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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56 views

What is the model behind Heston-Nandi functions in the fOptions R package?

I am dealing with Heston model in R and for this purpose I am using the package fOptions from RMetrics. The calibration formula requires the specification of some parameters (omega, lamda, alpha, ...
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Volatility of a stock basket

to determine the volatility of a basket of stocks, I often use the following formula: $\sigma_{basket}=\sum_{i}\sum_{j}w_i w_j \sigma_i \sigma_j \rho_{ij}$ where the $\sigma$ are the constituents' ...
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361 views

How could one trade volatility skew if you think it's too flat or steep?

We all know that you can trade on a forecast of volatility by dynamically hedging, but I'm wondering if there's a similar technique where in you can trade the skew specifically? Let's say you travel ...
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Pricing forward start Cliquet option with implied volatility with Dupire

I have the following implied volatility matrix of a stock index downloaded the 15th February 2019, the value of the stock was 3188.44 at the time: ...
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Question on Local Volatility

In Gatheral's book The Volatility Surface (Wiley, 2006), a local volatility model is defined as... $$ dS_t =S_t \mu_tdt + S_t \sigma(S_t, t)dZ $$ The famous Dupire Equation is given by... $$ \sigma^2(...
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GARCH(1,1) one-step ahead volatility forecast biased, higher than Parkinson's HL volatility

I am trying to create one-step ahead forecasts for the S&P500 using a GARCH(1,1) model. I am using the rugarch package in R. As you can see, the forecasted points are consistently higher than the ...
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1k views

better estimator of volatility for small samples

One commonly used sample estimator of volatility is the standard deviation of the log returns. It is indeed a very good estimator (unbiased, ...) when the sample is large. But I don't like it for ...
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General assumptions for var swap replication

I've seen claims that the standard static-hedge for a plain vanilla variance swap holds so long as the underlying doesn't jump, but every derivation I have seen begins by assuming the asset follows a ...
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118 views

Volatility smile shows individual Put and Call IV or combination

IV is calculated per strike AND option type basis(for example WTI 50 CALL its x and WTI 50 PUT its y). The question is when its shown in "Smile" its just shown on strike basis, so does that mean lower ...
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What's the difference between demand elasticity and demand volatility? [closed]

What's the difference between demand elasticity and demand volatility? Demand elasticity: https://www.investopedia.com/terms/d/demand-elasticity.asp Demand volatility: https://www.sdcexec.com/home/...
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stochastic volatility and smile

Can we say that the volatility smile contain for sure stochastic volatility information ? If yes why ? Saying that BlackScholes does not explain the smile does not necessary mean there is an ...
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390 views

CBOE Index Minute Data

I am doing a small research and looking for a place to purchase historical minute CBOE Index data. I am interested in: VIX - CBOE Volatility Index VVIX - CBOE VIX VOLATILITY INDEX VXV - CBOE VIX ...
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How is a LIBOR Market Model volatility skew determined?

LIBOR based interest rates are derived from the prices (supply / demand) of swaptions, caps and floors. These prices are generally quoted in yield vols. Their prices are given by the Black formula. ...
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155 views

1 day VaR vs 10 day VaR

Even while using historical simulation VaR, 1 day VaR is converted into 10 day VaR by multiplying 1 day VaR by Sqrt(10) for regulatory reporting purposes. What are the underlying assumptions for ...
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791 views

Evaluation of portfolio other than Sharpe Ratio

Is Sharpe ratio always the best way to evaluate a portfolio? I'm not really sure what this potential interview question wants me to answer. I have read that Sharpe ratio essentially explains how ...
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Proof of no arb condition after shifting SABR’s rho

Does anyone know of any paper or research where they shift SABR’s skew and rebuild the surface? In particular, I would like to prove theoretically whether the no arbitrage condition hold for the ...
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1answer
119 views

VaR equivalent volatility meaning

I have a hard time with interpreting VeV. I mean - I see its just standard deviation derived from Cornish-Fischer VaR, but I don't really know how to interpret it. The formula for VeV is: ...
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Vega for long long-term ATM call and short short-term ATM call

You are long a long-term ATM call and short a short-term ATM call. The ratio is adjusted to make the total vega zero. If before expiry of the short-term option, spot is again at the strike price. ...
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Regime-Switching Model for detecting market shifts

I'm always wondering whether anyone has utilized regime-switching models successfully in forecasting or trading. Academia has long discussed this topic in-depth, such as using Regime Switching ...
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107 views

Fitting a forecasting S&P500 roll volatilities

I have a time series of S&P500 prices, for which I have calculated log-returns and roll-volatility. My goal is to forecast daily realized volatility and test a straddle strategy based on it (I ...
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Why historical volatility is calculated as N-days annualized?

Annualized historical volatility is always calculate with 10-, 20- days time window. I don't quite understand. Compare with annualized historical return, annualized historical return is never ...
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2k views

Which volatilities should I use for Quanto Options?

Quanto options pricing formula, as described in this paper is a function of two volatilities: one from the underlying asset and another from the exchange rate. How can I read the "right" volatilies ...
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92 views

Inherent volatility of selling longterm options and buying short term options

A two-month option has an implied vol of 60%, the corresponding 2-year option has an implied vol of 34%. You buy the short terms and sell the long terms. What is the inherent volatility of the total ...
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Transforming log return volatility into standard return volatility

If I have a forecasted volatility of the log returns of say, 0.03, this is obviously transformed relative to the log I took of the returns. It strikes me that I should raise ...
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1answer
458 views

Volatility swap hedge

What are the hedging methods for volatility swap (rather than variance swap)? What are the possibilities of setting up a static, semi-static or dynamic hedging? I am aware of but have not yet read ...
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359 views

What does Volatility Smile tell? [closed]

Could you please share your opinions about Volatility Smile? What does it tell us when it gets more convex or when its level changes over time or any other change on it. Any paper/work/blog ...
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Is the VIX more similar to a volatility swap or a variance swap?

I am reading the following paragraph on the VIX wikipedia article and I find it confusing: The VIX is calculated as the square root of the par variance swap rate for a 30-day term[clarify] ...
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Break-even volatility for delta hedge portfolio

After simulating practical and theoretical PnL of a delta hedged portfolio on some data from the SPX500 under 0.15 management Vol I want to find the Vol which gives me an accumulated PnL of 0. ...
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Negative theta in Log-linear stochastic volatility model

I was asked to simulate the following geometric Brownian motion to get paths for the SPX stock price. the process follows a Log-Linear stochastic volatility. $dS_t = \mu S_tdt+e^VS_tdW_1 $ where ...
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Finding Lead-Lag Relationship [duplicate]

Given two series of data, volatility and returns, is there a way (Excel) of finding which one is the leading factor and lagging factor? Thank you for your help.
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307 views

Derivation of VIX Formula

I've read a lot of derivations about VIX formula. I can say it is -adjusted- fair strike of variance swap. But I can't see how it goes from variance swap rate to VIX formula. In particular I can't see ...
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92 views

Option value with different spot prices [closed]

I found this post online which is plotting different results for option value and greeks depending on spot price. Why would someone want to do calculate the value of the option with different spot ...
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202 views

Mixed local-stochastic volatility model in Quantlib

At a conference the speaker mentioned that it is a standard approach today to use a mix of local and stochastic volatility model in equity, FX and interest rates. Can you please suggest the most ...
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Threshold to consider the daily change of a bond price unusual?

In the context of compliance and market abuse monitoring, what relative change threshold would you choose to decide if transactions should be looked into? For example, if a bond price had a relative ...
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Understanding Yang-Zhang Volatility Estimator

I am using TTR in R and I am trying to understand the Yang Zhang volatility estimator (without drift). The following equations seem to imply a single value: $$ \sigma = \sqrt{{\sigma_o^2}+k\sigma_c^2+...
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293 views

How is volatility different from variance?

I always thought volatility was just variance ^ (1/2). Now I'm reading this book and it's saying that the two are different concepts. Excerpts include: Partly due to its use in Black-Scholes, ...
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What are the different indicators to measure historical volatility for stocks on individual basis?

Google search shows there are three indicators to measure volatility: 1. Average True Range 2. Standard Deviation / Variance 3. Bollinger Bands. What are the indicator(s) that you use to identify ...
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240 views

Vanilla Option Prices from Local Vol Surface (using neither MC nor PDE)

There are numerous papers that describe the derivation of the Local-Vol equation using available market prices of options. For example: Dupire's formula (see e.g. OpenGamma (2013)) gives us LV in ...
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Whats the big deal between volatility and the risk free rate?

I am trying to understand asset price volatility. Many of the news articles I read link how stock market volatility is linked to asset price volatility? To give an example, in Mike Mackenzie's (...
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Volatiliy in a at-the-time call option [duplicate]

I understand that the vega of the Black-Scholes equation is a positive function, which means the value of the option is an INCREASING function of the volatility, since vega is the derivative of the ...
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Does your Parkinson volatility ratio work as Taleb explained?

According to Dynamic Hedging: Managing Vanilla and Exotic Options (Taleb, 1997), the Parkison volatility estimator has several meaningful properties. It is defined $$P=\sqrt{\frac{1}{n}\sum_{i=1}^{n}\...
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What is the formula for Intraday and overnight volatility?

I'm a noob trying to calculate IntraDay and Overnight Volatility. For Intraday volatility we can get the annualization factor with the following: Length (hours, Open to Close): 6.5 Time frames per ...
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Intuitive description of the Spillover Index by Diebold and Yilmaz

I am struggling to grasp the steps outlined in the 2009 paper by Diebold & Yilmaz, which introduces the framework for a spillover index. The final expression for a spillover index for a two ...
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311 views

Rolling forecast using GARCH model

EDIT This is not a duplicate of my original question linked, since I have since overcome that problem and have posted an answer. Since solving the previous problem, I have run into the problem ...
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303 views

Is this the correct way to forecast stock price volatility using GARCH

I am attempting to make a forecast of a stock's volatility some time into the future (say 90 days). It seems that GARCH is a traditionally used model for this. I have implemented this below using ...
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390 views

Proof of approximation formulas for implied volatilities

I am trying to calibrate a local volatility model to observed implied volatility smiles (not surfaces!, just a smile given for fixed maturity). I ran into the following approximation, and thought I ...
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63 views

Estimating an GARCH(1,1) model? Long hand method

I am really trying to invest some time to estimate a GARCH(1,1) method, I know there is many statistical packages that will do this for me (Eviews, MATLAB, R), but I am trying to do this by hand, so ...
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In search of nice (approx) function forms of the volatility of cumulative simple returns

Let's consider a period $t\in[0,T]$, and let the simple return over year $t$ ($1\le t\le T$) be $r_t$. Assume $r_t$ are iid normal. The cumualative simple return over the whole period $[0,T]$ is $$R_T=...
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How rapidly should estimated volatility and volume change for estimating market impact in small markets?

The cost of market impact is usually modeled as: $$ \Delta{P} = \delta \sigma (\frac{Q}{V})^{1/2} $$ Where: $ \Delta{P} $ is the change in price of the asset caused by the transaction size $Q$ $\...
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Difference between volatility measures of a basket of assets

I am trying to understand intuitively the difference between two different measures of realized variance of a basket of assets. The first measure I am aware of is when you take the realized variance ...