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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279 views

Why is Bachelier implied volatility more skewed than the Black-Scholes implied volatility?

I found the following explanation in a paper by Grunspan (see attached paper page 6) but have trouble understanding it: By differentiating Formula (3) with respect to m, it turns out that the ...
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215 views

Frequency Arbitrage

We know that the volatility is lower when the sampling period is longer, for example $\sigma_{7days} < \sigma_{1day}$, Then I came across this strategy that I cannot quite understand how to exploit ...
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44 views

Looking for material on volatility forecasting with a focus on market/news events

I'm hoping someone can direct me towards any books/papers that approach volatility forecasting from the perspective of market specific events (fed meetings, USDA reports, OPEC announcements etc). From ...
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164 views

Unconditional variance of an E-GARCH model

I am attempting to calculate the unconditional variance of an E-GARCH model: $$\log(h_{t+1}) = \beta_{0} + \beta_{1}\log(h_{t}) + \beta_{2}\left[|\varepsilon_{t} - \lambda| + \gamma(\varepsilon_{t} - \...
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404 views

GARCH Option Pricing Model (Duan 1995)

I am trying to replicate Duan's results from his 1995 Paper, "The GARCH Option Pricing Model". I have written this code in Python myself, and using his parameters I consistently seem to obtain results ...
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330 views

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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455 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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159 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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169 views

OHLC Covarianc Estimation

Is there an R package which can estimate a covariance matrix using OHLC (Open/High/Low/Close) share prices for upwards of 40 shares using the Yang & Zhang method using daily data? I google ...
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384 views

How to calibrate volatility surface for Interest Rate Cap&Floor pricing

I'm using Black model to do interest rate Cap & Floor pricing. The volatility is determined by using the bootstrapping methodology. However, afterwards, how should I do the calibration, or ...
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99 views

Testing for the presence of a positive or negative gamma effect

I am currently analyzing a statistic that I believe will have the effect of hedgers having a positive or negative gamma position in certain stocks. In the case where I believe hedgers have positive ...
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74 views

robust regions in grid search

I have a strategy f that takes parameters x,y (for x,y taking values in integer ranges). I get two grids (of returns and volatility values) from computing f(xi,yi) for integer ranges x1 <= xi <= ...
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99 views

How to measure if variance is greater at a certain time of day?

I'm not very fluent in the quant vernacular, so perhaps the nature of my question will be better illustrated as a hypothesis. One market has closed and another market elsewhere on Spaceship Earth is ...
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1answer
483 views

Instantaneous Volatility Estimator

Suppose a Stock follows an Itô process with instantaneous volatility $\sigma(S(t),t)$. Precisely $$dS(t)=\mu S(t)dt+\sigma(S(t),t)S(t)dW(t)$$ I have a historical data for the values of $S(t)$.How ...
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24 views

Swaption pricing and strategies

I am looking for resources (books, papers, websites, etc.) that deal with Vanilla and Exotic swaptions from a more advanced and quantitative perspective. I am interested in both the pricing side (e.g. ...
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41 views

Dorfleitner's Standard Deviation

Can someone please advise how to compute the following (as my results go into thousands): E.g. I have used and the result (for T=12) = 580103.7261 Thanks
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59 views

What is the cause of a “broken” volatility surface?

I am currently working on a project for which I need the implied volatility surfaces, to estimate the value of plain-vanilla European options with different strikes (cannot be observed directly in the ...
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49 views

How to properly hedge a short vol taking into account hedge stop loss?

Suppose a short straddle. In practice, hedging with long/short futures exposes to the risk of hitting a stop loss when market movements are wide. Eventually, it may very well happen that the hedge ...
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1answer
143 views

Understanding the ZABR model (an extension of SABR)

http://janroman.dhis.org/finance/SABR/ZABR%20Andreasen.pdf In this acticle the SABR model is first presented in another form ( see equation 7 in the article ) and then extended to the so called ZABR ...
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1answer
106 views

In-sample volatility measurement

I would like to know what is the most reasonable way to measure volatility in a sample of past observations. Aside from standard deviation, are more complex models like GARCH used for (historical) ...
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36 views

Log Contract payoff function

I can’t get where Dr. Rouah gets payoff function of log contract. Could you please take a look at that? https://frouah.com/finance%20notes/Variance%20Swap.pdf It’s on page 2, section 3. I couldn’t ...
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56 views

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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35 views

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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95 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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1answer
218 views

Volatility surface for Swaptions

I understand the volatility surface for swaption is built using implied vols of ATM swaptions. I had a question on the instruments that are used. Should the instruments used change depending on the ...
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113 views

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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63 views

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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37 views

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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151 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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37 views

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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58 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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134 views

Poor results forecasting stock price volatility using Python's GARCH model

As far as I understand, forecasting stock price volatility should be more achievable than forecasting absolute prices or returns. It seems as though GARCH models are the traditional and most widely ...
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46 views

How to reasonably aggregate returns across both different assets and different time-horizons?

This might be a somewhat open question, so any suggestion of improvement is welcome. Suppose at time $t=0$, we have $N$ different assets whose weights are $w_1,\cdots,w_n$ ($\sum w_i = 1$), and they ...
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1answer
132 views

Relationship between asset volatility and debt and equity value

So how I understand it, higher asset volatility implies a higher call option price. The Merton Model holds that the value of equity is a call option. This therefore implies that the equity value must ...
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162 views

How accurate are Black-Scholes estimates of Vega, Volga, Vanna

Wikipedia provides analytical formulas for calculating Greeks. I can get Delta, Gamma, Theta all from Bloomberg. I need Vega, Volga, Vanna for my research. Should I use these analytical formulas for ...
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102 views

Can prediction of realized volatility for next day improve delta hedging (gamma scalping)?

Im quite confused. As I understand from standard delta PNL of option + underlying position, pnl is equals to difference between realized and implied vol weighted by gamma. However, as I understood, ...
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163 views

Forward implied vol vs Instantaneous vol

In the Discrete Stochastic Implied Volatility Model which is from the standard Heston Model, the model shows the evolution of forward implied volatilities with time. I thought forward implied ...
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89 views

Rough Volatility Prediction - Gatheral, Jaisson, Rosenbaum Paper

I just read through the paper "Volatility Is Rough" by Gatheral, Jaisson and Rosenbaum. There is a website (link: http://tpq.io/p/rough_volatility_with_python.html) that details the simulations they ...
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42 views

Does it make sense to calculate an option price in future (at t+1)?

Often I ask myself whether it makes sense to calculate the price of a Call at t+1 supposing for example that underlying asset does no move i.e. $S_{t+1} = S_{t}$ ...
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Identifying primary share class of U.S. firms and deleting excess observations

I have a fairly large dataset of CRSP firms with their daily closing prices from 2006 till 2017. I need to filter the data so that I have one daily observation per unique firm. I've identified the ...
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108 views

Modelling VIX futures backwardation

I have VIX futures trading algorithm and would like to perform Monte-Carlo simulation of VIX and understand how my algorithm performs on each simulation. In this case, not only VIX should be modeled, ...
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83 views

Autocall Calibration

I'm trying to price autocalls. In theory my pricing method is ok (I followed Bouzoubaa's book procedure) but I'm not sure I read anything on calibration of autocalls. Basically my question is what ...
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91 views

Dynamically adjusting the size of a Constant Range Bar (on an intraday fx chart)

Constant Range Bars (CRB) is a type of candlestick charting method that does not draw a new candle every unit of time (like every 1/5/15/30 minutes), but every time the range (high-low) of the ...
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DCCfit speed up formula

I am estimating the covariance matrix by using GARCH DCC model with function dccfit from package rmgarch. My code is something like: library(rugarch) library(rmgarch) ...
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71 views

Mix a Forward Delta Premium Adjusted and a Forward Delta to construct the volatility surface

I have two brokers who give me delta strategies for USD-COP, but one of them gives me the issue with forward delta, the another one is premium adjusted. Besides, how can I mix them for construct a ...
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125 views

Vega with SVI Gatheral bumps

How would one go about computing a vega profile of an exotic derivative where the volatility surface is modeled using Gatheral's SVI parameterization? In particular, I am thinking about bumping each ...
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82 views

Pricing and hedging OTC vanilla options

Most OTC option textbooks are about exotic options. I'm curious how sell-side price and hedge OTC vanilla options e.g. European option. What models do they use? How to forecast volatility (using GARCH?...
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82 views

Calibrating Heston paremeters based on market data for Implied Vol for Call options

Several questions have been asked in here regarding calibration in Heston yet I have not found what I have been looking for, so I will ask: I am looking at a Heston model: $$dS_t=\lambda \sqrt{v_t}...
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36 views

Volswap: fair strike and number of fixings

Let’s assume 1y vol is at 10.0% and there is no skew and the term structure is flat. Let’s assume there are 252 fixings and the annualisation factor is 252. 1) In a BS world, is it correct to say ...
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280 views

Calculating realized volatility of high-frequency data

I am wondering how to calculate the realized volatility. Sources such as say that the realized volatility is the sum of squared log returns sampled at a given frequency. So using 30 minute frequency ...