14
votes
Accepted
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 ...
- 823
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}{\...
- 16.6k
10
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 ...
- 14.5k
9
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 ...
- 2,531
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 ...
- 4,307
6
votes
Accepted
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 ...
- 1,739
6
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 ...
- 16.6k
5
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) ...
- 14.5k
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 ...
- 267
5
votes
Accepted
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
$$ X= \frac{\ln(S_T/S_t)-\mu_\tau}{\sigma_\tau} $$
...
- 5,008
5
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, ...
- 749
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 ...
- 14.7k
4
votes
Accepted
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 ...
- 1,739
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 ...
- 268
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 ...
- 1,219
3
votes
Accepted
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 ...
- 2,531
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 ...
- 16.6k
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 ...
- 2,436
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 ...
- 823
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 ...
- 5,041
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.
- 8,438
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 ...
- 1,736
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 ...
- 9,332
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 ...
- 2,543
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, ...
- 16.6k
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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