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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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 ...
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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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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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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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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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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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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 ...
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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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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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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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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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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: ...
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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 ...
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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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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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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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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'...
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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 ...
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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? ...
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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) ...
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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 ...
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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 ...
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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 ...
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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 ...
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Strike arbitrage in discrete implied volatility grid

I need to test strike (butterfly) arbitrage on a discrete implied volatility grid. I know that the traditional procedure for continuous case is (for a given maturity T): See the Dupire formula in ...
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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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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 ...
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4 votes
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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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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 ...
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Precise Implied Volatility of Heston Model

I wish to calculate precise implied values from Heston model for extreme inputs (deep in/out of the money or short time to expiry) There is a good demonstration for using QuantLib library for this in ...
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Calendar arbitrage in implied vol grid with discrete and proportional dividends

I have an implied vol discrete grid, obtained from market data. To obtain prices from these implied vols, a dividend model with discrete and proportional dividends is used. How can I verify if there ...
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Why do VIX spot and futures converge if there is no cash and carry arbitrage?

Since VIX spot is not tradable, why do the futures and spot converge @ expiration? By what mechanism does this occur if arbitrage is not one of them?
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Option implied risk neutral distribution vs BKM risk neutral moments

I am doing some research on the option implied risk neutral distribution and methods calculate it, and so far have come across two ways to do so. The first way is through the Breeden-Litzenberger ...
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Calculating model-free implied volatility [closed]

I am trying to come up with model-free implied volatility as in Britten-Jones, M. and Neuberger, A. (2000) Option Prices, Implied Price Processes, and Stochastic Volatility, Journal of Finance, 55, ...
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Maximum entropy probability distribution for $S_T$ implied from discrete market quotes

Consider a maturity $T$, for this maturity I have some implied volatility from market denoted $\sigma^{0}_{i}$. I want to interpolate these volatility using Entropy approach, by using $\sigma^{0}_{i}$...
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Pricing caps/floors on backward-looking USD SOFR with forward-looking LIBOR model

The payoff of a cap/floor is calculated as a payoff of constitutient caplets/floorlets. The SABR volatility model has the implied volatility approximations of Hagan et al. $$\sigma^f_{IV}\approx \...
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Option Chain Simulator Using Historical Index Future data, VIX, Implied volatility for Calculation ( Pls Review the Idea & give your suggestions )

Recently I started trading in options, for Learning purpose I am Planning to Create old European Option chain like previous week or last year particular entire week Weekly expire option chain with the ...
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Implied Volatility is the harmonic average of Local Volatility

I am trying to demonstrate the famous result that states that when $T \rightarrow 0$, the Implied Volatility is the harmonic average of Local Volatility. I am st the final stage, and I have the ...
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Closed formula for computing Implied Volatility from Local Volatility function

The main result of this paper (Asymptotics and Calibration in Local Volatility Models, Berestycki, Busca, and Florent. Quantitative Finance, 2002) is equation (16) on page 63, that states that: In the ...
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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. ...
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Dividend adjustment on SABR formula for interpolating implied volatility

We are using a SABR model to interpolate the implied volatility surface. The model yields a formula for implied volatility that contains the following term: $\ln \left(\frac{K}{F}\right)$ It is ...
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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/...
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Calculating Expectation of Stochastic Volatility

I have a question while reading THE NELSON–SIEGEL MODEL OF THE TERM STRUCTURE OF OPTION IMPLIED VOLATILITY AND VOLATILITY COMPONENTS by Guo, Han, and Zhao. I don't understand why the above equations ...
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Caplet stripping in the bwd-looking RFR world with/without maturity adjustment

Since the beginning of this year, LIBOR rates have ceased in some markets like GBP, CHF, and JPY and rates pricing has moved into the RFR space, using compounded overnight rates as the underlying for ...
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Should you compute the greeks on realized or implied volatility?

I am reading Trading Volatility by Collin Bennett and he says that you should compute the Greeks using realized volatility rather than implied volatility? Is this actually true? As far as I know the ...
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