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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How to derive the volatility of options PL (hedged) as a function of implied volatility and measured realized volatility
This is my first time asking a questions. Apologies in advance if I mess something up. If this happens, please let me know if I do and I'll try to fix it.
My question is regarding the equation Euan ...
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Expected variance between 2 expiries of the same underlying
Let’s say I have two options expiries:
One expiring this month ($M_0$).
Another expiring next month ($M_1$).
I know that the expected variance ($EV$) in the underlying for each expiry can be ...
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Shape and level of swap rate historical volatility VS swaption implied volatility
When comparing realized swap rate volatility and implied ATM swaption volatilities, should one expect the shape across tenors of the implied volatility to be reflected in the realized and their level? ...
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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 ...
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Option Prices less than intrinsic value with Implied Volatility Solver
I have recently received a dataset with SPX options.
I tried solving for implied volatilities using a root solver. I noticed errors consistently popping up that is solvable via the answer given below:
...
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Caplet volatility formula
Consider an ATM caplet with maturity $T$ and delivery $T+\tau$.
In the book Interest Rate Models (Brigo and Mercurio), page 81, the authors define the model caplet volatility
as the unique value of $\...
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Taylor expansion or Itô's formula
Consider a risky asset whose price at time $t$ is $S_t$, and an option whose price at time $t$ is $P(t,S_t)$.
I do not understand how to justify the following Taylor expansion without using Itô's ...
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How to reconstruct the vol surface given Level, Slope and Curvature
Assuming I have a prediction of Realized Vol, Skewness (Slope) and Kurtosis (Curvature) of the underlying of an Equity European option.
How to get IV(log(S/K)) at any point on the curve as a function ...
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Cant replicate implied vols from yahoo finance [closed]
I am not able to replicate implied vols for Amazon calls using Yahoo Finance data, this is sample data I have
strike
lastPrice
volume
impliedVol_yh
lastTradeTime
expirationTime
underlyingPrice
...
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Difference between VIX9D and IV of 7 days near the money calls on S&P500 [duplicate]
What is the difference between VIX9D and IV of 7 days near the money calls on S&P500? (Or the VIX and 30day calls)
I was wondering if there is a thumb rule about this.
Looking at the current SPX ...
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How many options are necessary in computing a "model-free" measure?
The VIX itself is computed via a "model free" measure, or rather, using a continuum of OTM option prices to come up with an "P-measure" of implied volatility.
It is perhaps obvious ...
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Why is an Autocallable dependent on the vol-of-vol and forward smile?
I am trying to build an intuition on why an Autocallable is dependent on the vol-of-vol and forward smile, justifying why we should use LSV model. I have a simple intuition for the latter: I am ...
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Is there such a thing as monthly/yearly skewness and kurtosis?
As the title suggests, when performing regression analysis or portfolio optimization, one must adjust the frequency of his variables to match the frequency of other variables in the problem. For ...
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Inverted volatility smile OMXS30 Sweden?
I am researching volatility smile for school and have just calculated the implied volatility for OMXS30 call options with different strike prices. However, my OTM options have lower implied volatility ...
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Compare historical volatility of swap rates with implied swaption volatility
Say I have 6 months daily 1Y swap rates historical and I can calculate the variance. Now I want to compare with the implied swaption volatility, say 3M1Y. If on the implied surface I read 10%, then in ...
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An approximate lower bound for options on variance
Question:
I am wondering if anybody has looked at the following lower bound, based on the most-likely path approximation, and/or tested it?
Let $dS_t = \sigma_t S_t dW_t$, where $\sigma_t$ is a ...
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Suggestions for using implied variance covariance matrix of rates for PCA
Looking to feed PCA an implied variance covariance matrix of swap rates instead of historical one.
Taking advantage of available swaption and capfloor implied volatility surfaces, any suggestions on ...
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Volatility surface PCA and SABR explanation gap
I am wondering how would the results of PCA on a volatility surface would be used differently than the SABR parameters. Given the first three components of a PCA are related to level, smile and skew, ...
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Why is there no formula for implied volatility?
While there are methods, none is a closed form solution. My question is aimed at mathematic problems, rather than the practical.
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Long vs Short Volatility Skew
This question is purely on the structure or maybe even jargon of being long or short volatility skew. Realistically, we do know that when we are long skew, we are long an OTM put and short an OTM call,...
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Modelling the relationship between the Implied and the Realized Volatility [closed]
I am trying to statistically model the relationship between implied volatility of European ATM options (expiring in 1 month) and the realized volatility of the underlying.
I am interested in the ...
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Are there publicly available measures of option-implied skewness and kurtosis?
As mentioned in the title, are there publicly available measures of option-implied skewness and kurtosis? (that represent the skewness and kurtosis of the option-implied risk-neutral distribution, ...
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Interpretation of first and second moments of Risk Neutral Densities for AMD
Suppose I have correctly computed the option-implied risk neutral density for AMD options expiring in exactly 1 week, and discounted this expectation with the correct risk free rate, using the Breden ...
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Heston Stochastic Vol and the local volatility in Gatheral's Book
I have been reading Gatheral's Book "The volatility Surface" and in the case of Chapter 4 ( The Heston Nandi model), the author provides the following graph.
It shows that implied ...
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Hagan formula for normal volatility
I am not sure I understand how Hagan normal volatility formula works. Basically I have:
Lognormal volatility of 0.059 (5.9%)
Forward price of the bond 134.5
Bond Strike price 132.5
Option maturity 0....
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Relationship between implied swaption volatility and bond yield volatility
What would be a relationship between swaption implied volatility/skew and implied bond yield volatility? How these are comparable and exploitable to trade volatility?
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Which delta for hedging?
I want to dynamic delta hedge an option but I'm confused of what delta shoud I use to hedge it.
Let's suppose I buy at T(0) a long CALL at strike 100 with implVol(0) = 30% and Delta(0) = 62
Let's ...
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Realized vol, implied vol, and gamma scalping
First of all, apologies for my lack of knowledge in derivatives trading. So I've been spending a lot of time, in the past few days, trying to understand gamma scalping... and got really confused.
Here ...
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Do bias adjustments make sense in the context of measuring realized volatility to compare to implied volatillity?
I've been considering constructing a volatility cone to compare implied volatility to realized close-to-close volatility. However, I was wondering how the typical bias adjustments you might make to an ...
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Bachelier implied volatilities in the Libor market model
There are various papers on how to derive a Black76 implied volatlity for a given specification of a Libor market model (especially for deterministic but time dependent volatility of forward rates and ...
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Volatility Surface Stress Testing - PCA
I’m currently working on creating historical and hypothetical stress tests, but I’m facing challenges in implementing a method to realistically stress volatility surfaces.
In terms of data, I have ...
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Delta volatility curve construction in practice
I want to construct a volatility curve $\Gamma = \{(\Delta_i, \sigma_i)\}$ but notice that the call and put with the same delta have a different vol (which shouldn't be the case in theory). Is the ...
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How do i calculate breakeven black scholes volatility for 12 monthly option to hedge a yearly option?
If I own a 1 year call option of 30 black scholes implied vol and i want to hedge it by periodically selling 12 monthly option of same strike, how can i calculate minimum vol needed on monthly option ...
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What is implied volatility relationship with time?
My take on the question is that, with all else being equal, as time to expiry approaches, the option price decreases (due to theta). And since implied vol is the price of the option in volatility ...
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Selecting volatility for stress scenario
I would like to stress my position in options, changing underlying price $S$ and volatility $\sigma$ at the same time.
Let's assume that after some analysis of the price history I concluded that my ...
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Best approach to solving for an option’s mid price IV?
As the title implies, I’m having trouble figuring out which approach is best suited to solving for mid price IV, given only a bid price and ask price for an option (assume we also have all necessary ...
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Difference between Stochastic Volatility (SV) model and Stochastic-Local Volatility (SLV) Model
I cannot get what's the difference between SV and SLV models.
The SLV model contains a stochastic volatility component represented by a volatility process and a local volatility component.
Based on ...
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Canonical choice of inputs for Black76 model?
What is the canonical choice of inputs (e.g. interest rate, forward price, option price, time to expiration, etc) for the Black76 model? For concreteness let's say on the SPX index.
I am using the ...
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Options on Futures: Estimating implied volatility
In a commodities futures market, where there are options for the terminal expiry, whose implied volatility can be determined, I am interested in understanding what the implied volatility for an early-...
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What $T$ to use a few hours till expiry when calculating implied volatility?
I am trying to calculate the implied volatility given an option price that is a few hours till expiry. The issue I am having is that I am not sure if it's better to use $T=\frac{1}{365}$ (case 1) or $...
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Heston Model numerical instabilities
I hope that all is well,
I am working on creating a neural network to compute the implied volatilities of options using the Heston Model. However, I am coming across some issues with the numerical ...
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Change in Option Price given Change in Implied Volatliity, Moneyness, and Maturity
I have an implied volatility surface parametrized into moneyless-maturity coordinates. At each period of time, I only have access to an option's moneyness (K/S), maturity, and change in implied ...
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Question about Example in Dynamic Hedging (Strong smile causing Put-Call Parity to not hold for American options)
On page 28 of "Dynamic Hedging" by Nassim Taleb, he uses the following example to demonstrate the fact that a rising volatility curve could separate puts/calls for American options because ...
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Comparing the volatilities of a strip of options to a terminal option's volatility
Imagine a strip of European options on a Future, each expiring every business day for the next year, for which I have implied volatilities.
I also have a single European option expiring the same day ...
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Comparing implied volatility in 2 different correlated assets
The general idea here is that I am trying to compare the volatility surface of two different financial assets whose prices and returns time series exhibit a strong relationship/correlation :
The ...
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Delta of ATM barrier option
Can you please share the intuition behind the delta of a ATM down & in PUT being less than a ATM plain vanilla put (usually around 0.3 instead of 0.5)?
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Logical mistake in PL attribution
We are attributing the PnL of a single stock option to risk factors, solving the PLA problem. We have desk quotes $MV(T-1), MV(T)$, and $PnL_{T}=MV(T)-MV(T-1)$. We associate $MV$'s to $\sigma_{iv}^{T-...
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The difference in Skew forward sensitivity of spot vs forward start payoffs?
Are spot starting exotics like callables sensitive to forward skew ( skew dynamic) the same way a forward starting option like a cliquet is sensitive to the forward skew ?
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Vol Shift by Term over Time
Below is a plot of AAPL vol vs. Strike for October and November, last market close vs 3 weeks prior. The plot shows that both curves shifted up by an approximately constant amount with the October ...
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Implied Vol under CEV model
Consider the following steps:
Suppose the underlying equity follows a CEV model $dS_t = rS_t dt + \sigma S^{0.5} dW_t$.
Use the above CEV model to simulate Monte Carlo paths and price a large set (...
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