# Questions tagged [volatility]

A measure of the variation in price over time. Also a measure of the risk of a financial instrument.

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I’m currently working on a project to build a local volatility model out of implied volatility data and am struggling in the selection of an appropriate method to interpolate the volatility surface. I ...
268 views

I've been experimenting with end-of-day volatility-based stock trading strategies and I'm looking to see if it's possible to use similar strategies over shorter time frames. Given that market ...
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### 1 Factor Hull And White Swaption Calibration

I'm trying to calibrate a Hull and White model with constant volatility, mean reversion and theta such that the model can reproduce the initial Term Structure. I'm using this python code adapted from &...
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### Entropy-implied volatility requires itself to be calculated?

\begin{align} H &= \frac{1}{2} \ln (2\pi\sigma^2) + \frac{1}{2}\\ &= \frac{1}{2} \ln (2\pi e \sigma^2) \end{align} is the analytical solution for the entropy of a Gaussian random variable, ...
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### Probability of an Option maturing In-the-money vs. Volatility

How will the probability of an option ending up in the money change if the volatility of the underlying stock increases? Intuitively, I think the answer to this is that if volatility goes up the ...
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### How does volatility affect an option payoff diagram? [closed]

I am a beginner to financial mathematics, and my lecturer asked me to ponder about how volatility may affect the value of an option (as a function of spot price). For example, if an option had a (...
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### Close Volatility - Open-Close Volatility

Could anyone please give the detailed expression of either the close-close or open-close volatility ? Thanks
283 views

### Can we model Implied volatility using GARCH?

Can I use Implied volatility as a dependent variable in a GARCH model? I believe my IV data shows ARCH effects and hence can I use it to model volatility of the volatility? I know literature has used ...
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### Availability of historical data on variance swaps [duplicate]

I want to do research on variance swaps. Where can I get/buy historical data (other than Markit)?
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### Is there a relation between the so-called volatility drag and the sigma term in Black-Scholes' model? [duplicate]

The closed-form solution of Black Scholes Dynamics $dS_t=S_t(\mu dt +\sigma dW_t$) is $$S_t=S_0 e^{(\mu -\sigma ^2/2) t+\sigma dW_t}.$$ The $-\sigma^2/2$ term is quite similar to the volatility drag ...
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### Relationship between risk and return for GBM and riskless bond

Suppose we have $S$, a stock following geometric Brownian motion ($dS_t = S_t (\mu dt + \sigma dZ_t)$ for $Z =$ Brownian motion) and $B$, a zero coupon bond with rate $r$, i.e. $dB_t = rB_t dt$. In ...
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### Estimating constant and local volatility based on passage times

Consider a Brownian motion B_t with constant instantaneous volatility σ and zero drift where ...
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### transforming variables

I am would like to create a regression model with different variables however before using these variables in my regression model I would like to transform the variable in order to make it more ...
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### How to get exposure to realised volatility while being vega neutral?

Let's say I am predicting the realised volatility of a stock index. I am buying or selling straddles based on whether the predicted vol is higher or lower than the implied ATM volatility for the ...
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### garch(1,1) Annualised Volitility with python

I am trying to calculate the annualized Volatility of given returns for a stock with Garch(1,1) on python using a code I found online. The value I should be getting is around 27, but the value I am ...
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### Why a model like GARCH is only good for daily volatility and not for intraday volatilities?

I´m currently looking to implement an intraday volatility model and I´m new at the quant world and I learned how superior is GARCH family is for daily volatilities, but in the research stage I found ...
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### Behavior of Vega PnL for 6 month ATM S&P500 option

I am interpolating the vol surface for 6 months maturity from price data for S&P500 options. For this vol smile I compute the ATM strike. I then assume I can buy a call option at this strike, ...
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### Trading butterfly a long vol or short vol [closed]

Sorry for what could be a naive question. When is the right time to trade a butterfly i.e. (buy 10d call and put vs sell atm all notional flat) is it when implied vols are high or low (relative to ...
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### Hedging predicted volatility

Q. If you predict the volatility of the stock is 10% a year from now and current price is X dollar, how do you hedge the risk? Im not sure why I am finding this so hard. How do we use options (...
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### Price volatility short-term (10 seconds) forecast

Dataset: list of all realized trades (BTCUSDT) from a certain cryptoexchange with timestamps (15 days worth of data) Problem: predict the "price volatility" (standard deviation of realized ...
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### Black Scholes implied volatility [closed]

I am reading up on implied volatility and I encountered the term Black-Scholes implied volatility which I haven't heard before. What is the meaning of this term? Say I am looking at the Heston model ...
175 views

### Valuation of Variance Swap

Let say I have a Variance Swap contract which is based on daily closing prices (not the continuous variance calculation) and will last between the day interval $T_1$...
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### Why are FX options vols quoted in 25RR and 25BF terms instead of by strike like credit options?

Credit options follow a quoting convention for the vols based on strike, which fits in neatly with the Black-Scholes framework. So why are FX options vols quoted in terms of 25-delta Risk Reversals ...
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### Rugarch function ugarchdistribution fail to invert hessian for sGarch but it converges for gjrGarch

I have the following Garch model ...
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### forecasting hourly variance with higher resolution data available

Assume one has price data $P_{1}, P_{2}, \dots, P_{n}$ with one hour resolution and aims to forecast the variance for one hour ahead return. The first approach to try is ARCH or GARCH models. There ...
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### Calculating implied volatility index

What are common methods to compute implied volatility index? One could use VIX method on other underlying. It is also easy to limit the method to 4 atm strikes. Is this a good idea though? What are ...
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### Volatility forecast on SPX option expiration day

I am looking for methods and papers on forecasting SPX option at-the-money implied volatility or realized volatility within its expiration day. What are some stylized facts and forecasting methods?
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### Optimal bandwidth for Realized Kernel

If I want to estimate Realized Kernel for 1 min bins, is there a way to compute the optimal bandwidth? In the reference paper: Realised Kernels in Practice: Trades and Quotes (Ole Barndoff-Nielsen et ...
As per the Wikipedia, the SABR model looks like below - $dF_t = \sigma_t \left(F_t\right)^{\beta} dW_t$ $d \sigma_t = \alpha \sigma_t d Z_t$ I have 3 questions - ...