All Questions
Tagged with implied-volatility options
307 questions
49
votes
6
answers
119k
views
A simple formula for calculating implied volatility?
We all know if you back out of the Black Scholes option pricing model you can derive what the option is "implying" about the underlyings future expected volatility.
Is there a simple, closed form, ...
- 2,138
36
votes
4
answers
30k
views
How to derive the implied probability distribution from B-S volatilities?
The general problem I have is visualization of the implied distribution of returns of a currency pair.
I usually use QQplots for historical returns, so for example versus the normal distribution:
...
- 1,200
26
votes
3
answers
6k
views
What does the VIX formula measure and how does it work?
I have read the CBOE's white paper on the VIX and a lot of other things, but I need to honestly say, I don't really get it, or I am missing something important.
In semi-layman's terms, is the VIX ...
- 1,872
25
votes
6
answers
31k
views
What is the implied volatility skew?
I often hear people talking about the skew of the volatility surface, model, etc... but it appears to me that there isn't a clear standard definition unanimously used by practitioners.
So here is my ...
- 4,613
22
votes
2
answers
32k
views
Gamma Pnl vs Vega Pnl
Why does Gamma Pnl have exposure to realised volatility, but Vega Pnl only has exposure to implied volatility? I am confused as to why gamma pnl is affected (more) by IV and why vega pnl isnt affected ...
- 2,662
20
votes
8
answers
16k
views
Why does implied volatility show an inverse relation with strike price when examining option chains?
When looking at option chains, I often notice that the (broker calculated) implied volatility has an inverse relation to the strike price. This seems true both for calls and puts.
As a current ...
- 963
20
votes
4
answers
18k
views
Why is realized volatility typically lower than implied volatility?
A number of quantitative finance textbooks mention something along the following lines, without further explanation:
A typical feature of implied volatility from stock index options is that it is ...
- 621
18
votes
2
answers
8k
views
How to extrapolate implied volatility for out of the money options?
Estimation of model-free implied volatility is highly dependent upon the extrapolation procedure for non-traded options at extreme out-of-the-money points.
Jiang and Tian (2007) propose that the ...
- 13.6k
18
votes
1
answer
6k
views
Bergomi: Skew arbitrage
In his paper "Smile Dynamics IV" (https://www.fields.utoronto.ca/programs/scientific/09-10/finance/derivatives/bergomi.pdf) as well as in his book "Stochastic Volatility Modeling" (...
- 263
16
votes
3
answers
32k
views
Does implied volatility vary for calls vs puts?
Volatility skew tells us that options with the same maturity at different strikes can have different implied vol. However, can a corresponding call and put for the same strike and maturity have ...
- 2,138
15
votes
2
answers
7k
views
Variance replication using options
I would like to understand the intuition behind the following question:
Why a certain weighted sum of prices of put and calls is equivalent to the implied variance of an underlying?
A variance swap ...
- 438
15
votes
2
answers
14k
views
Long Gamma vs Vega
What is the difference between being long gamma and being long Vega?
I understand that gamma is the vol of delta and that vega is the vol of the underlying. However, I have also found that being long ...
- 153
14
votes
3
answers
13k
views
How to exploit calendar arbitrage?
Say we are looking at European Call options in a toy environment with zero deterministic interest rates, a stock paying no dividends, no repo rates etc...
Let $C(T,K)$ be the price of a call with ...
13
votes
2
answers
3k
views
Beta vs. Implied Volatility statistical arbitrage using options
Let two underlyings, $S_{1}$ and $S_{2}$, are correlated and $\beta$ is the slope of their returns linear regression, that is, it says how much $S_{1}$ co-variates with $S_{2}$ variance.
For instance,...
- 2,153
12
votes
4
answers
5k
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 ...
- 6,490
12
votes
1
answer
520
views
What drives changes in implied volatility on ETFs/ETNs?
I thought implied volatility, as well as the VIX, primarily increase due to increases in the underlying asset's volatility, as well as the options themselves being bid up because more people were ...
- 1,872
11
votes
3
answers
4k
views
Model to Predict the Change in IV of an Option
I am looking for a model that would allow me to predict the change in the Implied Volatility of an option based on a hypothetical change in the market. The goal is to create a better simulation of ...
- 1,912
11
votes
2
answers
6k
views
Implied Volatility from American options (binomial)
I am trying to get the implied volatility from options on commodity futures and I know it's possible to get it from the binomial american options (on an non-dividend paying stock).
I believe it is ...
- 111
10
votes
1
answer
3k
views
Options Market Making Used Implied Volatility Surface
Suppose you are a market maker with a model that is producing an implied volatility surface for you. Suppose you quote bid/ask prices (vols) around the prices given by your implied vol surface. In ...
- 1,029
10
votes
2
answers
3k
views
How to calculate the most realistic historical option prices with additional publicly available parameters
This is a follow up question of this one.
My aim is to create the most realistic historical option prices possible with publicly available data. I want to do this for backtesting purposes.
The ...
- 27.7k
9
votes
2
answers
895
views
What are popular metrics for Option Skew?
What are popular metrics to track skew? Would it be the difference between OTM option and ATM option IV? Would it be a percentage difference in IV?
Also, if both are valid, would a % change be ...
- 717
9
votes
3
answers
2k
views
How to calculate Implied Volatility for out-of-the-money options?
I'm trying to calculate the implied volatility for out-of-the-money options, and to a lesser extent, in-the-money options. Most of the literature estimations I could find for implied volatility were ...
- 239
9
votes
1
answer
862
views
The Holy Grail of Volatility Modelling: The SPX & VIX - Why?
I am currently researching a pre-print article by Julien Guyon & Jordan Lekeufack (2022): Volatility Is (Mostly) Path-Dependent.
Their model is quite impressive in both its simplicity, as well as ...
9
votes
1
answer
1k
views
Vanilla Option Prices from Local Vol Surface (using neither MC nor PDE)
There are numerous papers that describe the derivation of the Local-Vol equation using available market prices of options. For example:
Dupire's formula (see e.g. OpenGamma (2013)) gives us LV in ...
- 1,052
9
votes
1
answer
129
views
Difference between Option-Implied Skewness/Kurtosis and Historical Realised Skewness Kurtosis
As the title states, what is the difference between option-implied skewness/kurtosis and historical realized skewness/kurtosis?
It is often the case that option-implied volatility is higher than ...
- 2,231
8
votes
3
answers
7k
views
What really drives option implied volatility?
A common and oft repeated belief regarding options volatility is that implied volatility increases due to people bidding up a contract, usually related to anticipation of the outcome of an expected ...
- 1,872
8
votes
1
answer
3k
views
How to approximate the time to mean reversion for implied volatility
Given an option and its implied volatility, and also the mean value of the implied volatility over the last 30 days, if we find that the current IV is significantly (> 1 std dev.) away from the mean, ...
- 1,404
8
votes
1
answer
640
views
How are the BKM risk-neutral moments derived?
I've been doing a lot of research on implied volatility skewness, and one of the most commonly cited papers I've come across is "Stock Return Characteristics, Skew Laws, and the Differential Pricing ...
- 81
8
votes
1
answer
1k
views
How sensitive are vertical spreads to changes in implied volatility?
How sensitive are vertical spreads to changes in volatility / implied volatility in the money, at the money, and out of the money?
I'm thinking for 1 point spreads this would be very small / neutral ...
- 503
8
votes
2
answers
1k
views
Vega of exotic options
I'am wondering if there is a standard definition to the Vega of an exotic product when the underlying model is not Black-Scholes.
Let me give some examples :
What is the Vega if the price is ...
- 446
8
votes
3
answers
691
views
Parameters for pricing option on EDF
Ladies and Gents,
Im writing a quick routine to calculate implied vols for options on EUR$ futures with Bloomberg data. My question concerns the part where I have all my inputs and am ready to pass ...
- 801
8
votes
1
answer
2k
views
Implied volatility and greeks for american option with discrete dividends
What methods are available to calculate IV and greeks for an american option with discrete dividends, and how do they compare?
Should I use Roll-Geske-Whaley and solve for a given option price?
- 1,210
8
votes
1
answer
2k
views
Measuring implied move priced into an event
It's well known that options price in an expected move in the underlying going into events, such as earnings announcements. I currently measure this implied move by computing the forward variance ...
- 243
7
votes
4
answers
890
views
Implied volatility of a complex options position
Assume I have a "complex" options position like a straddle, strangle, or iron condor. In other words, several options traded together as a single position against one underlying asset (not a basket ...
- 2,126
7
votes
3
answers
2k
views
Why is there greater demand for OTM and ITM options than for ATM options?
I´m currently writing a project on volatility trading and dynamics.
The literature often states higher demand for OTM (out-of-the-money) and ITM (in-the-money) compared to ATM (at-the-money) options ...
- 191
7
votes
1
answer
2k
views
Vol, Gamma, Vega -- essentially all the same?
When talking to traders I hear this sentence a lot
I am a buyer/seller of X
where X = {vol, gamma, vega}
Is X basically all the same -- they are just saying -- I think implied volatility is cheap or ...
7
votes
4
answers
11k
views
How to calculate the implied volatility using the binomial options pricing model
I want to calculate IV for american options with dividends. So far I have found algorithms to calculate the option price given a volatility.
Please can you point me to paper or implementation (R, ...
- 1,210
7
votes
2
answers
3k
views
Constructing an approximation of the S&P 500 volatility smile with publicly available data
Besides of the VIX there is another vol datum publicly available for the S&P 500: the SKEW.
Do you know a procedure with which one can extrapolate other implied vols of the S&P 500 smile with ...
- 27.7k
7
votes
2
answers
642
views
Implied volatility and nonconstant volatility
John Hull states in his text that "AS the maturity of the option is increases the percentage impact of nonconstant volatility on (option) prices becomes more pronounced, but its percentage impact on ...
- 1,549
7
votes
1
answer
5k
views
SABR calibration: simple explanation and implementation
I would like to learn more about the SABR model and ho it is used in modeling smiles in equity, FX and rates markets.
How would you explain the process and its implementation in simple steps? Any web ...
- 569
7
votes
3
answers
2k
views
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?
There's something I've been trying to understand for a while now, and I just can't quite understand, with regards to skew. In the same month, why can't you buy a option that has low implied vol on the ...
7
votes
2
answers
656
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 (+) = ...
- 568
7
votes
1
answer
409
views
implied volatility and strike price
Assume for simplicity that the expiration time of an option is $1$ the initial stock price is $1$ and there is no dividend yield and the risk free return is $0$.
How is it possible to show that the ...
- 71
7
votes
0
answers
143
views
Implied vol bounded if and only if instantaneous vol bounded
I'd like to show that in diffusion models IV is bounded iff instantaneous vol is bounded if there is to be no arbitrage. So, assume a model under the pricing measure of the form
$$
dS_u = \sigma_u S_u ...
user34971
6
votes
3
answers
4k
views
Which volatilities should I use for Quanto Options?
Quanto options pricing formula, as described in this paper is a function of two volatilities: one from the underlying asset and another from the exchange rate.
How can I read the "right" volatilies ...
- 863
6
votes
1
answer
1k
views
Volatility Surface Constituents, do's and dont's
Recently I have been working a lot with implied volatility and volatility surfaces.
The basic idea is easy to follow:
1) Gather market prices of options at different (Strike,Expiry)
2) Calculate ...
- 523
6
votes
2
answers
3k
views
Lower bound of ITM Calls when computing Implied Volatility
Assuming the Black Scholes model and pricing formula of a European call option. Then, if the call is ITM, i.e. if $ln(\frac{S}{K})>0$, the $d_1$-term will go towards infinity as $\sigma$ goes to ...
- 920
6
votes
2
answers
15k
views
How can I calculate the strike price or implied volatility from a given delta?
I have calculated the implied volatility for all strikes of a certain product (options on futures) and approximated the ATM volatility. My question is how can I figure out the implied volatility for a ...
- 377
6
votes
1
answer
2k
views
Modified bisection formula for deriving implied volatility for a dividend paying american option
I am trying to work out the formula for calculating the implied volatility of an american option on a stock paying dividends (discrete payments or annualized yield).
On page 171 of Haug
The ...
- 1,398
6
votes
1
answer
648
views
what's the relationship between forecasted stock volatility and implied volatility?(option)
what's the relationship between forecasted stock volatility and implied volatility? I know that implied volatility is the volatility calculated by BS formula, is there any relationship between implied ...
- 63