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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1answer
117 views

What is the connection between the risk neutral implied density and the real world density?

I understand that we can use option prices to imply volatilities and ultimately to imply a risk neutral density. I also understand that this implied density is not the same as the "real world density"....
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45 views

Instability in risks using local volatility

I am valuing vanilla call options using FDM with Crank Nicolson discretization and Rannacher smoothing (mind you, I am having the same issue on MC) and I am getting unstable delta, gamma and theta. I ...
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88 views

Robust bounds or approximations on implied volatility skew when $\lvert \rho \rvert \rightarrow 1$

Are there any robust / non-parametric results for pure stochastic volatility models, in terms of bounds or preferably accurate approximation, for the implied volatility skew $\partial IV(k) / \partial ...
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1answer
68 views

Calculating Implied ATM Volatility with Vega

Can we calculate Implied ATM volatility with Vega? Normally, Vega is derived from Volatility, but I wonder the availability of the opposite way.
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1answer
85 views

Since implied volatility is the standard deviation of returns, why do people treat it as the standard deviation of the price process?

In the Black Scholes framework, the parameter sigma (volatility) is the standard deviation of the underlying's returns NOT the standard deviation of the underlying price process. But I often see when ...
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2answers
63 views

calibration - negative call price [closed]

Im trying to calibrate a stochastic volatility model to market. I end with an MSE of 2-3 with approximately 500 quotes. Some out of the money options with call-price under 1 dollar ends up being ...
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26 views

In building volatility curve for etf options, should I use synthetic forward price or cash price

Assuming option market moves faster than ETF cash price in intraday high frequency setting. That means at each time point, when implied volatility is calculated by black-schole model by using cash ETF ...
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1answer
63 views

Should we calculate the implied volatility surface with Put+Call?

We have Sungard data (MarketPlace8), but for nearby maturities the ask-bid of the calls are all the same when we are out of the money (call), so should we calculate the implied volatilities of calls ...
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3answers
269 views

Intuitive explanation for the smile in FX

What is the intuitive reason for the smile in FX? For equities this usually down to crash risk.
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1answer
120 views

Measuring implied volatility

I'm a new in financial engeneering and trying to understand basic principles of volatility modelling. I wrote many papers and articles about different models (garch, local vol, stoch vol and ect.) and ...
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1answer
72 views

Why does implied volatility increase when we lower the risk-free interest rate?

I don't understand it, when I calculate it I see it, but I can't explain it. Plus, $\frac{\partial C}{\partial \sigma}$ is positive so, could you explain me please ? Is it because the market is more ...
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82 views

What is the point of volatility curve fitting?

What is the point of fitting curves to the implied smile in the market? (Other than pricing exotics where the hedging instruments are vanillas). How does fitting a vol curve help you trade/market make ...
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46 views

FX Volatility surface bid/ask

I have bid/ask vols (straddles, risk-reversals and market strangles) for FX pairs, I want to create a mid/bid/ask volatility surface in strike/maturity space after a consistent smile calibration ...
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1answer
61 views

Downward-sloping volatility skew in equity prices

I’m learning the market price for FRM, and I’m having a hard time understand a question in the assessment: From my understanding, the volatility skew for equity is the graph on the right upper corner:...
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1answer
98 views

How many options would be required to dynamically replicate the VIX nowadays?

The VIX is a portfolio of OTM options on the SPX with non-zero quotes. From CBOE white-paper: Only SPX options quoted with non-zero bid prices are used in the VIX Index calculation. [...] As ...
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2answers
177 views

Deriving implied volatility programmatically

I'm working on a project to calculate the value of options using Python. I'm using the Black-Scholes model, and I can get accurate results by plugging in a given ...
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1answer
134 views

Different volatility surface ( Local vol, Stochastic vol etc.)

Despite many questions about local and stochastic volatility available on this forum, i still have a few doubts left. Essentially I am seeking validation whether I am interpreting things correctly. ...
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86 views

Intraday and Intra-Week Pattern of Implied Volatility in FX market

Q1. How does implied vol changes from market opening time to market close time? I have read that it decreases during the day i.e. it opens high and closes low. what is intuitive and mathematical ...
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2answers
157 views

Relation between Implied and Historical Volatility of GBPUSD and USDGBP

Q1. How is the implied volatility of GBPUSD and USDGBP related to each other mathematically? Please explain this intuitively as well. Q2. How is the historical volatility of GBPUSD and USDGBP ...
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1answer
85 views

Are vega vanna volga methods/models used in equity derivatives or only in FX and why?

Vega vanna volga models seem to be popular is the FX derivatives market and are often calibrated via 25 delta risk reversal, vega weighted butterfly, and ATM straddle quotes. I am wondering if they ...
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29 views

Reading this ichimoku cloud how do you read this wdfc chart?

Having trouble reading the charts as the breakouts aren’t clear What do you see in this chart?
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1answer
88 views

Fair Strike for Variance Swap with no Skew in IV Surface

I am reading through Derman's 1999 research notes, "More than you ever wanted to know about Volatility Swaps." In equation B4 of Appendix B, the author takes the Taylor Series of the variance swap ...
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2answers
144 views

Interesting Undergrad Thesis [closed]

I'm searching for an undergrad thesis in finance. I already have some ideas, but still wanted to ask: Is there a an interesting topic that jumps to your mind, when you think about implied volatility (...
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1answer
200 views

Implied vol vs Realised vol on Event Days

How implied vol varies vis-a-vis realised vol on an event days?
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What model do market makers in equity derivatives commonly use to price, hedge, and fit the IV surface?

What is the industry standard/common model used by market makers in equity derivatives to trade across the IV surface?
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1answer
117 views

Local volatility and Stochastic Volatility

Please help me understand similarity and differences between local volatility and Stochastic Volatility both intuitively and mathematically.
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2answers
135 views

Why is the SVI parameterization in terms of variance?

The Gatheral SVI parameterization reads $$\sigma^2 = a + b \left[\rho(k-m) + \sqrt{(k-m)^2+s^2}\right]\,.$$ Why is it expressed in terms of variance $\sigma^2$ and not directly in terms of volatility $...
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170 views

What is the intuition behind “jumps” causing volatility skew?

Some models use jumps as a way to explain volatility skew. I understand that if jumps exist, then you are "mishedged" as you no longer can continuously hedge. Options have a gamma component and ...
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110 views

What are popular metrics for Option Skew?

What are popular metrics to track skew? Would it be the difference between OTM option and ATM option IV? Would it be a percentage difference in IV? Also, if both are valid, would a % change be ...
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56 views

How to shock the IV surface w.r.t VIX and keep AOA

I have to compute the sensitivity of a set of option prices on a single sotck (range of tenor is over the whole surface) to an increase of 100% in the VIX.. and I am trying to get to the most ...
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1answer
70 views

Arbitrage-free IV surface definition vs. real arbitrage process

In the context of BS implied volatility surface fitting. In the literature, it seems that conditions for arbitrage are defined in a way that assumes that options can be traded at the same price for ...
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24 views

What is the best method to factoring/calculating pre and post event volatility? Such as for company earnings

What is the best method to factoring/calculating pre and post event volatility? Such as for company earnings.
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3answers
70 views

Use cases for calibrated IV surfaces

What are common applications of a calibrated options IV surface when trading vanilla options only? Thank you!
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42 views

How To Calculate The Implied One Day Expected Return For Earnings

I am trying to figure out how to calculate the one day expected return given I have the event volatility. In his book Trading Volatility, Correlation, Term Structure and Skew, Collin Bennet (link) ...
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62 views

Local volatility Formula and How To use it

I'm new to Volatility Modelling, so the content of this question may be completely wrong and th question naive. I'm reading "The volatility surface" by Gatheral. I'm trying to get a sense of the first ...
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3answers
291 views

Why is volatility skew/smile for long term options flatter compare to short term options?

Volatility skew/smile for long term options is flatter compared to short term options, could someone help to explain why is that the case? Thanks
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1answer
305 views

Options Market Making Used Implied Volatility Surface

Suppose you are a market maker with a model that is producing an implied volatility surface for you. Suppose you quote bid/ask prices (vols) around the prices given by your implied vol surface. In ...
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1answer
73 views

Why and how is Implied volatility directly related to stock price but inversely related to strike price?

I know that in equity markets there is a volatility smirk which results in higher IV for lower strike price options because of crashophobia and leverage related factors but I can't wrap my head around ...
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35 views

Procedure of model calibration

Say that your end goal is to price an equity exotic derivative under both Heston and the local volatility models (Black Scholes model with vola dependent on strike and underlying level). Do the ...
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1answer
70 views

B-splines: convexity in IV/Price

I see that the justification of the need to use cubic B-splines when interpolating in the strike-IV space is to impose a convexity constraint to get rid of potential arbitrage. I could easily ...
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1answer
52 views

Implied Risk Neutral Density Doesn't Integrate to Unity

There is a well known result that $\frac{\partial^2 c(K)}{\partial K^2}= e^{-rT}f(K)$, where $K$ is the strike and $f$ is the risk neutral density at time $T$. With the left calculated from market ...
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49 views

Vol surface fitting to options on commodity futures

Trying to fit variants of SVI (Zeliade method, SSVI etc) to options on futures price data. One of the core ideas of the SVI parameterization is the absence of calendar spread arbitrage. I think the ...
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31 views

How to derive the half slope rule from asymptotic relation between implied and local volatility?

In their paper(https://www.sciencedirect.com/science/article/pii/S0764444200017493) BERESTYCKI, BUSCA, and FLORENT proved an asymptotical relation(for short maturity) between implied and local ...
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1answer
215 views

Why do we fit volatility surfaces implied from a option pricing model to the empirical data?

As far as I understand volatility surface. It is made of 2 components, the volatility skew/smile and the volatility term structure. Together they form something like Implied volatility is ...
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174 views

Procedure/methodology for building equity volatility surface

EDIT: I update while making progress: I am trying to build (model implied) volatility surfaces for individual equities. I will use these surfaces to calibrate models to price different derivatives (...
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0answers
34 views

Dimension reduction for worst of basket on $min(S_1, S_2)$

Suppose we want to price an exotic equity which is a function of $min(S_1, S_2)$. To do this, I'm trying to compute an implied volatility surface for $min(S_1, S_2)$ and then price the option using ...
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1answer
79 views

Black Sholes option pricing with all but Delta [closed]

I'm trying to setup a little option pricing model in excel. I have all the information for the inputs (interest rate, IVs for different deltas, time to expiry, strike price, underlying price) but what ...
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39 views

Does convexity in the IV space means convexity in the price space?

Let's assume that we only look at OTM options to construct a Risk Neutral Density (RND). As the RND is the second derivative of the price of the option with respect to the strike, we would expect ...
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160 views

Why do coefficients flip after the including a lag in the optimisation? implied volatility/skewness/ivspreads

I'm hoping some of you guys can help me out. I am applying the paramametric portfolio optimisation of Brandt, Michael W., Pedro Santa-Clara, and Rossen Valkanov. in which the weights on specific ...
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1answer
153 views

How does the volatility skew/smile relate to hedging/trading vanilla contracts?

I know that obtaining and calibrating the smile is important in the hedging and trading of exotics since we use vanillas to hedge and price exotics. How is the smile important in the hedging and ...