sd ascribed more to commodities?

Commodities will readily go on a intermediate/long downtrend and uptrend. Thus, you can easily see a flipping of the high side of the skew. As well as pricing by moneyness to be consistent with the changing expectations. Commodities traders are bi-polar.

Is it a mechanical signal by which we flip our expectations? I don't think so. It is priced in when you see it. We are just seeing varying degrees of expectation. As a trader, you choose to go along or fade the trade with the risk reversal, there is just less convexity in the equity RRs.

 

[xandman]

Hello,
By delta means the forward vol surface conditional on a future spot has the same shape so the vol of a fixed strike moves around as it's delta changes. By strike means a given strike keeps the same vol so the shape of the smile evolves.
This effect is about the evolution of the vol surface in time: E(v(S(T),T,k)|S(t)). If we assume the volatility is deterministic the shape of the forward surface is completely determined by the marginal distributions of the inital forward variance. The initial smile and skew decreases as you move further out in expiry and you observe a much flatter forward smile and skew with a higher at the money. There is still a spot vol correlation and vol of vol but it is completely determined by the spot process given the initial surface. This regime is most similar to the sticky strike case. If instead you allow the variance to have a random component, which they call stochastic vol and is described by the sde:

Here theta is the speed of the mean reversion, omega the average instantaneous variance, epsilon the vol of vol and B(t) a brownian motion with [dB,dB*](t)=pdt the covariance process of the brownian spot and vol processes. Spot is assumed to be, as in BS, an inhomogenous lognormal diffusion with sqrt(v) the volatility. The initial surfaces must match the local vol so the expected value of the forward variance integrated across all strikes is still fixed but with epsilon very big the second moment of the distribution increases so you get a higher forward smile, lower at the money. The third moment, so how uneven the wings are which determines the dynamics of the risk reversal at a given forward spot is determined by the correlation between the spot and vol processes p so with p close to -1 more of the forward variance is in the left tail of the distribution so you maintain the downside skew as in the initial surface. These conditions then are much closer to the by delta case and are what you observe in practice. In path dependent options like barriers vol swaps and other exotics this more realistic model is used in pricing usually with an extra parametre in front of the epsilon representing a blending parametre (note with a zero in front it reduces trivially to the local vol case). There are many problems with the approach.

I think this guy is a nut case. I don't think the time dimension has any relevance. Please disprove me like a normal person...in easily digestible language.

 

[isabellavillareal]

I do not believe in any of your premises like skew reflects expected direction and none of your deductions follow from them using known rules of inference.

 

[xandman]

I do not believe in any of your premises like skew reflects expected direction and none of your deductions follow from them using known rules of inference.

Fair enough. So, why is the time dimension relevant?

 

[isabellavillareal]

Why is the time dimension relevent. Well a trading strategy is a set of stopping times. It appears to be fundamental to the nature of consciouness that time ticks by but perhaps it's entropy and time and space are interchangeable.

 

[xandman]

Why is the time dimension relevent. Well a trading strategy is a set of stopping times. It appears to be fundamental to the nature of consciouness that time ticks by but perhaps it's entropy and time and space are interchangeable.

Makes sense. Get this man a drink!