All Questions
Tagged with implied-volatility options
307 questions
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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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1
answer
59
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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 ...
9
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1
answer
129
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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 ...
- 2,231
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3
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211
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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:
...
- 2,231
2
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105
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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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2
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196
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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 ...
- 2,231
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90
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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 ...
- 2,681
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183
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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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2
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99
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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 ...
- 131
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102
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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, ...
- 2,231
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42
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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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68
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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?
- 139
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35
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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 ...
- 121
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81
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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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34
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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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163
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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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45
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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 ...
user72785
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47
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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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59
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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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51
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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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133
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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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106
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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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48
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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 ...
- 103
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63
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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 (...
- 301
1
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252
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Arbitrage between implied and realised spot-vol beta
Let's say there is a discrepancy is the market with respect to implied spot-vol beta (implied skew) and the actual beta of ATM vols with spot. Let's say Put vol > Call Vol but the atm vols are ...
- 108
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2
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128
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Why would you take a Loan when trying to Illustrate a Riskless Hedge?
I'm reading an article trying to derive option pricing with a simple approach, but I got stuck. In the second paragraph of this article (Name – Options Pricing: A Simplified Approach), which takes ...
2
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3
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454
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How to calculate overnight implied volatility?
I am trying to workout how to calculate the implied volatility of the overnight movement from market close to open. That is, the volatility of the from the closing price $S_t$ to the opening price $S_{...
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2
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103
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Describing the volatility skew with a set of options
Say you have a set of options data, and you filter the dataset based on certain criteria such as the bid-ask spread, open volume etc. and you end up with a set of liquid options based on said criteria....
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144
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Interpolation of IV based on delta
I have a dataset with options, all the same date and time to maturity but different IV and delta. Now, I want to find the IV for certain delta values (e.g 0.5) through interpolation. Do you think that ...
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99
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Summarizing the Volatility Skew as a Single Number
Related questions to this topic/subject:
Expressing Volatility Smile as One Number
Volatility skew and how to capture it?
In both posts, the authors/respondents recommend using the second derivative ...
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1
answer
99
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Heston model calibration to option prices and implied volatility
I hope that you are having a great day,
I am trying to write a research paper on the Heston model deep calibration. I noticed during my literature review that the most common approach is to calibrate ...
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2
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1
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174
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How should I go about computing the 30-day model free implied volatility (MFIV) daily?
As the title suggests, how can I calculate the MFIV daily (for a market index)? My MFIV follows the procedure described in DeMiguel et al. (2013) Improving Portfolio Selection Using Option-Implied ...
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120
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What is the informational content of the volatility skew?
The option-implied volatility is well-known as a measure for the risk-neutral future expected risk for the underlying asset. However, the market prices of options (across different strikes) imply ...
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2
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426
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Infer implied volatility skew/smile from implied distribution
My question is closely related to the answer of @LocalVolatility and his blogpost.
I am trying to reproduce his first figure and I am struggling with the implied volatility.
With the help of
$$
f(S) = ...
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249
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Vol Smile Call/Put Wing calibration
Is call/put wing volatility smile calibration approach used in practice? To calibrate an index (SPY) using only more liquid OTM calls/puts, to kind of use an "if" condition on K to S0 to ...
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178
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Expected underlying daily move from implied volatility
Suppose I have 3 ATM call options on an underlying with time to maturity 1, 2, and 3 months, respectively, priced at implied volatility level $\sigma_1$, $\sigma_2$, $\sigma_3$. Given that there will ...
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1
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142
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Derivation in Jaeckel's "By Implication" paper
In this paper by Jaeckel (2006), he derives the asymptotics for the option price $b$ as:
\begin{align*}
\lim_{\sigma \to \infty}b= e^{\theta x/2} - \frac{4}{\sigma}\cdot \phi(\sigma/2) \tag{2.7}\\
\...
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We can forecast the direction of (constant maturity) implied vol of various indices well. Is that useful?
We've been financial building ML models for years, and have multiple portfolios live - but we're new to the volatility space, none of us are options traders.
How could we effectively use implied vol ...
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31
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week-over-week impacts on IV of of options with close to before/after EOY expirations
Tomorrow is the last trading day of 2023. Compared to last week, I noticed that $SPY ATM or close-to ATM options for the end of month/quarter (Dec-29) exp experienced a spike in IV since yesterday, ...
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2
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158
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Price Option B Knowing The Price of a Similar Option A
How do we find the implied volatility from the price in a call option and apply it to another option without a calculator? Or is there actually a better way?
For example, given a 25-strike 1.0-expiry ...
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321
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implied volatility for close to expiry ATM options vs VIX
All throughout my MFE I was told that implied volatility for close to expiry ATM options is a reasonable estimate for current volatility and tracks realised vol pretty well. Then why does VIX measure ...
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211
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Approximating implied price vol from implied yield vol?
I am wondering if there are any approximations that exist to convert yield vol to price vol? I am dealing options on SOFR futures, which can be quoted in yield and price (i.e. 3% put and $97 call are ...
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3
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552
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Implied volatility greater than realized volatility at all strikes?
It is usually stated that the implied volatility is statistically generally --- not always --- greater than the realized volatility. It seems this statement is made with regard to the implied ...
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164
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If there was a way to back out implied volatility (IV) from a stock, would it be the same as the IV backed out from an option on that same stock?
I know that it is not possible to back out an IV for a stock, because the concept of IV is based on a model with underlying assumptions applied to pricing an option.
I was thinking of why IV is ...
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850
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Python - yahoo finance options data - volatility smile plot
I have plotted the IV of TSLA options using yahoo options data, but the scatter plot doesn't look right, can anyone advise why the plot looks like this? I would expect to see a vol smile plotted.
EDIT ...
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145
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In the paper "By Implication" by Jaeckel, he says that put-call parity should never be used in practic
In this paper by Jackel (2006), on page 2, he writes:
The normalised option price $b$ is a positively monotic function in $\sigma \in[0, \infty)$ with the limits
$$
h(\theta x) \cdot \theta \cdot\left(...
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233
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How did Jim Gatheral come up with the SVI parameterization?
I know it has nice properties relating to Roger Lee's moment formula and the Heston model asymptotics, but I am just curious how Jim Gatheral came up with this formula in the first place. I read a ...
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498
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Using Cubic Spline with Vol Skew for Equity Options in R
I was recently attempting to replicate a part of the paper - DeMiguel, Plyakha, Uppal and Vilkov (2013), where they compute a model-free implied volatility (MFIV) quantity.
In the paper, the MFIV is ...
- 2,231
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135
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What does it mean with regards to market conditions that the historical volatility is twice the implied volatility
I am trading the Indian market indices. I calculated the last three years historical volatility. Noted down 1 standard deviation of this value.
Then I took a weekly expiry of options on this index and ...
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212
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Volatility Surface Construction: Ask IV, Bid IV and Mid IV
I am presently engaged in a project wherein my objective is to construct a volatility surface utilizing either the SVI parameterization or the SABR model, leveraging real market data. Initially, I ...
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