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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Compare equity option volatility under SOFR vs LIBOR

We know that after the big bang from LIBOR to SOFR, LIBOR will eventually disappear. This brings up one question that I do not have a clue to answer: How to evaluate derivative in a consistent manner ...
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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 ...
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How to interpolate on an implied volatility surface based on forward moneyness?

Should be a simple matter, but perhaps I'm misunderstanding something fundamentally. Look first at the below image of the BVOL surface from Bloomberg, to my understanding from looking at the white ...
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What is the SVI model? [closed]

What is the SVI model? And how does one calculate its parameters?
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Is there a Dupire's Formula for put options?

Generally, Dupire's formula is taking derivatives on the call option prices. Here it only uses information of the call options. If now we have the data including both call and put options, is there a ...
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Arbitrage Free Interpolation of Implied Volatility on Time Dimension

I’m working on a project to build a local volatility model out of implied volatility data and I’m currently testing the no-arbitrage version of SVI model as described in this paper Section 5.1 [...
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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" (...
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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 ...
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Annualizing intraday volatility

I've been experimenting with end-of-day volatility-based stock trading strategies and I'm looking to see if it's possible to use similar strategies over shorter time frames. Given that market ...
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Valuation of Corridor Variance Swaps

Given that the payout of the Corridor Variance Swap (CVS) is $V \left(\frac{\sum_{n=0}^{N}I}{T_2 - T_0} (\sigma^2 - K^2) \right)$, where $\sigma^2$ is the realized variance within the pre-specified ...
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Entropy-implied volatility requires itself to be calculated?

\begin{align} H &= \frac{1}{2} \ln (2\pi\sigma^2) + \frac{1}{2}\\ &= \frac{1}{2} \ln (2\pi e \sigma^2) \end{align} is the analytical solution for the entropy of a Gaussian random variable, ...
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Seed Values guaranteed convergence of Implied Volatility Calculation

Looking for good seed values for Newton Raphson to guarantee convergence of implied volatility calculation for a few models, all of which are for equities that have divs. 1) Bjerksund-Stensland 2002; ...
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Sensitivity to changes in the volatility

I have a sample payoff function shown below: How do I find a formula which gives the sensitivity to changes in the volatility of the underlying stock. In other words, I want to find a formula for $\...
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Can we model Implied volatility using GARCH?

Can I use Implied volatility as a dependent variable in a GARCH model? I believe my IV data shows ARCH effects and hence can I use it to model volatility of the volatility? I know literature has used ...
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Availability of historical data on variance swaps [duplicate]

I want to do research on variance swaps. Where can I get/buy historical data (other than Markit)?
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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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Can you use the SABR implied volatility in the Black Scholes formula?

The SABR implied volatility is often used as an input in Black's model to price swaptions, caps, and other interest rate derivatives. I'm wondering whether you can use the SABR closed form solution of ...
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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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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 ...
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Relationship between Beta and implied volatility

Is there any way to make use of the Beta of an underlying and index, and the implied volatility of options on that underlying and the index? To specify, if we have available the implied volatility of ...
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How can deep learning methods measure implied volatility?

Why and how should we utilize deep learning methods to calculate implied vol of options? I've also heard that finding the fair price of the option is not nearly as important as finding a numerical ...
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Option Price vs. Implied Volatility

I was doing an exercise on investigating the relationship between European Call option price and its volatility. I was asked to compute $\frac{\partial^2C}{\partial \sigma^2}$ and find out the domain ...
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Implied volatility quote vs. Price quote

After reading this and this, I still don't understand the reason for why options are quoted in terms of implied volatilities. My question is: can somebody give an example that shows the value/...
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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: ...
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Is the implied volatility different for forward starting caps?

Suppose we know (from looking at an available volatility surface) the implied volatility (flat volatility) of a cap with a maturity of 10 years and strike of 1%. This would correspond to a cap that's ...
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Implied Volatility - Historical data

I'm wondering if there's a place where I can find free or very cheap historical implied volatility data. Specifically, I'm looking to get at least a few years' worth of daily IV data for maybe a few ...
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Newton's Algorithm for Implied Volatility

I was studying the implied volatility for European Vanilla Call option. My notes said that we can apply Newton's algorithm to calculate implied volatility numerically. I understand how the algorithm ...
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Why does the implied volatility on options (with the same underlying and maturity) vary? [duplicate]

Having studied the basic premises behind option pricing, I thought it would be interesting to look at some real-world options data. I found the following quotes for options on APPL: https://finance....
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Normal vs Log normal implied volatility

I am referring to an earlier discussion at How do we know if the volatility which is quoted in market is Normal (Bachelier model) or log normal (Black 76)? For the short rate case, is there any ...
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Empirical equivalent for implied vol

Implied volatility is supposed to show volatility of the underlying over next k days where k - maturity of the option. Say our stock price is $S_t$ and percentage return is $r_t$. Then which empirical ...
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CBOE VINXE or VIX9D Index Construction

I have not been able to find a White Paper on how the CBOE VIXNE index is constructed. Any lead to short term volatility index calculations would be appreciated. Thanks
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Question on choosing the optimum expiration with cheapest extrinsic (time) value

Ok, here is the scenario - Trying to enter into long deep ITM call position with target of about 4 weeks and considering following cases Buy weekly call options and roll them into next week on the ...
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Implied volatility data

I am looking for historical implied volatility data, and I see that QUANDL has this data from two sources - ORATS and Quantcha. I was wondering if people have any views on which data is higher quality ...
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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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VIX vs historical volatility

I'm relatively new to this field and would like to ask a couple of questions. I'm doing some analysis and I would like to compare/plot VIX vs historical volatility of SPX. I have daily VIX and SPX ...
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How are the call and put slopes in the SVI-JW parametrization derived?

In the SVI-JW parametrization, we have $$ w(k; a, b, \rho, m, \sigma) = a + b \left [ \rho(k-m) + \sqrt{(k-m)^{2} + \sigma^{2}} \right ] $$ Which gives us $$ \begin{align*} \sigma_{BS}(k) &= \frac{...
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Can we use a VIX-like method to calculate implied volatility for Black Scholes model?

So I understand that the VIX is an estimate of implied volatility. Volatility can also be calculated from the Black Scholes model. My question is can we use a VIX-like method to calculate implied ...
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Are Levy models useless after the financial crisis of 2008?

I calibrated (by minimizing RMSE) the Black Scholes, VG and CGMY models to data from 2005 (before the crisis) and to data from 2020. The results surprised me. I do not understand why for data from ...
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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, ...
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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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How does the real market calculate the option prices when strikes are very small?

I'm working on the S&P500 European index options data(call options). On 2017-10-23, we have the closing price as 2564.98, and risk free rate is 1.09%(3 months treasury bill). If I choose the ...
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Why are model-free implied volatility indices (like VIX) only available for large indices and a few large stocks?

The CBOE VIX (i.e. model-free implied volatility) is only available for larger stock market indices and a few large stocks (see the CBOE website). As I am currently working on deriving VIX for a ...
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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 ...
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asymptotic behavior of the pdf constraints due to Roger Lee

In a beautiful paper, http://math.uchicago.edu/~rl/moment.pdf, Roger Lee (2004) shows that implied variance is bounded above by a function linear in the log-strike k. Does anybody know how it ...
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Autocallable option Delta

There have been numerous exotic trading desk blow ups lately, related to various reasons. However, in particular, one bank had some issues where they were pricing autocallable notes with Local ...
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Finding option price using intraday data [closed]

I have the option price at a rate which is much smaller than the rate at which I have tick data for the underlying. If I have option price at times $t_1, t_3, t_5$ and I have tickdata at $t_1, t_2, ...
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Black Scholes implied volatility [closed]

I am reading up on implied volatility and I encountered the term Black-Scholes implied volatility which I haven't heard before. What is the meaning of this term? Say I am looking at the Heston model ...
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Volatility input for American options

I have to price an american option on a daily basis and I have some questions regarding the CRR binomial tree model: Is it correct to use implied volatility as an input? Or is it better to use ...
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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. ...
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Computing the Probability Density Function (PDF) for the Heston model

I am trying to compute the PDF for the Heston model using the Breeden Litzenberger formula. I have calculated the the Heston implied volatilities for a strike range (which i have interpolated using ...

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