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8 votes
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Option Pricing for Illiquid case

Warning upfront: I have NO experience with crypto currencies. I believe I do have a relatively decent experience with options in general though. What follows will be a generic explanation, largely ...
AKdemy's user avatar
  • 8,924
5 votes

Does Gatheral formula for local volatility translate to a constraint on implied volatility

This is actually explained in the article "Arbitrage-free SVI volatility surfaces" by Gatheral : It means that the surface is free of butterfly arbitrage.
servabat's user avatar
  • 171
4 votes

Is negative forward variance an arbitrage?

Let $$ V_t^{T_1,T_2}=\frac{(T_2-t)V_t^{T_2}-(T_1-t)V_t^{T_1}}{T_2-T_1} $$ be our forward variance where $t<T_1<T_2$, $V_t^{T_1}$ is the ATMF implied vol as seen at time $t$ for slice at maturity ...
fwd_T's user avatar
  • 747
4 votes

implied-information in american option

I observe that Christoffersen et al. (2012) consider the implied volatility from European options, as calculated under the BS model and other extensions of it. Therefore, implied volatilities from ...
alexbougias's user avatar
  • 1,416
4 votes
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Can a Call and a Put with same strike price and expiration date and underlying asset have different implied volatility?

In theory, they shouldn't, but in the real world, it is possible. In Theory: Call and put options of the same strike and expiry should obey put call parity and thus have the same IV. In Practice: Call ...
KaiSqDist's user avatar
  • 1,277
3 votes

Volatility Forecasting

From what I have seen yes. Yang & Zhang showed that their estimator is less biased and less volatile compared to the close-to-close estimator. However, as mentioned, high-frequency data is ...
herminat0r's user avatar
3 votes

How to calculate overnight implied volatility?

The limit you created is misleading because: $lim_{t→∞}σ_{daily}$ is defined w.r.t a sequence of values and is not the same as $σ_{daily}$, which is a single value and NOT 0 in a squeezed time ...
Arshdeep's user avatar
  • 2,175
2 votes

When calculating VIX, how to deal with the problem of asymmetry of put and call data?

I have dealt with this problem in my research, here are my findings and takeaways: Not enough options are a problem: Jiang and Tian (2007) showed that an insufficient range of strikes leads to a ...
Martin Georg Haas's user avatar
2 votes
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Filtering options data

It's possible they want you to remove short dated options as the vol of implied volatility increases. In real price terms this isn't visible as much, that's because $\frac{dC}{d\sigma_i}$ decreases ...
Newquant's user avatar
  • 769
2 votes

Strike of a Variance Swap in a Sticky Strike World

The fair strike computed via replication equals the integral of weighted prices of out-of-the-money options over all strikes. As you wrote correctly, these weights are being inversely proportional to ...
AKdemy's user avatar
  • 8,924
2 votes
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Optimal Fitting Criteria of SABR

In practice (at least in the rates world), $\beta$ is preset and $\alpha$ is solved for to calibrate to the atm vols $\sigma_{ATM}$ (which are the most liquid and reliable of the market data available)...
user35980's user avatar
  • 1,396
2 votes

Heston Calibration - how far OTM can an option be before it's not considered ATM anymore?

A1: Volatility implied by what model? :) A2: Check what the volatility smile is and how it affects your model. UPD: As @frido insisted, I would add more details. "Why not 1 year IV" Because ...
Alex D's user avatar
  • 51
2 votes

What's wrong with calibrating implied volatilities with polynomials?

First of all, you don't calibrate IVs. You interpolate and extrapolate IVs in order to calibrate a model. There is nothing wrong with interpolating and extrapolating with polynomials, as long as no-...
Frido's user avatar
  • 1,854
2 votes

Calibration of Heston using implied vol as $v_0$

Using the ATM implied vol of short term options is indeed a common practice for $v_0$ as in your Scenario 2. Linear interpolation should be enough, given that 1 week is somewhat arbitrary anyway. In ...
jherek's user avatar
  • 1,394
2 votes

implied volatility for close to expiry ATM options vs VIX

This question was asked the day before Thanksgiving ? Then an option that expires in 3-4 days is Friday ? Or Monday ? It doesn’t much matter, the point is that the market doesn’t expect much action ...
dm63's user avatar
  • 17.1k
2 votes

implied volatility for close to expiry ATM options vs VIX

Bonus: Dividend yield concerns the underlying, not the option. It is a cost of carry no arbitrage logic that is used to price options and as such you need to take dividends into account. The VIX index ...
AKdemy's user avatar
  • 8,924
2 votes
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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?

Yes, IV is indeed possible, at least in theory, to back out of stock prices. This lies, I would say, in the core of the so called structural bond models, which, as far as I know, started out with ...
Mats Lind's user avatar
  • 1,412
2 votes

Option price calculation using Local Volatility and Monte Carlo

Surfaces are used to compute prices of exotics. For vanilla pricing, there is no need to fit a surface. LV is applicable for non-path-dependent exotics. LV essentially boils down to a static ...
Yike Lu's user avatar
  • 266
2 votes

Value of Call Option as Volatility goes to Infinity

When you delta hedge, you make a PnL equivalent to gamma times the difference between implied and realized vol. You want on average the realized vols to average out to the implied vol, in a central ...
Arshdeep's user avatar
  • 2,175
2 votes
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Vanna Volga Price of an Up and In Put

I do not think you should (can) use the opposite probability (going from p touch to p no touch) because there exists a so called In-out parity: $$European \ vanilla\ option = European\ KI + European\ ...
AKdemy's user avatar
  • 8,924
2 votes
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Derivation in Jaeckel's "By Implication" paper

As you mentioned, we know the Abramovich-Stegun approximation for the CDF $$\Phi(z) = h(z) − \dfrac{\varphi(z)}{z} \left[ 1 - \dfrac{1}{z^2} + \mathcal{O}\left(z^{-4} \right)\right], \quad \text{for} \...
KT8's user avatar
  • 855
2 votes
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Python Quantlib for the calibration of interest rate caps

I think you should use something like TreeCapFloorEngine for cap/floor calibration with G2. BlackCapFloorEngine is for closed ...
user35980's user avatar
  • 1,396
2 votes
Accepted

Infer implied volatility skew/smile from implied distribution

This is not an answer to the question but too long for a comment. There are a bunch of issues with your code. In roughly decreasing order of importance: Sanity-checking your prices should immediately ...
LocalVolatility's user avatar
2 votes
Accepted

How should I go about computing the 30-day model free implied volatility (MFIV) daily?

If you read carefully their paper they are not using the raw options data from OptionMetrics but the smoothed surface file: We use the volatility surface file, which contains a smoothed implied- ...
phdstudent's user avatar
  • 8,371
1 vote
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Forward Black Implied Volatility For Within Risk Neutral European Option Pricing

The 'model free forward implied volatility' is pretty useless for your purposes. First of all, it doesn't say anything about the price of future IVs, which you need, and worse it's pretty much ...
Frido's user avatar
  • 1,854
1 vote

Creating Implied Volatility surface using log moneyness

Both ways are possible, and are not the same thing. There is a difference between using log-moneyness (or some other convention) for the input quotes, and using log-moneyness (or some other convention)...
jherek's user avatar
  • 1,394
1 vote

week-over-week impacts on IV of of options with close to before/after EOY expirations

Implied total variance is the actual volatility quantity being bet on with options. IV is a convenient way to discuss total variance because the numbers are more intuitive. Let $\tau$ be the total ...
Yike Lu's user avatar
  • 266
1 vote
Accepted

Price Option B Knowing The Price of a Similar Option A

Solution: I've found the answer to this. Assuming $r = 0$ and using Black Scholes: For our 25-strike call option, we know that $$ 20N(d_1^c)-25N(d_2^c) = 0.90, \text{ where } d_{1,2}^c=\frac{\log{20/...
Kai's user avatar
  • 123
1 vote

Price Option B Knowing The Price of a Similar Option A

Welcome Kai, I am Kai. Hopefully this answers your question? A Review on IV Calculations https://www.sciencedirect.com/science/article/pii/S0377042717300602 I don't think there are exact mathematical ...
KaiSqDist's user avatar
  • 1,277
1 vote

Moneyness, implied volatility and option greeks

For the first question: The differences in IV across strikes is largely due to the market having a different view on potential movements than a constant-volatility model (like Black-Scholes) would ...
D Stanley's user avatar
  • 1,441

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