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14 votes
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Bergomi: Skew arbitrage

Great question. Let me try to provide some insights and thoughts regarding the points and questions you raised. It may not be a full answer but hopefully it will help connecting the contents in the ...
SI7's user avatar
  • 843
13 votes
Accepted

Skew and shadow delta

Basically, the author is saying that the delta of an option, $dC/dS = \frac{\partial C}{\partial S} + \frac{\partial C}{\partial v}\frac{\partial v}{\partial S}$, where the $\frac{\partial C}{\...
dm63's user avatar
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11 votes

Why is a variance swap long skew?

As I've mentioned in a comment, it would be wrong to think that entering a variance swap specifically amounts to being "long skew". What you can say however is that, in the absence of jumps (i.e. in ...
Quantuple's user avatar
  • 14.7k
10 votes

Why is a variance swap long skew?

If you take Quantuple's stuff a little further, you can really see whether you're long skew. You can pretty easily see the dependence on convexity too (though it should be obvious that you're long ...
will's user avatar
  • 2,581
6 votes

How are the BKM risk-neutral moments derived?

Let's focus on the volatility contract price. Generalisation to cubic and quartic contracts is straightforward. Following the paper's notations, the evaluation date is $t$ and the (European) ...
Quantuple's user avatar
  • 14.7k
5 votes

What are popular metrics for Option Skew?

Volatility Skew is generally quoted in terms of Risk Reversals. I know that for FX products and because of Delta stickiness, the quoted Risk reversals are regarding the 10% and 25% Delta. Edit: To ...
Xman's user avatar
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5 votes
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At-the-money forward implied volatility

Let $$\ln\left(S_T/S_t\right) $$ have mean $\mu_\tau$ and standard deviation $\sigma_\tau$, where $\tau=T-t$, and density of its standardized form $$ X= \frac{\ln(S_T/S_t)-\mu_\tau}{\sigma_\tau} $$ ...
ir7's user avatar
  • 5,043
5 votes
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Is variance swap long volatility of volatility?

My two cents: Let's agree that a derivative is long an underlying if the payoff of the derivative increases with the price of the underlying $S$. Then buying a variance swap is going long the ...
Frido's user avatar
  • 1,906
5 votes

Is variance swap long volatility of volatility?

What about the following argument: a variance swap can be replicated with a portfolio of vanilla options, nearly all of which are out of the money (OTM) . But it is well known that OTM options are ...
dm63's user avatar
  • 17.2k
5 votes
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Calculating skew for an options structure

There are many definitions / concepts of skew. For a good overview of 'skew' you might like Mixon, What does implied volatility skew measure? What you have done in your example is calculate the slope ...
Frido's user avatar
  • 1,906
5 votes

Options related factors forecasting cross section of returns

There is plenty of research! Below I list but a few examples of options being used to predict future stock returns (either in aggregate or in the cross-section). Of course, you can also use current ...
Kevin's user avatar
  • 16k
4 votes

Evaluating trading strategies by the skewness of returns

You do not state whether your evaluations will result in potentially implementing multiple strategies or just one of them. This matters because if you are going to be combining multiple ones then you ...
Brian B's user avatar
  • 14.9k
4 votes

Fitting Function for Skew

Why don't you just use SSVI (https://arxiv.org/abs/1204.0646) or maybe even eSSVI (https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2971502)? With this parametric approaches an arbitrage free ...
JohnDoe's user avatar
  • 278
4 votes

Is variance swap long volatility of volatility?

Since the variance swap is linear in variance. Its local volatility exposure is 2σ, with second derivative = 2. If one was to hedge this local volatility exposure using options or a volatility swap, ...
Newquant's user avatar
  • 804
3 votes

How does volatility skew change with underlying spot?

I'm surprised that no one has yet mentionned the Christoffersen, Heston and Jacobs paper entitled "The Shape and Term Structure of the Index Option Smirk: Why Multifactor Stochastic Volatility Models ...
Stéphane's user avatar
  • 2,486
3 votes
Accepted

Common Quanto adjustment

First of all, quanto options (options denominated in FOR currency but whose value we wish to determine is in DOM currency) are mainly traded over-the-counter, hence their prices are not likely ...
JejeBelfort's user avatar
  • 1,219
3 votes
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Detailing a proposition about option pricing model coherence

The value of a call option at expiry is $V=\mathrm{max}(0, S_t-K)$. If you set $K=0$, then you have $V=\mathrm{max}(0, S_t)$, and since $S\geqslant0$, $\mathrm{max}(0, S_t) = S_t$ - i.e. ie's ...
will's user avatar
  • 2,581
3 votes
Accepted

How does volatility skew change with underlying spot?

This is a very interesting question and obviously (as almost any reasonable question w.r.t to spot-vol-skew correlation) does not have a unique answer. Rather, different regimes may exist. In one of ...
SI7's user avatar
  • 843
3 votes

A PARADOX? - relationship between risk reversal (slope of vol smile) and digital price

I think you have a misunderstanding here, the fact that the vol is higher on the downside doesn't mean the probability of the price going down is higher, it means that the magnitude of down moves (if ...
Lliane's user avatar
  • 2,908
3 votes

What is better: A negatively skewed return or a positively skewed returns distribution?

The usual answer is that most risk assets tend to exhibit left-skew, with correlations ->1 into the left tail (ie diversification breaks down). And so positively skewed assets have attractive ...
demully's user avatar
  • 5,071
3 votes

Confusion with the equity option skew

It’s relatively more expensive compared to the BS price with flat volatility. The option premium of the 5% OTM put is higher than the 10% OTM put.
Bob Jansen's user avatar
  • 8,562
3 votes

Does skew flatten with a decline in volatility?

The description by Bennett is not very clear, but the reference to the Figure 103 in the text at the end of the paragraph that you cite should resolve the issue. Bennett is saying that once the sudden ...
Hans-Peter Schrei's user avatar
2 votes
Accepted

Vol skew and spot-vol correlation

Suppose you were to price 2 instruments: a strongly OTM put and a strongly OTM Call. In the standard BS settings, instantaneous volatility is assumed to be constant. Consequently, the implied ...
Quantuple's user avatar
  • 14.7k
2 votes
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Volatility Smile/skew in volatile markets

Actually, you are going to find that the vol premium on the wings is lower in volatile markets, purely due to the "cabinet effect" when vol is very low. I think, however, that you are mixing up ...
Nivel Egres's user avatar
2 votes

Is there a popular curve fitting formula of options skew vs strike price or vs Delta?

In the public domain, there is SVI (stochastic volatility inspired) curve invented by Jim Gatheral. If you need curves which can fit very liquid names or handle W-shape curves (e.g. on earning), you ...
Misha Fomytskyi's user avatar

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