10
votes
Book/ Articles recommendation for Volatility models
I have also currently started to learn about the subject. This is some of the material I have encountered:
Many people recommend the book "The Volatility Surface: A Practitioner's Guide" by ...
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9
votes
Accepted
Different volatility surface ( Local vol, Stochastic vol etc.)
I'll answer both of your questions in one go:
Your ideas are correct. If the Black-Scholes model was true, the implied volatility surface would be flat but it is not in real life. Thus, the geometric ...
- 15.3k
9
votes
Is it possible to have only one volatility surface for american options (that fits both calls and puts)?
Usually, there is only one vol surface (I have never seen or heard of anyone using two). Almost certainly the most advanced commercially available vol surfaces are built by voladynamics. They also ...
- 8,143
8
votes
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What does it mean to "calibrate vols"
You are an investment bank. You trade a multitude of vanilla and exotic options. You want to make sure the option prices you quote as a client are arbitrage-free with respect to liquid option prices ...
- 7,999
8
votes
Why is volatility skew/smile for long term options flatter compare to short term options?
One possible reason could be jumps. Over the longer maturity, there could be more jumps so the jumps average out in a way; whereas over the short term, a jump can make a bigger difference and hence ...
- 6,204
7
votes
Accepted
Implied Volatility Surface - log forward moneyness
The reason is that, as shown in Proposition 2.1 of that paper, in order to exclude static calendar arbitrage, the total variance has to be strictly increasing in forward moneyness. See also the below ...
- 5,959
7
votes
Accepted
Interpolation of FX Vol Surface from non-uniform strike vs tenor grid
I tried something along these lines in Quantlib python a few weeks ago. Slightly more simple compared to your approach I think:
start with a standard delta quote convention for FX vols (10D puts, 25D ...
- 1,231
7
votes
Interpolation of FX Vol Surface from non-uniform strike vs tenor grid
In the end I found that fitting a SABR smile to each tenor (borrowing a result from this answer) was sufficient to build a local vol surface that was smooth and well-behaved enough to build a variance ...
- 2,996
7
votes
Theoretical and practical drawbacks of using Deep Learning for calibration and pricing
The essence of the problem is the "bias-variance" problem in machine learning. Which you can wiki (or find dozens of papers on; it's a famous issue).
You can, with ever greater complexity, ...
- 5,041
6
votes
FX smile extrapolation
This is a big industry, but here are some alternatives(as usual, the best choice depends on purpose and desired accuracy):
Fit a quadratic in delta space: $\sigma_{\Delta}=a + b \left( \Delta
- \...
- 6,204
6
votes
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Intuition for the Effect of Vol of Vol in Heston Model on Volatility Surface
Maybe it would help you to think of it the following way.
The strike $\sigma^2(T)$ of a fresh-start variance swap of maturity $T$ in the Heston model only depends on parameters $(v_0,\theta,\kappa)$, ...
- 14.5k
6
votes
Why use moneyness as an axis on a volatility surface
First off, there are different types of moneyness one can use when constructing a volatility surface. Each have their own advantages.
Absolute-moneyness: using absolute spot-strike comparison as a ...
- 123
6
votes
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Does shifting/scaling the IV surface relatively/absolutely introduce arbitrage?
Long story short: yes both might introduce static arbitrage opportunities if performed blindly.
There are 3 types of static arbitrage to consider:
Calendar arbitrage: total (implied) variance should ...
- 14.5k
5
votes
Accepted
Question about volatility surfaces
Let's take a step back to look at what implied volatility (IV) really is. If we know the price of a call option, the interest rate (we can use the spot rate corresponding the option maturity) then ...
- 1,627
5
votes
Proof of arbitrage-free implied volatility surface in relation to local volatility surfaces
This is not quite true, in either direction.
If you have an arbitrage free implied vol surface, you might not have a well-defined local vol surface. An example comes from a discrete model. Consider ...
- 1,875
5
votes
Why use moneyness as an axis on a volatility surface
If you use constant strike, the moneyness changes as the underlying changes. Out of the money equity options tend to trade at a premium to at the money options (smiles/skew). Therefore, the ...
- 5,662
5
votes
SABR model - beta
In my experience, $\beta$ is frequently pre-selected from a priori considerations because there is a large degree of redundancy between $\beta$ and $\rho$ (both affect the vol smile in similar ways).
...
- 8,143
5
votes
Accepted
How to structure a trade using vanilla equity options to get vega exposure to forward volatility?
Let $I(K_1)$ be the IV of a vanilla option with strike $K_1$ and maturity $T_1$ and similarly $I(K_2)$ corresponds to strike $K_2$ and maturity date $T_2 > T_1$.
What I'd suggest you try to trade ...
- 1,739
5
votes
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Option Pricing for Illiquid case
Warning upfront: I have NO experience with crypto currencies. I believe I do have a relatively decent experience with options in general though. What follows will be a generic explanation, largely ...
- 8,143
4
votes
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How to get the local volatility from IV surface?
You can convert the implied volatility to local volatility using this formula:
$\sigma^2 \left(T,y\right)=\frac{\frac{\partial w}{\partial T}}{1 -\frac{ y}{w} \frac{\partial w}{\partial y}+\frac{1}{2}...
- 6,204
4
votes
Accepted
Warrant volatility surface differs for each issuer
This is a really good observation. Warrants issuers systematically overprice their products compared to the listed options market. Different issuers will show different degrees of overpricing in ...
- 5,959
4
votes
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Is there some reason for volatility smile minima to be displaced from ATM?
It really depends on the market you are interested in. Currently, almost every market has some peculiar shapes in the volatility smile driven by different dynamics or upcoming events.
One famous ...
- 823
4
votes
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Statistical metric to measure how well does the volatility surface fit the market
I suspect you want to use a weighted norm: https://math.stackexchange.com/questions/394237/understanding-weighted-inner-product-and-weighted-norms
Generally, your volatility surface (or volatility ...
- 9,215
4
votes
Is negative forward variance an arbitrage?
Let
$$
V_t^{T_1,T_2}=\frac{(T_2-t)V_t^{T_2}-(T_1-t)V_t^{T_1}}{T_2-T_1}
$$
be our forward variance where $t<T_1<T_2$, $V_t^{T_1}$ is the ATMF implied vol as seen at time $t$ for slice at maturity ...
- 747
3
votes
FX ATM-volatility quotes
Here are my thoughts.
Let's take for example the pair EURUSD and USDEUR. The fx rate for EURUSD will be $X_t$ and USDEUR $1/X_t$. Now assume that $d{X_t} = \mu{X_t} dt + \sigma{X_t} dW_t $ then thanks ...
- 106
3
votes
Accepted
Is the moneyness of a barrier option based on the strike value or the barrier when mapping to a volatility surface?
If your barrier is american and your market has any sort of volatility skew then trying to map some sort of moneyness measure to the vol surface will almost certainly fail. That is due to the fact ...
- 940
3
votes
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How would one construct a volatility surface given only the spot price?
This is the illiquid option problem, which hasn't and I doubt can be solved in a nice mathematical way. I have seen a few methods used in this space
GARCH + some fanciness to get a feel for the ...
- 940
3
votes
Is it possible to have only one volatility surface for american options (that fits both calls and puts)?
I think the issue from a practical perspective is still open and not so clear. AKdemy correctly described the process, which is broadly used in practice and I'm also sure that Vola dynamics and other ...
- 823
3
votes
SABR model - beta
A tentative answer as a practitioner.
SABR is over-specified, meaning you could fit a market smile to any arbitrary, non-pathological $\beta$. The so-called redundancy between $\beta$ and $\rho$ is ...
- 31
3
votes
Accepted
Volatility swaps hedging
Although this question seems Taylor-made for me, I shall resist promoting my own work and refer you instead to Carr and Lee's seminal paper Robust replication of volatility derivatives.
Basically what ...
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