Questions tagged [implied-volatility]
The volatility of the price of the underlying security that is implied by the market price of an option based on an option pricing model.
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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 ...
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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 "...
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How does volatility skew change with underlying spot?
We know that generally ATM implied vol is negatively correlated with the underlying spot for equity indices, i.e. implied vol goes up when spot moves down. Therefore I wonder if there are any ...
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What is the point of volatility curve fitting?
What is the point of fitting curves to the implied smile in the market? (Other than pricing exotics where the hedging instruments are vanillas). How does fitting a vol curve help you trade/market make ...
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Why do we need to calibrate vega?
I was going through some paid video on options. The tutor in the video asked the following question:
Person $A$ has the following portfolio at the start of April
Portfolio of options with vega $20,...
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Autocallable pricing under stochastic vs. local volatility
I am interest in the reason why an Autocallable (structured product) is cheaper under local volatility compared to stochastic volatility.
I thought this was due to the following:
when thinking in ...
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Delta Hedging with fixed Implied Volatility to get rid of vega?
I'm wondering if i should use a floating IV or a fixed IV to delta hedge my options every day.
I've read this post but would like different information :
Delta Hedging with fixed Implied Volatility ...
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Is there a better way to price options than with historical volatility?
I know that annualized historical volatility calculated with closing prices is a much rougher estimate than implied volatility for the correct "volatility" parameter in options pricing models. ...
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European Swaptions: does implied volatility of swap rates decreases both with start and tenor?
Does implied volatility of swap rates decreases both with start and tenor?
Given a Swaption price and a discount curve I calculate the swap_rate from the curve, then
I define implied volatility as ...
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Why does volatility increase the expense of delta-hedging?
Consider someone that writes a call, and wishes to delta-hedge against it to remain delta neutral. For this to be profitable, the price they sell this option for should be greater than or equal to the ...
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What is "implied skew" and "spot/vol beta"?
I saw a chart which showed implied skew and spot/vol covariance (I assume) and I was wondering what these terms actually mean and how to "back them out" of Option prices or vols?
Here is the ...
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How does Volatility Pairs Trading work?
I've read some material related to pairs trading for equities and I understand the process of finding non-stationary pairs price series that can be cointegrated to form a stationary series. The basic ...
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Implied Volatility for Asian option
I am new to the topic of Asian options. Assume I want to price an Asian put (fixed strike, discrete average) in the Black Scholes world. I know implementations to calculate the value but what is the ...
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When does the underlying become the derivative?
Since options contracts are created by open interest in the contract, it is conceivable that the notional of the total options contracts can exceed the value of the underlying. If that happens, does ...
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Implied vol vs Realised vol on Event Days
How implied vol varies vis-a-vis realised vol on an event days?
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Understanding the ZABR model (an extension of SABR)
http://janroman.dhis.org/finance/SABR/ZABR%20Andreasen.pdf
In this acticle the SABR model is first presented in another form ( see equation 7 in the article ) and then extended to the so called ZABR ...
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Basic questions on options, implied volatility and SPY
I am a bit confused about the impact of implied volatility on options, SPY options especially. I know that option's price decays with time and that is positively correlated with implied volatility but ...
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Realized volatility forecast vs Implied volatility
I have forecasts of realized volatility, as well as implied volatility for individual traded options of the S&P500.
I want to simulate a simple trading strategy; that is, buy signal=1 if ...
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Constructing a minute-by-minute volatility curve
For market making in front month vanilla commodity options we need a volatility curve that updates every second or so as the underlying and the options change prices.
If all the strikes have a good ...
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Volatility Return Distribution/Garch Modeling
For simplicity sake, if stock returns are normally distrusted, would that imply that second moment, variance/volatility, is chi-squared distrusted? If so wouldn't that imply the statistics(employed to ...
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Does skew flatten with a decline in volatility?
In Trading Volatility by Bennett, he says:
If there is a sudden decline in equity markets, it is reasonable to
assume realised volatility will jump to a level in line with the peak
of realised ...
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Equivalent BS volatility formula under the Heston model?
Is there an equivalent BS volatility formula for the Heston model, something like Hagan's formula for the SABR model? Of course, such a formula will be an approximation as in Hagan's formula.
Under ...
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How is Emanuel Derman's implied tree model implied volatility skew derived?
I am reading Emanuel Derman's paper Patterns of Volatility Change. The section, Implied Volatility In The Sticky Implied Tree Model has the linear skew approximation near the old underlying $S_0$
$$\...
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Intuitive explanation for the value of a binary option being lower when volatility skew is positive?
According to the formula for pricing binary options with a volatility skew, it appears that the value of the binary option for a given strike gets lower, the higher the volatility skew at that strike. ...
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Splitting theta from vol carry
What is the best way to splitting theta and vol carry on say a long calendar trade?
Basically trying to split the "good" carry component of a trade from the "bad" carry (theta) which could be earned ...
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Option price calculation using Local Volatility and Monte Carlo
The below formula is used to convert the implied vol into the local volatility,
my question is, once I have converted it into the LV ( and have built the full surface), what models do I use to ...
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Asian option IV less than vanilla option IV
I was wondering whether the following handwaving line of thought can be used to show that the IV of an Asian option is less than the IV of a vanilla option with the same strike and time to maturity:
...
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Modern market conventions for interpreting interest rate swaptions quotations in a negative interest rate environment
I have broker data and I see three sets of swaption vol data:
Lognormal (Black)
Shifted Lognormal (Black with displaced diffusion)
Normal (Bachelier)
The quotes are given by the following key (Date, ...
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MTM Hedging Performance of Vanna-Volga
I was wondering how well Vanna-Volga (VV) Implied Vols "perform". So I experimented with the following option parameters
$$S_0=100,\ K=92,\ r=0.03,\ q=0.01,\ T=2$$
and VV parameters
$$K_1,K_2,K_3=...
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Relation between IV and SD
In option pricing, volatility naturally appeared through the Black-Scholes (BS) model where it was a coefficient for the linear diffusion term $\sigma S\,\mathrm dW_t$, and as such represented the ...
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Interpreting QuantLlib implied volatility numbers
I am using QuantLib to calculate implied volatilities.
I am trying to understand the calculated figures (especially, when compared to historical volatility). The calculated implied volatility numbers ...
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Realizing the same PnL as Gamma Vs Vega
Consider a delta hedged option postion.
Futhermore assume that I can perfectly forecast realized volatility over the life of the option.
Vol I buy the option at = Implied Vol (IV)
Realized volatility ...
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How much does a rise in volatility in a short-term option affect a longer-term option
How would a rise in implied volatility on a short-term option affect the implied volatility of another short-term option with the same strike, but with slightly-longer expiry?
Assuming that the short-...
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Implied/Realised Vol ratio for negative rates?
I'm trying to calculate the implied vs realised vol ratio for different swaptions across major currencies. This works fine for the likes of USD and GBP as rates are positive. However I'm struggling ...
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Dependence of implied volatility on spot-vol correlation
I have the following general SV model:
$$
dS = \sigma S dW_S
$$
$$
d\sigma = a(\sigma,t) dt + b (\sigma, t) dW_\sigma
$$
$$
dW_S dW_\sigma = \rho dt
$$
where $a , b$ are deterministic functions of $\...
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Is there a simple, intuitive derivation (using Taylor series) of the following approximation to Vega-weighted Implied Volatility?
The approximation is:
$$\sigma \approx \frac{\sum V_j\sigma_j}{\sum V_j}$$
Background information from the first answer to this post:
"Say that you have a portfolio of options with prices $P_j$. ...
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What is the Brownian motion in the model for the return of a stock price trying to capture?
I have read that in the derivation of the Black-Scholes PDE, we assume that the return of a stock $S$ is given by
$$\frac{dS}{S}=\mu dt+\sigma dB$$
where $\mu$ is the average growth of $S$, $\sigma$ ...
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Estimating at-the-money volatility where at-the-money option is absent from the market
I am trying to estimate the intraday ATM volatility in a market where the the strike prices are relatively sparse thus the ATM option may not exist (let's say the closest strike is about 2% away from ...
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Tradable information from BS Implied volatility
These are two follow up questions to:
Implied volatility as price transform
I understand that the BS model is used as a 'Blackbox' that takes a market price and maps it in a 1to1 fashion to a 'BS ...
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What equation will convert implied yield volatility to implied price volatility?
I am trying to figure out how to turn implied yield volatility of a short-term interest rate into implied price volatility. Is there an equation to do this?
I have come across the equation for a ...
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Why does Skew measure remain more-or-less constant for Listed Expiries?
I have looked at the Variance Swap Papers published by GS-VarSwap and JPM-VarSWap where they talk about approximation to VarSwap strike using ATMF vol and Skew (slope of the volatility skew for 90-110 ...
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How is option pricing related to the correlation between implied volatlity and the underlying?
The correlation between the index returns (e.g SPX) and its changes in option-impled volatility (e.g. VIX), is strong, stable and negative (the implied volatility feedback effect). To me at least, it ...
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Black-Scholes implied volatility using a GARCH model
Why I'm not getting the same Black-Scholes implied volatility values as the ones given in the paper "Asset pricing with second-order Esscher transforms" (2012) by Monfort and Pegoraro?
The ...
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Bates Model on Quantlib
I am actively trying to price an option using bates model on Quantlib.However,when I input my volatility I find the same Black Prices with the basic Heston Model.I wanted to know if my code was right.
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How does VIX interpolate implied volatilities?
In the CBOE VIX white paper (direct link to PDF), it is explained that once the implied volatility of the near and next-term options $\sigma_1^2$, $\sigma_2^2$ are found, the constant-maturity 30-day ...
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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:
$$
\biggr\langle \int_0^T e^{-rt}s^2 \frac{d^2P_{\hat{\...
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$\frac{\partial C_{BS}}{\partial T}$ in local volatility derivation in terms of implied volatility
In Gatheral's book, in the derivation of local volatility in terms of implied volatility, we use the regular Dupire formula
$$
\frac{\partial C}{\partial T} = \frac{1}{2} \sigma^{2}K^{2}\frac{\partial^...
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R: How do i finish the tails in the risk neutral density, obtained from option prices
Im currently working on constructing the risk neutral probability distribution of a stock, based on the option prices. In doing so, i calculate the implied volatilities from the option prices, and ...
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The error term of Hagan's approximation of Black's vol in SABR
Hagans approximation of Black's implied vol in SABR is very! difficult to understand fully. But I want to ask in here if anyone can tell me more about the error term.
Consider the paper:
http://web....
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Volatility of a stock basket
to determine the volatility of a basket of stocks, I often use the following formula:
$\sigma_{basket}=\sum_{i}\sum_{j}w_i w_j \sigma_i \sigma_j \rho_{ij}$
where the $\sigma$ are the constituents' ...