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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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ATM-implied volatility

I am trying to understand the methodology that researchers used to compute ATM-implied volatility with real data. The problem is giving the discrete sets strike prices of one particular option with ...
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1answer
276 views

Why do regulators assume a risk-neutral world?

It is clear that when pricing derivatives we do this in the risk-neutral measure for known reasons. In the calculation of the VaR equivalent Volatility (VEV) in the KID-SRRI calculation (see page 9 ...
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582 views

Can a VaR equivalent Volatility (VEV) be negative?

As from title, can a VaR equivalent Volatility (VEV) as defined by KID/PRIIPS law be negative?
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2answers
183 views

How do I estimate the volatiliy of my portfolio with an estimator that requires High, Low, Open, etc

I have obtained the daily returns of my portfolio $R^{port}_t$ using a certain strategy. Now I want to estimate the realized volatility $\sigma^{port}_t$ using the past 60 days. An obvious way to do ...
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295 views

How can I use a more efficient volatility estimator to improve the co-variance matrix?

Using mean-variance, I need to estimate a co-variance matrix $\Sigma$ to obtain the best weights in my portfolio. However, there are other ways to compute the volatility $\sigma$ than historical ...
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347 views

How is VIX different from SPY/SPX IV?

Maybe I should have read the CBOE whitepaper but I never did... Now I cannot find it. I was looking at SPY/SPX just a moment ago and noticed that spot VIX doesn't match with SPY or SPX IV. Why not? ...
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187 views

Distribution of realized volatility for stock prices from a GBM

If you generate random stock price paths according to a GBM with daily increments, what will be the distribution of the realized volatility? Assume that the realized volatility is measured over daily ...
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507 views

Wrong pricing of Asian Option

Issue short: I have values for Asian Options which I'm trying to replicate using a self-build vba calculator. The values I have to hit is from FinCAD and I'm using a discrete arithmetic average rate ...
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85 views

Monte Carlo volatily

I was wondering if we could do a forecast on volatility using monte carlo on an underlying asset. For example EUR/USD : Simulating a lot of possible paths on 1 year then calculate the volatilty for ...
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461 views

Why is there greater demand for OTM and ITM options than for ATM options?

I´m currently writing a project on volatility trading and dynamics. The literature often states higher demand for OTM (out-of-the-money) and ITM (in-the-money) compared to ATM (at-the-money) options ...
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132 views

Black Variance Surface

I came across black variance surface in quantlib code. For options, usually volatility surface is used for pricing. When you will use variance surface for pricing or any advantages over volatility ...
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786 views

Is an autocorrelation of the abs returns just a consequence of the volatility burst?

In Pfaff's "Financial Risk Modelling and Portfolio Optimization with R" the following stylized facts are stated (among the others, p.26): The volatility of return processes is not constant with ...
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1answer
377 views

GARCH mean and volatility spillover R commands needed

I analyzed an MA(1)-GARCH(1,1) model in R, and now I want to test the conditional mean and volatility spillover effect between the two time series (exchange rates) (based on Hamao et al., 1990). ...
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95 views

Estimate Options Delta By Hand [duplicate]

Underlying = 100 K = 90 1 year Put at K is trading 5. What's the approximate delta of the put?
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1k views

Implied Volatility Surface - log forward moneyness

I'm reading this paper by Fengler (2005) and have came across the below snippet. context: Implied volatiltiy surface plot has 3 dimensions IV, Strike, Time to Maturity. Author replaced Strike with ...
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1answer
106 views

Detecting stochastic volatility

I have a time series extracted from a financial time series (so my series of prices is described by an arithmetic model $X(t)+Y(t)+Z(t)$, my series is $Z(t)$). I'm trying to model $Z(t)$ by a Levy ...
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84 views

What are the current gold standards for volatility prediction error?

I'm working on volatility forecasting models for equities and currencies. I am using daily data and am interested in producing forecasts for the next n days. To ...
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1answer
135 views

Implied volatility in parametric VaR

I'm calculating 1-day parametric VaR estimates for a stock index under the simple assumption that the returns are normally distributed. My question is, what is your opinion of using a volatility index ...
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1answer
358 views

1-year Var calculated from 1 year volatility

I need to calculate Var with 1 year horizon. I think the correct way to do it is to calculate standard deviation of daily log returns, then calculate daily Var and multiply it by sqrt(250). But in ...
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1answer
193 views

Gamma of a Lookback Option

From this book, http://docs.finance.free.fr/Options/Exotic_Options_Trading.pdf, it states that The gamma profile of a Max lookback option becomes intuitive when viewing it as a ladder option. ...
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184 views

Why is $dS/S$ an estimate of realized volatility?

For one period, $dS/S$ is an estimate of realized volatility, which we can annualize by dividing with $\sqrt{\Delta t}$. But.... why? How is $dS/S$ an estimate of volatility? Volatility is, to me, ...
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798 views

Continuous delta hedge formula

When we buy a call and continuously delta hedge using some implied volatility $\sigma_i$, what is the formula for our aggregate profit given that the actual realized volatility is $\sigma_r$? Say $...
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113 views

How would you arbitrage this?

Assume it to be true that $dS = S\mu dt + \sigma(t)S dW$ where $\sigma$(t) is known. Consider a call option with expiry $T$, currently $t = 0$. For all $t \in [0,T]$, $\sigma(t) < \sigma_{impv}$ ...
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Trading strategies for increased realized volatility

Suppose once every 2-3 weeks I have a way to select a few equities that are likely to exhibit higher realized volatility in the future month (relative to the past month). Historically, the average ...
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1answer
194 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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397 views

When is implied volatility greater than realized volatility?

Assume it to be known that the volatility of a stock at any point in time is $\sigma(t)$. My question is, if we have a number of options priced using some implied volatilities $\sigma_1, ..., \...
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1answer
114 views

Explanation of formula for implied volatility given $\sigma(t)$

If $dS = S\mu dt + S \sigma(t) dW$, then we know that the implied volatility is $\int_0^T \sigma^2(s)/T \ ds$. However, if $\sigma(t)$ is a piecewise constant function, i.e. constant between $T_1, ...
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Historic Volatility calculation does not fit to given figures

First, I have to say sorry - my question is very basic. I do not have a good understanding of math and statistics. I did a lot of research before posting here, but I could not come to a 100% ...
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62 views

Estimating volatility

Why is $$\frac{ \left(\frac{ \Delta S}{S}\right)^2} {dt}$$ an estimator of volatility squared (as claimed by my book)? As far as I understand it, we estimate volatitility squared as $$\frac{ Var( \...
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4k views

Why is realized volatility typically lower than implied volatility?

A number of quantitative finance textbooks mention something along the following lines, without further explanation: A typical feature of implied volatility from stock index options is that it is ...
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1answer
483 views

Correct procedure for modelling GARCH for forecasting volatility of stock Index returns

I will be using Eviews and am looking to forecast volatility of stock index returns using ARCH/GARCH models. I've generated the logarithmic returns and done the unit root tests. I then proceeded to ...
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1answer
163 views

When computing Garman-Klass volatility in R why does it leave out the ten first values?

I ran this code in R vGK <- volatility(ohlc, n = 10, calc="garman", N = 260, mean0 = FALSE) and the ten first values appeared like this: ...
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3answers
447 views

Volatility and Counterparty risk for FX Forward

How does the change in FX volatility affect the counterparty risk of an FX-forward? Should it not be riskless since the forward itself is "protecting" the exchange rate fluctuations?
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472 views

How variance dispersion trades become short volatility

From this document, http://quantlabs.net/academy/download/free_quant_instituitional_books_/[JP%20Morgan]%20Variance%20Swaps.pdf, on page 56, it states that Losses from short correlation through ...
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How do the units compare inside the (rate - 0.5*sigma-squared) correction?

Usually, I find the units of the mean and the standard deviation of a distribution to be (quite obviously) the same. Can anyone come up with a really simple explanation (for MBA students, some of ...
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191 views

Variance swap “fast” models

As far as I understand, Variance Swap (VS for short) function as follows : no payment when entering the contract at maturity the VS buyer pays a strike $K^2$ and is paid (by the VS seller) the ...
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1answer
249 views

Hedge variance swapping by vanilla option(constant vega portfolio against underlying asset)

One book said hedging variance swaps $$I= \sqrt{\dfrac{1}{t}\int^t_0\sigma^2(S,t)}d t$$ by vanilla option,say value $V(S,E;\...
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relationship between volatility and equity premium

I am working on the equity premium. Does anybody know one or two authors who address the relationship between volatility and equity premium? I.e. how does vola influence the equity premium? In ...
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1answer
155 views

Will volatility smoothing effects exist for returns driven by geometric brownian motion?

Say I randomly simulate a one-year pathway of 252 prices, where the underlying price model is driven by geometric brownian motion. where $t = (1 / 252)$, $mu = 5$% and annual $st.dev = 10%$%. My ...
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1answer
597 views

Spot and Vol Correlation in Idealised Regimes of the Volatility Surface

From http://www.globalvolatilitysummit.com/wp-content/uploads/2015/10/Santander-Volatility-Trading-Primer-Part-II.pdf it states that there are the four idealised regimes of volatility surface. 1) ...
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1answer
175 views

Modelling option price change in N days

I need to understand how will my option price change if the price of underlying asset changes by, for example, 15% in 30 days. I would like to use BS formula, but in this case I know all parameters ...
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1answer
2k views

Skew and shadow delta

The presence of skew causes a correlation between volatility and spot. This correlation produces a negative shadow delta for all forward starting products (forward starting options have a theoretical ...
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1answer
89 views

Hedging equities portfolios with vol products

Quote Hedging with variance is not comparable to puts Due to the lack of convexity of a variance swap hedge, we believe it is best to compare long variance hedges to hedging with futures ...
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1answer
111 views

Implied Volatility of a stock?

I know that implied volatility is the result of backing volatility out of any one of the many options pricing calculations. However, I've noticed that on ThinkorSwim and other platforms they also ...
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1answer
135 views

Monthly returns annualized vs annual returns [closed]

Lets say that I have a stock with annual returns, $a_i $ for year $i\in \left\{1,...n\right\}$ and monthly returns $m_{i,j}$ for month $j\in \left\{1,...12\right\}$. Lets define monthly returns to be ...
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131 views

Relative Value Trading of American Style Options on Futures, Calcuating hedging ratios?

I am interested in Relative Value Trading of American style options on futures and have not found a whole lot of literature on it. The best resource I have discovered so far is a few pages in Colin ...
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1answer
80 views

Unicredit February 2017: would I have Lost 50 Percent of my Money?

Some of the news regarding Unicredit indicate that the stock price was reduced by 50 percent from Friday (3 Feb 2017) to Monday (6 Feb 2017) (e.g.: ...
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1answer
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Why is the statement “the volatility of a $T - t$-month prepaid forward on asset X is $\sigma$” the same as “the volatility of asset X is $\sigma$”?

I'm self studying and I'm having trouble with understanding the equivalent formulations of the volatility $\sigma$ of an asset $X$, as in the below problem. In the below the problem (and the first ...
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56 views

Cox-Ross-Rubinstein - getting volatility

i have exam coming on financial engineering, and need help asap with this thing. Basically there's a European put option ex dividend. We know that the stock price is $S_t = 85$, the exercise price is $...
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Economic variables' influence on stock market volatility: cross section vs. time series

I want to test whether a number of economic variables such as stock market liquidity, earnings per share etc. influence the volatility of S&P500 returns. Should I use a time series regression to ...