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12 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 ...
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  • 721
9 votes
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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}{\...
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  • 14.1k
8 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 ...
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  • 2,426
8 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 ...
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  • 14k
8 votes
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Why doesn't Variance-Gamma process flatten volatility skew for short term options?

VG belongs in the family of variance-mean mixture models. Given a horizon $T$ the distribution of log-returns $f$ is a mixture of Gaussians $f_G$ with randomised mean and variance. The randomisation ...
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  • 4,227
7 votes

Does the fact that volatility is not constant imply existence of skew?

It is not the fact that volatility is time varying that creates the skew per se, but the fact that volatility is negatively correlated with the spot. That is to say, as the stock/index price declines ...
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  • 4,227
6 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 $$ X= \frac{\ln(S_T/S_t)-\mu_\tau}{\sigma_\tau} $$ ...
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  • 5,038
5 votes

Skew in Black Scholes model

Well the terminal FX rate is lognormally distributed and lognormals are skewed. So this is not surprising.
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  • 6,763
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 ...
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  • 14.4k
4 votes

What are popular metrics for Option Skew?

My preferred measure for skew would be the difference between the implied volatilities corresponding to the strikes where the Black-Scholes $d_2 = 0$ and $d_1 = 0$. The reason I prefer this to others ...
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3 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) ...
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  • 14k
3 votes
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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 ...
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  • 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 ...
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  • 2,426
3 votes

volatility skew for lognormal model is flat?

The answer is that by definition, if the underlying stock obeys a lognormal distribution with std deviation parameter sigma, then the implied vol of options priced using this model will be sigma. Of ...
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  • 14.1k
3 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 ...
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  • 248
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 ...
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  • 4,926
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.
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  • 7,702
2 votes

Understanding skew of SPX - Why does IV of OTM puts increase with strike?

When I saw these curves they seemed very strange to me. I believe it is a data-quality issue.I went to Bloomberg and I retrieved the implied vols for 70 near ATM strikes of the weekly SPX options ...
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  • 9,107
2 votes

Why can't you arb skew by buying options with low implied vol and selling high implied vol in the same month and dynamically hedging?

It also depends on at what levels of the spot the higher vol gets realized. In your example: if you buy an option on a 40 vol expiring in a month and over the next month stock the average vol of ...
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  • 1,411
2 votes

Why can't you arb skew by buying options with low implied vol and selling high implied vol in the same month and dynamically hedging?

The market does not follow Black-Scholes assumptions, as you clearly know : there is a skew and vol levels change. Neither does it follow any other particular known model. So when you say "...
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  • 1,865
2 votes

How do I track implied volatility of specific delta?

Basically there are three steps to accomplish this. 1 - collect time series of options for several expirations and strikes. 2 - calculate implied volatility surface for every time period, and use ...
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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 ...
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2 votes

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

In optimiazation system, you have to weight the price for the different maturities in a way that reflect your confidence in each data point (influenced by liquidity). One way to do so is to weight, ...
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  • 31
2 votes

What is the implied volatility skew?

Old and golden question, and maybe a new perspective: As the previous answers have pointed out, distinction needs to made between "skewness" and "skew". The former is the third ...
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2 votes

Why vertical skew is same for puts and calls

put call parity guarantees that the implied volatility of a call and put with the same strike is the same. So the smile graph is the same as well and so are all quantities derived for it. In more ...
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  • 6,763
2 votes

Black Scholes - how to calculate delta with a vol skew

There's no best method. The question is : what is the behavior of the volatility structure (atm and skew) when the underlying moves? Each method assumes something different. In the real market, ...
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  • 14.1k
2 votes
Accepted

Spot and Vol Correlation in Idealised Regimes of the Volatility Surface

In black-scholes world, correlation between volatility and spot is zero. From the above details you can estimate how the implied volatility for a given option (note options have FIXED strikes) might ...
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  • 331
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 ...
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  • 14k
2 votes

How do you factor in skew when assessing implied volatility for a non-atm option?

First of all, you should understand where the IVs are coming from and the assumptions made in the model to derive the values. IVs are solved through option pricing models by the given market prices ...
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  • 382
2 votes

How skew in vertical put spreads change the payoff?

Well, the probabilities implied by the market are not equal. If you believe they should be equal, then go ahead and express yourself in the market. The point is , it is not an objective fact that ...
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