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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Mid vol from bid/ask vols for equity options

Given an arbitrary bid IV and ask IV is it possible to compute a mid IV in a model agnostic fashion? Is there anything else aside averaging the bid and ask vols or interpolation between bid/ask ivs ...
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Why IV surface over call price surface? [closed]

Why do options traders usually model and trade the IV surface? I appreciate that the IV surface is more standard across assets, but why do we go to so much trouble with the IV surface? To me it seems ...
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How to fInd relation between call and Put IV on expiry day without calculating?

During the expiry day, in the European style options, the effect of rho will be very less. Let on expiry day the market is exactly at some strike price S at some moment of time. At that moment if the ...
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Contradictory arguments for ATM/ITM/OTM option demand

I am trying to understand which of the options have the most demand, and found this discussion here. The arguments presented are as follows: ATM is more liquidly traded than ITM/OTM because they are ...
4 votes
1 answer
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Realized Variance (realized volatility)

I'm confused about realized variance. I roughly know the theory around Ito Calculus and quadratic variation and integrated volatility so I understand what realized variance measures (even though as ...
3 votes
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Very close local volatility and implied volatility using Dupire's equation

I used Dupire's equation to calculate the local volatility as in https://www.frouah.com/finance%20notes/Dupire%20Local%20Volatility.pdf and Numerical example of how to calculate local vol surface from ...
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Pricing Leveraged ETF option based on base ETF

I am following along with the paper linked here: https://math.nyu.edu/~avellane/thesis_Zhang.pdf . In section 4.4, equation (4.4.2) makes the claim: $$\sigma(k) = |\beta|\sigma_s(S_0k^*)$$ where: $$...
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Convert implied probability into real probability

In this article I have read that: A risk-neutral world is one where all investors are indifferent to risk and don’t require any extra risk premium for the risk they bear. In this world, all assets (...
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1 answer
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When calculating VIX, how to deal with the problem of asymmetry of put and call data?

I'm trying to calculate the VIX index according to the methodology of CBOE. I am looking at commodity options. I found that at some time, like at this minute, there are 13 call options out of the ...
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Converting implied volatilities into digital option prices

I have Black and Scholes (1973) implied volatilities computed and I would like to convert these IVs to digital option prices using a Black and Scholes type of formula, I can't find a formula to do ...
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Delta hedging when volatility is stochastic

From my understanding in a BSM world you can make a bet on volatility using options and delta hedging with the underlying. If you think realized volatility of the underlying will be higher than the ...
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Volga Vanna Pricing Approach

So when using this method to price exotic options , it's stated that we need to calculate the vanna (how vega changes with respect to change in spot prices) of the exotic option and the volga ( how ...
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3 answers
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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 ...
2 votes
2 answers
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How do market-makers profit & manage inventory when customers sell a lot of deep OTM options?

In a live example: Today is June 14, 1 hour before market close, and \$SPY (S&P 500 ETF) is currently at \$372.28 and the June 15 \$350 strike Put is being quoted for \$0.13 on the bid and \$0.14 ...
11 votes
3 answers
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Lib for Arbitrage-Free Smoothing of Implied Volatility Surface?

I'm looking for an implementation of Arbitrage-Free Smoothing of the Implied Volatility Surface - Matthias R. Fengler. Does anyone know of any existing libraries that have implemented this paper? Any ...
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Value at Risk on equity options, what is the right approach on historical simulations

Questions on Historical VaR for options, how do you actually do this. how you would evaluate Value-at-Risk for an equity option that has been recently listed on the exchange. The obvious is that you ...
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Eurodollar futures volatility

Considering each point is 2500, how can I get the volatility of the jun 24 contract? On tastyworks I'm seeing a 0.7% iv for the contract, how can I translate it to standard deviation? Ex:sp500 15%...
2 votes
1 answer
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Interpreting Implied Volatility in Commodities Options

I understand that implied volatility is the expected volatility of an underlying contract in the Black option pricing model. This is easy to interpret for assets delivered at a point in time. But how ...
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simple volatility surface interpolation

I'm trying to build an implied vol surface from some listed options. In particular I have data for calls and puts for different strikes and expiries. I'm not looking to price on the interpolated vols ...
5 votes
2 answers
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Conditions for implied volatility to attain a minimum (or maximum) value

Suppose $$ dS = \sigma S \left(\rho dW + \sqrt{1-\rho^2} dZ \right) $$ and $$ d\sigma = a(\sigma,t) dt + b (\sigma,t) dW $$ with $dW dZ = 0$. What are the conditions necessary such that the implied ...
15 votes
3 answers
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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 ...
1 vote
1 answer
853 views

Implied volatility as break-even delta hedge volatility

There have been some posts on this topic, but not what I am looking for, so a new post on an old topic.. I think some/most of us here are familiar with the following formula expressing implied ...
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QuantConnect: ATM IV is different for call and put

I am trying to use QuantConnect to run some historical analysis, which involves comparison of skew (more specifically, $\frac{25\Delta\text{ put volatility} - 25\Delta\text{ call volatility}}{50\Delta\...
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If $\Delta \log(V_{t})$ behaves like the increments of fractional Brownian motion, why do we model the rough volatility as follows

From Gatheral's paper, Volatility is rough and empirical evidence, it is clear that $\big\{\log(V_{t+1})-\log(V_{t})\big\}_{t}$ behaves like the increments of fractional Brownian motion $B^{H}$ with ...
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Implied volatility curve

I was trying to build the implied volatility curve from SP500 options. In order to adjust the liquidity issue, I used put-call parity to generate the call price from the OTM Put price.(plot 1) But ...
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Adequate model to payoff

Consider a payoff that pays a certain amount N of a vanilla Call (underlying: S, Maturity= T, strike:K). Every semester date Ts before T, if S>K(Ts), then N is increased by 1. This product seems ...
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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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Why can't the curve find the least squares parameters when I used it in SABR model? (SABR Calibration)

Follow is the SABR function part of my code in python: ...
5 votes
1 answer
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Implied volatility of Asian options under Black76 model

I found this repository (options pricing in Python) where they adjust IV for Asian options and they use it under the regular BS76 model. I could not find any proof of this result on the web, do you ...
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1 answer
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finding Black Scholes implied volatility

I am trying to imply BS volatilities using Yahoo Finance! API (MSFT options) and Reuters zero curves. I am ignoring dividends for the moment. Note that I've also cleant the options' data (e.g., I make ...
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Model-Free Implied Volatility: Data of Expired Options and Bond Price

I am attempting to calculate Model-Free Implied Volatility for several equity indices (S&P500, NASDAQ100, CAC40, FTSE100, DJIA, EUROSTOXX50, NIKKEI225, NIFTY50). I wish to get historical data of ...
4 votes
1 answer
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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 ...
3 votes
3 answers
4k views

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 ...
7 votes
1 answer
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compute time from FX forward, how use DEPO rates?

assume I have following delta-term vol data from broker: ...
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Interest Rate Volatility for Binomial Trees

Does anybody know where I can get the data or calculate interest rate volatility for modelling callable and putable bonds in binomial trees. I have swap curves data. Does any sources like Bloomberg ...
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Estimating difference in implied volatility from difference in PV

Le us assume that depo and repo rates are zero. And let us assume I can read the ATM implied volatility of 1y option from the volatility surface. I now have some algorithm to reprice this option (let'...
1 vote
1 answer
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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 ...
3 votes
1 answer
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When to use a Local Vol model vs Stochastic Vol Model?

I'm new to volatility modeling, I'm struggling to understand when to use a Local Vol model and when to use Stochastic Vol Model, Also now we use a hybrid model combining the two models ? Can someone ...
3 votes
1 answer
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MBS Market Duration & Convexity

Soft question...hopefully. I am working on a swaption hedging strategy. Part of this strategy calls for a forward looking indication of changes in implied volatility, using 1m10y implied as a proxy ...
4 votes
1 answer
329 views

ATM Implied Volatility and Expected Variance

This answer claims that $$\sigma^2_{ATM}\approx E^Q\left(\frac{1}{T}\int_0^T\sigma^2_t dt\right)$$ ie implied ATM vol = risk-neutral expectation of integrated variance. Is there some proof available? ...
7 votes
1 answer
352 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 ...
23 votes
6 answers
29k 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 a clear standard definition is not unanimously in place among practitioners. So here is ...
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1 answer
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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 vote
1 answer
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Calibrate the SABR model to the implied volatility surface

I'm currently trying to calibrate the SABR model. The question I have is that when I consider papers and other websites I only come across cases where the SABR parameters are calibrated to the implied ...
0 votes
1 answer
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What is the meaning of an implied volatility of an Asian option?

Suppose that an Asian option is quoted OTC in terms of its implied volatility. What is the meaning of an implied volatility in this case? Is it an implied volatility of a vanilla European option with ...
2 votes
1 answer
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how to do interpolation in the term structure of volatility surface?

everyone~ I am a newbee in the quantitative finance and I meet a problem in working out an equity option volatility surface. We use the reasonable market data to derive the implied volatility, then ...
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implied vol smile relative to atm vols

Am I correct in saying that most stochastic vol models are meant to behave in a way that as atm vol goes up the smile comes down and risk reversals become "less stretched?" - by that i mean ...
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Deriving strike from Delta

According to the following thread: How can I calculate the strike price or implied volatility from a given delta? To back out some strike given some Delta, you simply use realized vol (plus a few ...
17 votes
1 answer
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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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Best Way To Compute the Volatility Risk Premium

I'm trying to come up with a measure for the volatility risk premium (VRP) for a strategy I want to implement, but I'm not entirely sure how to proceed. My situation is as follows. The underlying is ...

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