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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Estimating Intraday Volatility with OHLC Data

I'm trying to estimate intraday volatility for some ETFs, but don't have the intraday data to actually calculate it. I do, however, have historical daily OHLC data for the ETFs. I thought I saw ...
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Fitting model between security price and intraday volatility

I'm trying to construct a model which shows how much the closing price of a security ($P_t$) differs from the VWAP of that security on that day ($VWAP_t$). I'm calling this measure the "VWAP ...
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mean return and volatility with transaction cost

What means that 5 bps per half-turn for transaction cost? How can I implement mean return and volatility with this transaction cost in formula or python code?
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Annualized rolling volatility? [closed]

I have 600 days of closing prices of a stock. I want to calculate the annualized volatility for 6 day window. How do i do that? If I calculate the std dev of the first 6 days, i get, say 1%. This is ...
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Computing the highest vol for worst-of basket

I would like to ask a very general question. I am not expecting a closed-form solution to this problem so, any, help, idea or suggestion will be welcome. Suppose that we have a bunch of X stocks (10 ...
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What is the consensus interpretation of index future dealer gamma?

I'm trying to confirm that I'm understanding this concept correctly: dealer gamma exposure. I can make sense of dealers / gamma in isolation: Dealers: make markets for certain securities, notching ...
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Estimating historical volatility from inconsistent time intervals

Given historical asset prices at consistent time intervals, one can estimate annual volatility as: SampleStDev(log(Si/Si-1)) / sqrt(interval) What's the correct way to do this when the time intervals ...
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How to optimize two highly correlated risky assets?

Suppose you have two highly correlated risky assets. Correlation coefficient: 0.9 Volatility: Asset 1 price varies 2.5% /day Asset 2 price varies 5% / day What can be done to do reduce the risk and ...
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Which is more valuable: a basket of optimal stopping problems or an optimal stopping problem on a basket?

Fidelity now offers direct indexing for individuals for 40 bps per year, as well as zero-fee total market index funds. Which one should I dollar cost average (I.e., invest $x every n-th month) in? ...
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Deriving strike from Delta

According to the following thread: How can I calculate the strike price or implied volatility from a given delta? To back out some strike given some Delta, you simply use realized vol (plus a few ...
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Deriving vol of vol from volatility futures price

From Colin Bennet's trading volatility (pg 117), he says: "A forward on a volatility future is short vol of vol. This means it is possible to back out the implied vol of vol from the price of ...
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Local volatility model for autocallable pricing

I am working on a pricer for an Autocallable product in Python. Coupons are accumulated at each observation and paid once the AC barrier is reached. At maturity, short down-and-in put. I am trying to ...
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Best Way To Compute the Volatility Risk Premium

I'm trying to come up with a measure for the volatility risk premium (VRP) for a strategy I want to implement, but I'm not entirely sure how to proceed. My situation is as follows. The underlying is ...
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Approximating SPX index skew using PutDex & CallDex

I hope someone can help me with this. As I don’t have access to historical options data I am wondering if it is possible to deduce SPX options skew from various volatility indices - in particular ...
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When does the underlying become the derivative?

Since options contracts are created by open interest in the contract, it is conceivable that the notional of the total options contracts can exceed the value of the underlying. If that happens, does ...
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Volatility Options

I'm working on a scenario needs to price an option on volatility. After googling, there is no clear relevants in this field. VIX options pricing is one way, while seems it takes the VIX (a volatility) ...
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How would one construct a volatility surface given only the spot price?

The traditional way to build a volatility surface is to pull options data and then do some form of interpolation. What happens if there is no existing options market and only a spot market for asset X?...
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Why do VIX spot and futures converge if there is no cash and carry arbitrage?

Since VIX spot is not tradable, why do the futures and spot converge @ expiration? By what mechanism does this occur if arbitrage is not one of them?
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Relation between historical volatility and ATR?

https://help.tc2000.com/m/69445/l/754439-historical-volatility-ratio "Historical volatility is calculated by taking the standard deviation of the natural log of the ratio of consecutive closing ...
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Transformation of local volatility model

Assume we have an SDE $$dX_t=\mu(X_t)dt + \sigma(X_t)dW_t$$ where $\sigma>0$ and $W_t$ is a Wiener process. Is there a transformation $y(X_t)$ that will make the dynamics of the transformed process ...
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How to calculate volatility with and without mean reversion?

How to model mean reversion in a stationary time series variable, Yt, using the following first-order autoregressive model: If the one-period conditional volatility of the change in Yt is denoted by ...
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How to determine which realized volatility estimator should be used?

There are so many realized measure have been invented in the past years like TSRV, MSRV, KRVTH, KRVC... But how to choose them in practice? I know we cannot find the "estimation error" of ...
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Implied vs historical volatility in option pricing

I discussed recently with a trader who told me that put options are priced using historical vol, and call are priced using the implied one. My guess would be that as the put option market is much more ...
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Lower volatility corresponds to higher market efficiency?

What are the general ideas about volatility? It is generally said that volatility signifies risk, which reduces liquidity and thus efficiency. Is it actually so? Can't volatility be associated also to ...
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realized volatility calculation in python

I am trying to do a standard realized volatility calculation in python using daily log returns, like so: ...
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Market Impact Estimation: Choice of Parameters and Scaling of Inputs

The standard market-impact model used is the square-root (or more generally speaking, power law) model that states that the temporary impact of a trade is given by: $$ I(V) = \sigma\cdot\alpha \left(\...
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Relation between SABR parameters and Taylor expansion parameters

Suppose a SABR model framework (with $\beta=1$) $$dF_t=\sigma_t S_t dW^{S}_{t}$$ $$d\sigma_t=\alpha \sigma_t dW^{\sigma}_{t}$$ $$dW^{S}_{t}dW^{\sigma}_{t}=\rho dt$$ I know that the Implied Volatility ...
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Closed formula for computing Implied Volatility from Local Volatility function

The main result of this paper (Asymptotics and Calibration in Local Volatility Models, Berestycki, Busca, and Florent. Quantitative Finance, 2002) is equation (16) on page 63, that states that: In the ...
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The relationship btwn RV-IV and realized skew

In studying skew I've been advised to focus on understanding on components that affect it. One such component that's been recommended to me is the relationship btwn RV-IV and realized skew. ...
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Calculating Expectation of Stochastic Volatility

I have a question while reading THE NELSON–SIEGEL MODEL OF THE TERM STRUCTURE OF OPTION IMPLIED VOLATILITY AND VOLATILITY COMPONENTS by Guo, Han, and Zhao. I don't understand why the above equations ...
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Hedging rates exposure in an FX options book

Fx options have exposure to the interest rates in the domestic and foreign currency. This risk can be hedged using currency forwards. In an ideal world, I suppose the best way would be to hold ...
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What are the volatility Indices for different asset classes? Particularly fixed income & RE? [duplicate]

As a part of my self learning process, I'm trying to gather the list of volatility indices for all major asset classes. Equity: CBOE VIX (US), VSTOXX (EU), ?? (UK), ?? (JPY) Commodities: ?? Interest ...
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Pricing binary options under volatility smile

I was asked to show that the price of a digital/binary option $D$ while a volatility smile $\sigma(K)$ is present is given by $$D= \exp(-rT)( \Phi(d_2) - K \sqrt{T} \phi(d_2) \sigma ' (K))$$ Where $\...
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Implied volatility plotted against the strike price in Heston model

How can I reproduce the implied volatility curve (plotted against the strike price) in the Heston model (i.e. the blue line in the graph below)? What's the equation that I have to set up and solve? ...
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Should future price scenarios be symmetric around the current market price?

Assume a financial instrument which has a (roughly) log-normal price distribution and behaves like a random walk. I would like to generate some possible scenarios for where the price might be tomorrow....
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Should daily log returns be "adjusted" by using the exponent?

For estimating the daily historical/statistical volatility of a financial instrument one can use the following procedure (which makes some assumptions, i.e. log-normal distribution of prices): ...
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You are long a hedged ATM SPX Call and the market moves down. Do you gain or lose in volatility terms?

The shape of the volatility curve in index options trading typically shows that the 'just' OTM Calls (ITM Puts) options have the lowest implied volatility. If you are long an ATM Call and the market ...
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Volatility-adjusted carry for FX Forwards

Has anyone ever heard of a volatility-adjusted carry for FX Forwards? What does it mean? I'm familiar with the concept of carry in this context, but why would it make sense to make any adjustments to ...
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Why is the price of an ATM straddle not the same as the "dollar move" from implied volatility?

Knowing that implied volatility represents an annualized +/-1 Standard Deviation range of the stock price, why does the price of an ATM straddle differ from this? Also for simplicity, no rates, no ...
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Gamma, Theta, Vega, Vanna and Volga PnL under Bachelier

Is there a PDE that decomposes the daily PnL as delta, gamma, vega vanna and volga but under Bachelier model (assuming normal vol) ?
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Conditional Value at Risk using GARCH models

In this paper: https://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=&ved=2ahUKEwjSlIHYnMj1AhWqNOwKHZfHDhkQFnoECAkQAQ&url=https%3A%2F%2Fwww.mdpi.com%2F2076-3387%2F9%...
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How do you hedge volatility risk?

Suppose I model an asset $S_1(t)$ under a stochastic volatility model. To price an option on $S_1$, I must assume the existence of an asset $S_2$ that is used to hedge against changes in the ...
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How To Construct A Volatility Spread Position?

Is there a simple way to spread the volatility of one product against another? By simple I mean one trade executed on each leg rather than constant delta hedging. I can see a lot of opportunity for ...
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Use Half-Normal to estimate Expected Loss

Say a stock return follows a normal distribution with 0% mean and 50% volatility. If I want to calculate the Expected Loss (ie. only the expected value of the negative returns), does it make sense to ...
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SPY-VXX relationship

As many will know, the VXX ETN tracks a 30-day weighted maturity of the front two months' VIX futures and SPY tracks the returns of the S&P 500. Typically, SPY gains coincide with decreases in ...
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Estimating volatility of a geometric Brownian motion at different sample rates

I have troubles estimating volatility (= standard deviation of log returns) when the data is re-sampled at different sample frequencies. Problem I have generated a time series data using a geometric ...
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Price stress testing

Good day everyone! I am looking to stress a Future curve of Power Prices to assess the possible future impact on Spot prices. My assumption is that Future prices are suitable to predict Spot prices. I ...
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Stocks' returns distribution

I understand that stocks' returns are not normally distributed. However, is there any method that we can rescale the stocks' returns so they look more like normal distributions? I managed to find a ...
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hedge with implied volatility, PnL formula

Notations are consistent with this answer. Selling and delta hedging the option $V^i$ using the implied volatility $\sigma_i$ while the actual volatility of the underlying asset is $\sigma_r$. Then ...
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Vocabulary: "Well Bid" and "Fading" Meaning?

I think it is important quants understand what traders are talking about. With that, what does it mean: "vol is well bid" "fade the trade" ?
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