Questions tagged [volatility-smile]
The volatility-smile tag has no usage guidance, but it has a tag wiki.
157
questions
-1
votes
1
answer
98
views
Help needed in replicating FX Implied Vol Surface
I am relatively new to this area and am doing some self studying on SLV model. I am however getting stuck on trying to replicate this implied vol surface (which I will use to calculate the local vol)
...
- 1
1
vote
1
answer
86
views
Deriving vol of vol from volatility futures price
From Colin Bennet's trading volatility (pg 117), he says:
"A forward on a volatility future is short vol of vol. This means it is possible to back out the implied vol of vol from the price of ...
- 21
0
votes
0
answers
23
views
Approximating SPX index skew using PutDex & CallDex
I hope someone can help me with this. As I don’t have access to historical options data I am wondering if it is possible to deduce SPX options skew from various volatility indices - in particular ...
- 21
0
votes
0
answers
47
views
Vanna-Volga consistency result
In the Vanna-Volga (VV) paper by Castagna and Mercurio they state that, once you build up a curve of prices by interpolating-extrapolating on $K$, you can recover the same exact curve by redefining ...
- 302
3
votes
0
answers
57
views
SABR LMM for RFR
Is there a research showing a way to use SABR LMM with new RFRs such as SOFR, i.e. pricing exotic path-dependent RFR derivatives with volatility smile and skew?
I'm aware that
Looking Forward to ...
- 301
1
vote
0
answers
134
views
Market models of implied volatility and no arbitrage
Something has been bugging me for a while, and I can't really find an answer to it in papers. Maybe somebody can help me out.
In addition to modelling the instantaneous vol, or modelling forward ...
- 4,789
2
votes
0
answers
51
views
Expectation of Product of two European Option when vol smile exist
Currently I'm thinking about how to calculate the expectation of the product of two euro option, which is
$E[(S_T-K_1)^+(S_T-K_2)^+]$
I can fit some parametric vol model from the market listed option ...
- 51
0
votes
0
answers
44
views
"Back-Transforming" Smile Strangle into Market Strangle
I was wondering on whether FX vol experts here can comment on the following question:
Suppose I have a properly stripped FX vol surface, which I constructed from ATMs and by market standard ...
- 553
0
votes
0
answers
46
views
The relationship btwn RV-IV and realized skew
In studying skew I've been advised to focus on understanding on components that affect it. One such component that's been recommended to me is the relationship btwn RV-IV and realized skew. ...
- 21
3
votes
1
answer
154
views
Calibration of a volatility smile model on a partial smile
I'm using a well-known SABR model in order to build an implied volatility surface of caps/floors on a very illiquid market which is entirely missing OTM quotes. What happens to SABR implied smile/...
- 301
1
vote
0
answers
80
views
How to calculate the strike for a sticky delta volatility curve
I am sourcing the implied volatility for pricing the option. I am getting the volatility against delta but not the strike amount for those. How do I convert the delta into the strike to find the right ...
0
votes
0
answers
147
views
Bloomberg OVML| FX option pricing | Python
Wanted to check if any API for python is available to replicate Bloomberg's OVML.
The objective is to perform FX options pricing for multiple positions, and we are getting stuck in calculating ...
1
vote
1
answer
390
views
Pricing binary options under volatility smile
I was asked to show that the price of a digital/binary option $D$ while a volatility smile $\sigma(K)$ is present is given by
$$D= \exp(-rT)( \Phi(d_2) - K \sqrt{T} \phi(d_2) \sigma ' (K))$$
Where $\...
- 113
0
votes
0
answers
67
views
Can call price increase in falling markets
Say SPX falls so much that there is panic and implied volatility(iv) increases so greatly that OTM call prices are increased during the fall due to high iv
In my observation in historical data this ...
0
votes
0
answers
46
views
Clarity regarding Skew adjustment for binary options
I am reading the section on Skew adjustment for binary options on wikipedia (https://en.wikipedia.org/wiki/Binary_option#Skew) and am trying to get my head around it and gain some intuition.
First ...
- 768
1
vote
1
answer
665
views
Fitting a volatility smile with pySABR -- Python implementation of SABR model
In order to model some volatility smiles I'm using the python's pySABR package.
I ran into a situation when I have two almost identical pieces of code for two different volatility smiles missing the ...
- 301
0
votes
0
answers
22
views
Local volatilty models for fixed maturity curves with sparse equity data
I'm implementing an options analytics platform - with sparse market data going out a few months. Mostly equities and fx options. Building a fixed maturity curve like the one on quikstrike by bantix is ...
- 1
0
votes
1
answer
297
views
Can't fit Bloomberg volatility smile with pysabr. What am I doing wrong?
I want to make sure that I can properly use SABR model on 1-period interest rate options, i.e. caplets, therefore I attempted to get lognormal volatilities for 4%, 6%, ATM, 8%, 10% strikes for 3Mx6M ...
- 301
0
votes
0
answers
74
views
what is option zeta?
Is this an option greek? I've come across this term in some option book, and also online definition e.g. HERE:
A measure that captures the premium difference between the value of an
option calculated ...
- 167
4
votes
0
answers
126
views
Why calibrate volatility Models to volatility surfaces rather than underlying's historical price data?
I'm trying to grasp the rationale for calibrating stochastic volatility models (i.e. Heston model) to empirical IV data from market prices. Doesn't this assume that the options are fairly priced and ...
- 41
1
vote
1
answer
116
views
How to extract volatility smile implied by a mixture model?
If one had to extract the implied volatility smile from a local volatility model, one can simply use the relationship:
$\sigma^2_{imp}(t, x)T = \int_t^T \sigma^2_{loc}(s, x)ds$
with $\sigma_{loc}$ the ...
- 85
0
votes
1
answer
209
views
Difference of polynomial interpolation for volatility smile
I am using 5 volatility points to build a volatility smile : put 10D, put 25D, ATMF, call 25D and call 10D. I have thus 5 pairs of data : (Delta, Vol) let's say for example (10;5.75) ; (25; 5.50) ; (...
- 63
1
vote
0
answers
58
views
is the concept of skew observed in fixed odds betting markets?
Bear with me if this sounds a little flippant, but this has got me curious. I know "sports arbitrage" is an active economic activity, although the arbitrage arguments, I think, are not ...
- 111
2
votes
1
answer
70
views
Do single name stock option volatility surfaces exhibit steeper volatility smiles after stock price crash episodes?
In index options, there was not much of a smile (on the put-side) until the 1987 market crash.
I'm wondering if the same applies to single name stocks? That is, do price crashes in individual stocks ...
- 1,080
6
votes
2
answers
380
views
Black-Scholes: Volatility Smile "sharpens" with time to expiry
I have tried to calculate IV and log-moneyness (=log(S/K)) for different times to expiry
(M = less than 1 month, Q = less than 1 quarter, S = less than 1/2 of an year, Y = less than 1 year, Y (+) = ...
- 197
0
votes
1
answer
228
views
The most appropriate volatility model
Which would be the most appropriate models to find volatility trading opportunities (i.e. plot a theoretical volatility smile I can rely on) for the following instruments:
Options on equity
Options ...
- 81
7
votes
1
answer
440
views
Bermudan Swaptions - Payer vs. Receiver (LGM)
There is abundant literature discussing the pricing of Bermudan swaptions and the relevance of single-factor Markov-functional models (e.g. LGM) versus multi-factor market models (e.g. LMM).
From a ...
- 13.9k
7
votes
1
answer
251
views
Negative Density in Local Stochastic Volatility (LSV) Model Calibration
I'm trying to calibrate Local stochastic volatility model using finite difference method, and I'm mainly following this referece: Tian (2015).
I met a problem when calibrating leverage function - the ...
- 121
2
votes
1
answer
319
views
What is the difference between a volatility smile and a correlation smile?
I understand to plot correlation and volatility smiles, we have to plot the implied normal vol vs strike and observe a U-shaped relationship. How are these smiles different? Does a vol smile plotted ...
- 579
4
votes
2
answers
272
views
Intuitive explanation for the value of a binary option being lower when volatility skew is positive?
According to the formula for pricing binary options with a volatility skew, it appears that the value of the binary option for a given strike gets lower, the higher the volatility skew at that strike. ...
- 41
4
votes
1
answer
167
views
Can we observe smile arbitrage from the implied and local volatility?
Here are graphs of implied volatility and local volatility. Our prof mentioned that we can observe that the short end low strike region has some smile arbitrage. I would like to know how?
Thanks
- 41
1
vote
0
answers
86
views
How could option vega be remapped on reduced volatility surface?
try to be clear to ask my question:
Suppose the original vol surface is a n by m matrix where n is the number of pillars in the volatility term structure and m is the number of strikes. According to ...
- 11
1
vote
1
answer
158
views
Clean noisy data from arbitrage
My problem is that I have a surface of implied black volatilites that is supposed to represent market data. However, the surface contains some slight arbitrage.
More precisely, the graph contains ...
- 561
2
votes
1
answer
303
views
Relationship between time decay and gamma
In a paper titled Investing in Volatility published in 1998 by Emanuel Derman, Michael Kamal, Iraj Kani, John McClure, Cyrus Pirasteh, and Joseph Z. Zou, I found the following assertion (on page 9) ...
- 510
2
votes
1
answer
277
views
Forward starting options concepts
Consider $t_0<t<T$, with $t_0=0$ (today date) and the standard payoff of a vanilla forward starting call option,
$F_{t,T} = (S_T - S_t\cdot K)^+$, with strike $K$.
If the price of this option is ...
1
vote
1
answer
110
views
How does a concave up volatility smile correct high kurtosis for ATM option contracts?
Theoretically speaking, if we are to assume the following:
Constant implied volatility throughout all strike prices
The underlying's prices change distribution is log-leptokurtic and symmetric
Then ...
- 13
3
votes
2
answers
578
views
Question About SVI and SSVI Tradeoff between Fitness and No-Arbitrage
I’m currently working on a project to build a local volatility model out of implied volatility data and am struggling in the selection of an appropriate method to interpolate the volatility surface. I ...
- 121
4
votes
0
answers
189
views
Angular bracket notation (physics)
In a few papers I have seen the following notation:
$$
\langle X_t \rangle
$$
Also, in Bergomi's book, at page 8, we have the following equality:
$$
\biggr\langle \int_0^T e^{-rt}s^2 \frac{d^2P_{\hat{\...
- 510
6
votes
0
answers
210
views
Hedging : effect of not matching the term structure of skew
Let us assume that we construct a pure stochastic volatility model calibrated to the implied volatility surface, but that the model does not replicate accurately the observed term structure of the ...
- 510
4
votes
2
answers
253
views
Is the volatility smile a thing of the past?
Looking for example at this image from bloomberg of the OMX volatility surface, there is only a faint resemble of a smile at the shortest tenors that quickly dissipates as maturity is increased. I ...
- 768
1
vote
0
answers
161
views
How does a volatility surface based on moneyness instead of strike stay consistent with put-call parity?
By definition due to put-call parity the implied volatility will be the same for puts and calls with the same strike price and time to maturity. Meanwhile, a volatility surface is often quoted in ...
- 768
1
vote
1
answer
162
views
Expected Forward Volatility vs. Different Strikes
While theoretical options prices are derived from models, such as Black-Scholes, IV and IV skew reminds us that options prices are ultimately based on supply and demand. My question is the following: ...
- 555
1
vote
1
answer
621
views
Interpreting SABR calibration model output
Calibrate a SABR model?
Following on from this question, I have used the same market data they attached but am unsure on interpreting the output.
When I plot the SABR probabilities against strike for ...
1
vote
1
answer
118
views
Non-Trivial ATM Volatility in Vol smile construction from Market data on US Equities
have 2 quick questions please help.
Constructing vol smile (OTM puts & OTM calls) from US equity market data. for Parabolas fit or other methods, the choice/method for ATM vol is non-trivial, ...
- 91
0
votes
1
answer
86
views
Trading butterfly a long vol or short vol [closed]
Sorry for what could be a naive question.
When is the right time to trade a butterfly i.e. (buy 10d call and put vs sell atm all notional flat) is it when implied vols are high or low (relative to ...
- 11
0
votes
1
answer
257
views
Implied Volatility vs Actual Volatility Calculation
To build a term structure I need different volatilities; as I don't get them at every strike, I use interpolation technique to calculate the rest and plot. This is how I calculate the implied vols. ...
4
votes
1
answer
504
views
What does it mean that model can reflect the ”volatility smile”
I know that implied volatility is the value for which the Black Scholes model returns the correct option price. I also know that if we plot the volatility on the strike price chart, we will see "...
- 423
5
votes
1
answer
277
views
Hedging a FVA in practice
A FVA (forward volatility agreement) is a forward contract on the ATM implied volatility. So at at maturity date $T$ the payoff of a FVA with unit notional is
$$
(I_{ATM}(T,T') - K)
$$
where $I_{ATM}(...
- 4,789
9
votes
4
answers
3k
views
Implied Vol Smile: from Calls, Puts or Both?
This might be a simple question, but I couldn't find the answer anywhere: is there a separate Volatility smile (and surface) based on Calls and a separate Volatility smile (surface) based on Puts? Or ...
- 4,961
1
vote
0
answers
56
views
Terminology : definition of skew for a volatility smile
Is there a generally accepted definition of skew for volatility smiles? Is skew always defined as
$$
\frac{\partial{\widehat{\sigma}(K,T)}}{\partial{K}},
$$
where $\hat{\sigma}:[0;+\infty)\times[0;+\...
- 510