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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46 views

Question on Realized Vol vs Implied Vol

I have heard the following argument- barring transaction fees, if my estimation of future realized vol is 30% and 1-month ATM implied vol is 20%, then I could potentially buy a 1-month ATM call/put ...
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1answer
36 views

Why are some currency pairs more volatile than others?

Why for example GBP/JPY is twice volatile as USD/JPY ? ... and many more cases involving other major forex pairs here: full list. thanks in advance!
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To use daily volatility or annual volatility

From Joshi's Quant Interviews books: The statistics department from our tell you that the stock price has followed a mean reversion process for the last 10 years, with annual volatility 10% and ...
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2answers
669 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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33 views

Robust Sharpe ratio

The denominator of the Sharpe ratio is sample portfolio volatility, $\sigma_p$, which is the square root of portfolio variance based on the quadratic squared loss, L2. Alternatives for the denominator ...
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1answer
64 views

Confidence Intervals for ARMA+GARCH forecasts

I have fitted an ARMA(1,1)+GARCH(1,1) model to my logreturns series. When it comes to my standarized error's distribution however, I have opted for a Skewed Generalized Error Distribution, because of ...
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121 views

Uncovering patterns in price timeseries using linear regression

I have some minute-bar data which my professor suggested I resample to 5 minute bars and then separate it into timeseries per bar period. For example, I get one time series for 12:00, another one for ...
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1answer
213 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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1answer
215 views

target market correlation for long / short equity portfolio

Given a long / short equity portfolio, I want to have some net long market exposure. My portfolio volatility is fixed to a target, so I don't think it makes sense to target market beta. I think I ...
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2answers
2k views

How to interpret Realized Volatility and TSRV using R

I am looking at some high frequency data and I would like to know how to interpret and compare Realized volatility (RV) and Two Scale Realized Volatility (TSRV). References below. Given X is the log ...
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1answer
166 views

VXX Put pricing

Last week at Friday's close, the Dec 14 37.5 Put options were selling for \$.68 with VXX at \$40.29. This week at Friday's close, the Dec 21 37.5 Put options were selling for \$.38 with VXX at \$40.50....
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38 views

Historical volatility calculation to price options with the Black-Scholes formula

I'm looking for a reference algorithm for calculating historical volatility to price options. I know there are several volatility calculation models that use the time series of the underlying's ...
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2answers
67 views

Are there volatility models dependent on returns?

When I look at the relationship between volatility and price, I see a clear negative correlation as shown in this figure (SPY and VIX prices today looking back 1 year). The common volatility models (...
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2answers
578 views

Measuring unbiased estimator for variance with RMSE?

The root mean squared error (RMSE) is considered by some to be the best measure of how good a variance estimate is. You often see it quoted as: $RMSE=\sqrt{\frac{1}{n}\sum_{i=1}^n(\hat{\sigma_i} - \...
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29 views

How to mathematically calculate the probability of GBM generating difference of less than some value

I have a custom index that follows Geometric Brownian Motion (GBM) with volatility v. I started this index at 10k with 4 decimal places i.e the starting price of ...
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1answer
165 views

Are “stylized facts” based on reliable evidence?

A highly cited article "Empirical properties of asset returns: stylized facts and statistical issues" by R. Cont use the Figure 8. below to illustrate the well-known phenomenon of volatility ...
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9answers
52k views

What is the difference between volatility and variance?

How do volatility and variance differ in finance and what do both imply about the movement of an underlying?
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58 views

GARCH Model Estimation with Standard Deviation

I want to examine exchange rate volatility on Stock Returns. Please, if I Generate Exchange rate volatility (ER_vol)using standard deviations approach, can I include the (ER_vol) as a regressor in the ...
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1answer
63 views

Greeks, European puts

I'm trying to solve this question but i have a lot of problems with it. European puts with maturity 6 months are written on an asset with current price $S_0=150.$ The annual interest rate is $r=16\%$ ...
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1answer
74 views

how does stochastic volatility models generate smiles?

When calibrating call price with the BS-model, we achieve some parameters and especielly we achieve $\sigma^*$. Now, lets say I will price call options using these parameters. Then we achieve, lets ...
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1answer
68 views

Estimation of volatility into Black-76 formula

I am trying to estimate the (annualized) volatility that should go into an European Swaption (such as 2y5y). Given we take the black76-formula, where the discounting is the term outside the ...
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51 views

Calibrating Heston model parameters using the Active-set method and Levenberg–Marquardt

Background: We're estimating the parameters of the Heston model from current market data of options. This is to be implemented using the active-set method (see section 16.5 here) and the Levenberg-...
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16 views

Portfolio construction with volume based bars

In the book Efficiently Inefficient, Lasse Pedersen interviews Myron Scholes: LHP: Why do spreads tend to widen during some periods of stress? MS: Well, capital becomes more scarce, both physical ...
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104 views

SABR Calibration

I need to generate the Volatility Surface of call options on S&P500 index, my dataset contains implied volatilities regarding various expiration dates for various strike prices. My doubt is, ...
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1answer
121 views

Measuring implied volatility

I'm a new in financial engeneering and trying to understand basic principles of volatility modelling. I wrote many papers and articles about different models (garch, local vol, stoch vol and ect.) and ...
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1answer
97 views

Portfolio Systematic Risk, Breaking it down into factor % contributions

I have a portfolio (p) of N equities, with let's say weights vector (m) at the start of the calculation period. Each equity has its own set of factors (like corresponding country, industry index, etc.)...
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68 views

Calculating Implied ATM Volatility with Vega

Can we calculate Implied ATM volatility with Vega? Normally, Vega is derived from Volatility, but I wonder the availability of the opposite way.
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784 views

Variance swap volatility - ATMF vol, Skew and Curvature

In a pure diffusion setting, it is a well known result that the volatility $\sigma_T$ of a fresh-start variance swap of maturity $T$ as seen of $t=0$ verifies \begin{align} \sigma_T^2 &= \Bbb{E}_0^...
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58 views

Anyone working on rough volatility modelling? Need relevant books to read

Just wondering if there is anyone working in the field of rough volatility? I know the rough volatility modelling is quite new in the field. Can I get some books recommendation to go through?
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2answers
64 views

calibration - negative call price [closed]

Im trying to calibrate a stochastic volatility model to market. I end with an MSE of 2-3 with approximately 500 quotes. Some out of the money options with call-price under 1 dollar ends up being ...
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42 views

Extreme AUDJPY FX vols

I'm seeing levels of -12% of market strangle vol at 25 delta for AUDJPY at 20Y onward that is causing havoc with my pricing routines, the 10 delta market strangle is trading around -6% which is again ...
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1answer
219 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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1answer
287 views

Multivariate Markov Regime switching GARCH

I have a regression with 4 independent variables and a dependent variable. I want to implement a Regime switching GARCH model but have been unable to find a package in R,Python or Matlab. MSGARCH ...
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2answers
1k views

Value of Call Option as Volatility goes to Infinity

Why would the value of a call option go infinity as volatility goes to infinity? I understand how you could solve this question by taking $\sigma \rightarrow \infty$ in the solution to the black ...
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0answers
53 views

Ultra high frequency TSRV

I'd like to verify my approach to calculate high-frequency RV estimator, as introduced in Ait-Sahalia, Myklad, Zhang 2011. After reading the paper a couple of times, it seems to me, that the only ...
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3answers
270 views

Intuitive explanation for the smile in FX

What is the intuitive reason for the smile in FX? For equities this usually down to crash risk.
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539 views

what's the relationship between forecasted stock volatility and implied volatility?(option)

what's the relationship between forecasted stock volatility and implied volatility? I know that implied volatility is the volatility calculated by BS formula, is there any relationship between implied ...
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2answers
110 views

What are popular metrics for Option Skew?

What are popular metrics to track skew? Would it be the difference between OTM option and ATM option IV? Would it be a percentage difference in IV? Also, if both are valid, would a % change be ...
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2answers
74 views

Future Volatility Trading

I want to find a way to long volatility of a future time period such as longing (march,april) vol from today. My idea is to short a straddle for march and long one for April for example. Will that ...
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2answers
7k views

What is the difference between conditional volatility and realized volatility?

I am working on conditional volatility and realized volatility but the difference between these two measures is not clear to me. Can anybody explain how these two volatilities are related? Does the ...
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1answer
83 views

Adjusting volatility while constructing portfolio

I am trying to construct a portfolio based on a macro momentum strategy for backtesting purposes as outlined in https://www.aqr.com/-/media/AQR/Documents/Insights/White-Papers/A-Half-Century-of-Macro-...
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Measure how different forecasted volatility is from realized volatility

Hi Quantitative Finance Stack Exchange, I'm looking for an opinion on a simple question. Suppose I use a Garch(1,1) model to make a volatility forecast. At time $t$, I have realized volatility $\...
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1answer
99 views

How many options would be required to dynamically replicate the VIX nowadays?

The VIX is a portfolio of OTM options on the SPX with non-zero quotes. From CBOE white-paper: Only SPX options quoted with non-zero bid prices are used in the VIX Index calculation. [...] As ...
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Option Selection (rollover rules) in calculating intraday CBOE VIX (post 2014)

In calculating the CBOE VIX (post 2014) one has to select near- and next-term options, which are defined as options with >23 days and <37 days to maturity. As time moves on, a currently selected ...
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1answer
903 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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How to price a volatility-index option?

There exist several volatility indices, such as the CBOE Volatility Index (VIX). There are also options on such indicies. What is the best way to price a volatility-index option? Is there a simple ...
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1answer
49 views

Heston model with jumps in both variance and underlying dynamic

How can I build on Matlab a Heston model using characteristic function adding jumps in both variance and underlying dynamic ? Suppose that the number of jumps is Poisson-distributed but the jump size ...
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1answer
314 views

Mixing Black Scholes with SABR

I am new to the whole concept of stochastic volatility so I am experimenting with option pricing. I think the concept is really difficult to understand / grasp. I was wondering if the following ...
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60 views

Variance of a spread for options on spreads

I was reading the paper: https://people.umass.edu/nkapadia/docs/Negative_Vega.pdf In the equation $(5)$, he is defining the variance of the spread as: $$\sigma_1^2S_1^2 + \sigma_2^2S_2^2 - 2\...
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Interpretation conditional volatility plot

I have plotten the log differences of exchange rates and in the same plot, I show the conditional volatility $\sigma_t^2$. The conditional volatility follows approximately the same path, but is much ...