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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108 views

Rebonatos's formula in C++

I'm trying to code in C++ Rebonato's formula for swaption volatilities $$ v_{\alpha,\beta}^2=\frac{1}{T_\alpha} \sum_{i,j=\alpha+1}^{\beta} \frac{w_i(0)w_j(0)F_i(0)F_j(0)}{S_{\alpha\beta}^2(0)}\rho_{i,...
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47 views

Is scaling the standard deviations in the VaR formula (parametric) equivalent to scaling the VaR figure at the end?

I have come across people calculating parametric VaR who scaled the standard deviations by say square root of 10 to scale up to a 10 day horizon. Elsewhere I have seen textbooks suggesting that it is ...
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116 views

How does trndbot generate buy/sell signals?

I was looking at trndbot and it's buy/sell signals are pretty good - what algorithm are they using to generate these signals? Although it maybe similar to bollinger bands, it algorithmically ...
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109 views

Is there a HAR that deals with the leverage effect?

The EGARCH is a special GARCH model that treats the leverage effect of the volatility. The HARV does not make a distinction between negative and positive returns. Is there a special HARV that deals ...
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1answer
110 views

Dupire (Local Vol with Imp Vol)

I am trying to implement a local volatility pricer using Monte Carlo and Dupire's equation in function of implied volatilities and I was told that first of all I have to check Dupire is well ...
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67 views

Forecasting returns and volatility using ARIMA-GARCH model in R

I am using rugarch package in R to forecast returns and volatility of a stock. I train an ARIMA (p ,d q) + GARCH(s, r) model on ...
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69 views

How to annualise hourly returns?

I have hourly open,high,low,close candles data for a particular asset. I wrote my own algo and some back testing code that replays the data from the past hourly candles to calculate the total return ...
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152 views

Stochastic Volatility vs Vanna-Volga

I'm working on the calibration of the Heston Stochastic Volatility Model for some FX option data for my bachelor thesis and I was asked "Why should people use Heston instead of other simple ...
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73 views

Short the difference between implied volatility and realized volatility of SPX

A professional trader said that the way is not to short VIX or other volatility products, but to short the difference between implied volatility and realized volatility of SPX This has to do with VRP ...
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63 views

Swaption extrapolation

I have some ATM swaption volatilities with the following characteristics: (-IBOR) payment frequency: 1M Underlying swap maturities (tail): 1Y, 2Y, 5Y, 10Y, 15Y and 20Y Swaption expiries: 1M, 3M, 6M, ...
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Estimation of time series using GARCH on Eviews

Firstly I should mention that I am new to both Eviews and GARCH models. Anyway, I am conducting some research into the effect that different macroeconomic factors have had on stock index volatility ...
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109 views

Options Weighted Vega Derivation

Does anyone have a good reference on how to derive time weighted vega for options? The only literature I found was in this presentation: http://www.topquants.nl/wordpress/wp-content/uploads/2015/01/...
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47 views

Quantlib error initializing CapFloor C++ Class

I'd like to use QuantLib as a C++ library to price interest rate derivatives, in particular Cap&Floors. To semplify things a little, let's say I have a vector of EURLibor1Y rates for different ...
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52 views

Volatility of basket with constituents priced in different currencies

I'm wondering how the volatility of basket of constituents priced in different currencies can be calculated (without upfront bringing constituent price to basket currency) form volatilities of ...
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84 views

Why are these two methods to calculate standard deviation gives very different answers? [closed]

Values=[100, 101, 102.01, 103.03] Method 1: Sum of the squared differences from the mean Mean = 101.51 std = sqrt(((100 - 101.51)^2 + (101 - 101.51)^2 + (102 - 101.51)^2 + (103 - 101.51)^2) / 4) = 1....
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46 views

What's a sensible way to measure correlation in the volatility surface?

Lets say I construct a parametrisation of the volatility surface that lets me infer dynamics i.e correlation between strike vol. Is computing the sample correlation (after controlling for spot-vol ...
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1answer
135 views

Clean noisy data from arbitrage

My problem is that I have a surface of implied black volatilites that is supposed to represent market data. However, the surface contains some slight arbitrage. More precisely, the graph contains ...
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332 views

What is IV really? Why does an option that is about to expire have such high IV for OTM options?

I was reading this definition: https://investorplace.com/2018/08/what-is-implied-volatility-concern-investors-invtlk/ If its IV stands at 20%, a movement of 20%, or $20 per share, over a 12-month ...
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113 views

Resources to learn the applications of SVD in quant finance?

I have been searching for quite a while on how singular value decomposition is used in analyzing stock price behavior. I know how to perform it on a matrix of stock prices, have the results in python ...
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47 views

Local volatility from Impled Volatilty by Dupire (interpolation)

Hellow, I'm doing my final project and now i have to implement Dupire's formula to get local volatilities from Implied volatilities. I have already got the implied volatilities by Newton so i have the ...
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13 views

Determining relative volatility without referring to an index or another security?

Say I am looking at the S&P 500, what is a quantitative way to determine whether the index is currently volatile or not? For example, if volatility > x, it is highly volatile. If volatility <...
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33 views

comparing volatilities of 2 different commodities when no delta is provided

If I wanted to compare the relative volatilities of options on 2 different commodities, but the deltas are not provided, is it sufficient to compare by the % each commodities strike is in or out of ...
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64 views

Spread and volatility

I look for any references where one consider how bid-ask spread depends on volatility (may be it is more correct to say 'volatility measure'). I would be grateful for any references.
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80 views

Portfolio Volatility Calculation

The question: you have a portfolio of risky assets that with a 90% probability (normal state of the world) has an expected annual return of 10% plus a random variable with a standard deviation of 15%. ...
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1answer
90 views

What is the difference between log volatility and simple volatility in a GBM? [closed]

What difference do they make? Why do many people seem to find more accurate simulations with log volatility? standard volatility in GBM is defined as $\sigma = \frac{1}{N}\sum_{i=1}^N(x_i-\mu)$ where $...
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52 views

First Principal Component Large Volatility

I am conducting PCA on several return series of funds and am finding that when I look at the first principal component the values are huge and this the volatility is also enormous relative to the ...
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145 views

How much does a rise in volatility in a short-term option affect a longer-term option

How would a rise in implied volatility on a short-term option affect the implied volatility of another short-term option with the same strike, but with slightly-longer expiry? Assuming that the short-...
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103 views

Comparison of results given by volatility estimators: Garman-Klass Vs Garch(1,1)

I am pretty new with volatility estimators and I am trying to see if Garman-Klass estimator and Garch(1,1)estimator are closed. So I implemented a python code for the two estimators (an also for the ...
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88 views

Implied volatility model-free

I know that $\operatorname{IV-model \space free}=2 \int_{0}^{+\infty}\frac{c_0(T,Ke^{r(T-t)})-c_0(t,Ke^{r(T-t)})}{K^2}\operatorname{d}K$ is calculated using an iterative procedure, i.e. setting a ...
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19 views

PRIIP Stressed Volca Calculation

Hello dear Finance mates, i have a question regarding the calculation of the stressed volatility for the stress scenario. I hope I actually typed the right formula for calculating the scenarios for ...
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1answer
52 views

Constructing Idiosyncratic Risk Factor

I am studying idiosyncratic volatility. After applying the Fama Frech 3 Factor model with its Marktet, SMB and HML factors I want to build a factor based on idiosyncratic volatility. Can I just build ...
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100 views

What is the market standard for measuring historical volatility?

Hope to get some help with the following questions: Can someone explain what is the industry standard to calculate stock options historical volatility? I am using this estimator https://portfolioslab....
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156 views

Relationship between time decay and gamma

In a paper titled Investing in Volatility published in 1998 by Emanuel Derman, Michael Kamal, Iraj Kani, John McClure, Cyrus Pirasteh, and Joseph Z. Zou, I found the following assertion (on page 9) ...
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154 views

Calculating Daily Realized Variance with Non-Constant Sampling

I was able to obtain some tick data on a particular asset and I wanted to calculate the daily realized variance of the asset. After browsing through a few threads here, it seems the formula to ...
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57 views

Do you need multi-period ahead covariance forecast, in order to construct portfolios with weekly/monthly rebalancing?

Suppose I want to rebalance my portfolio each week. Do I then need weekly covariance forecasts, from some multivariate volatility model to do this? Ie. Insert the weekly covariance forecast $\Sigma_{t+...
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140 views

Implied Gamma VS Implied Volatility

Reading this paper, I'm struggling to understand what the author is saying with paragraphs below (see pages 39-42): We define Implied Gamma ($\Gamma_{\operatorname{implied}}$) as the value of the ...
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81 views

10-day VaR for a portfolio

So, Bank ANZ owns a portfolio of options on the USD/GBP exchange rate. The delta equivalent position of the portfolio is GBP 56.00. The current exchange rate is 1.5, with a daily volatility of 0.7 ...
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87 views

Looking for a good introduction to modelling ARCH-type models

I am starting to think about my dissertation topic for my undergraduate degree. I am interested in comparing volatility of stock indices during COVID-19 to the years leading up to the pandemic. I have ...
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45 views

Squared Residuals equal Variance of Dependent Variable (ARMA-GARCH)

My understanding of ARMA-GARCH models for a variable $X$ is as follows: I estimate a conditional mean of a variable $X$ by use of the ARMA part of the model. I estimate the conditional variance of ...
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32 views

GARCH model with exogenous events

GARCH models capture positive serial correlation in volatility. Sometimes events occur "out of the blue", causing volatility that a GARCH model cannot be expected to predict. One example is ...
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35 views

EGARCH and GARCH effects with White Noise squared residuals

I'm asked to model a series which it's returns are white noise and after adjusting a regression like $r_t=c$ and looking it's squared residuals (white noise too) I'm asked to adjust a GARCH and EGARCH ...
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54 views

Volatility of a function of an asset

Suppose that $ G $ is a function of the underlying asset $ S $, which follows a geometric Brownian motion. Suppose that $ \sigma_{S} $ and $ \sigma_{G} $ are the volatilities of $ S $ and $ G $, ...
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21 views

Performance metric that integrates market volatility?

Is there a performance metric like Sharpe that takes into account the volatility of the current market instead of only the volatility of the fund? I believe investors may have different degrees of ...
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78 views

European call option on constant volatility or drawn from a volatility distribution

Which is more expensive: A European call option on constant volatility of 30% or or drawn from a random distribution of mean 30%? The answer in A Practical Guide To Quantitative Finance Interviews, ...
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68 views

The shape of the volatility smile for bimodal outcome

Let's say that we have a biotech company that awaits FDA approval. In the case of approval the company gets a cash injection and in the case of denial it is pretty much bankrupt. Clearly, this is a ...
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2answers
165 views

Jump diffusion simulation

I want to simulate a geometric Brownian motion and we assume that the volatility of the stock can take just two values $\sigma_1=0.2$ and $\sigma_2=0.8$. We also assume that the jumps up from lower ...
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115 views

Is there a Dupire's Formula for put options?

Generally, Dupire's formula is taking derivatives on the call option prices. Here it only uses information of the call options. If now we have the data including both call and put options, is there a ...
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100 views

Arbitrage Free Interpolation of Implied Volatility on Time Dimension

I’m working on a project to build a local volatility model out of implied volatility data and I’m currently testing the no-arbitrage version of SVI model as described in this paper Section 5.1 [...
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799 views

Bergomi: Skew arbitrage

In his paper "Smile Dynamics IV" (https://www.fields.utoronto.ca/programs/scientific/09-10/finance/derivatives/bergomi.pdf) as well as in his book "Stochastic Volatility Modeling" (...
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285 views

Question About SVI and SSVI Tradeoff between Fitness and No-Arbitrage

I’m currently working on a project to build a local volatility model out of implied volatility data and am struggling in the selection of an appropriate method to interpolate the volatility surface. I ...

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