A measure of the variation in price over time. Also a measure of the risk of a financial instrument.

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9
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137 views

Estimate Beta of CAPM from Implied Volatility?

In the CAPM theory Beta of asset $i$ are estimated in this way: $ \beta_i = \frac{\sigma_{im}}{\sigma^2_m} $ where $\sigma_{im} = \rho_{im} \sigma_i \sigma_m$ But all these data are historical data. ...
0
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0answers
49 views

Impulse response function interpretation

I would need a quick help with Impulse response function interpretation which I have done after Vector autoregression model in stata. I need to understand how to interpret IRF graph or table values ...
6
votes
1answer
237 views

Density forecast of a GARCH model

I am currently working on developing a series of density forecasts and I am encountering some problems. I am working on weekly S&P 500 returns and the returns process is described as $r_{t} = \...
0
votes
1answer
97 views

How do I track implied volatility of specific delta?

I'm a newbie with respects to volatility trading and options. I recently purchased a book on the topic called "Trading Implied Volatility -An introduction" by Simon Gleadall. It's been one of the most ...
2
votes
1answer
145 views

Volatility Surface Constituents, do's and dont's

Recently I have been working a lot with implied volatility and volatility surfaces. The basic idea is easy to follow: 1) Gather market prices of options at different (Strike,Expiry) 2) Calculate ...
0
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1answer
73 views

pricing with implied volatility surface

I am a newbee in Quantive finance. supposing I calibrate a smoothing implied volatility surface with cubic spline now. A minute later I want to price K=100,t=1 option, can I just find the point on ...
0
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1answer
47 views

volatility skew for lognormal model is flat?

Does anyone know why the volatility skew for lognormal model, such as BK, should be a flat line, meaning that implied black volatility for options will be same for those with different strike prices? ...
1
vote
1answer
72 views

MSRV estimation in R

What are the R packages that let you estimate Multi Scale Realized Volatility (MSRV)? So far I've only found highfrequency (which comes with Realized Kernel as well), but from what I understand it ...
2
votes
1answer
250 views

High frequency price forecast model ARMA GARCH or another?

Can you reccomend model for high frequency data (1 second and less) (returns and volatility forecasting)? Most papers use ARMA, GARCH etc in 1 minute and lower time frame. PROBLEM ARMA does not know ...
2
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2answers
131 views

Calibrating stochastic volatility model from price history (not option prices)

For stochastic volatility models like Heston, it seems like the standard approach is to calibrate the models from option prices. This seems a bit like a chicken and an egg problem -- wouldn't we ...
2
votes
1answer
410 views

Value at Risk from Delta of a single asset portfolio

I am trying to figure out the following, for me unfamiliar type of question: Given is a single asset portfolio: the Delta of the portfolio is 15, the value of the asset is 10 and the daily volatility ...
1
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0answers
85 views

Comparing Implied Vol. to Historical Vol. using intraday data

I'm interested in estimating what my profit/loss would be for continuously gamma scalping a delta hedged option over the course of one day, using historical intra-day price data. I found an equation ...
1
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0answers
44 views

Motivation for hedging volatility using VIX ETNs

i wondered what the motivation for professional investors could be to engage in VIX ETNs. Would they even think about trading this kind of product? (they normally should have access to VIX options, ...
0
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0answers
36 views

Lambda in RiskMetrics for fixed income

What is the default lambda proposed in RiskMetrics for fixed income?
1
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2answers
106 views

Smoothing factor of Exponential Moving Average

I'm trying to implement an Exponential Moving Average indicator, but I'm sort of stuck on the smoothing factor. What I've come up with: $$\frac{1}{N}\sum\limits_{k=0}^N \alpha^{k} P_k$$ Where N is ...
2
votes
1answer
337 views

2-step estimation of DCC GARCH model in Python

Embedded in this thread are multiple questions. I'm currently im the process of implementing a DCC GARCH forecast model on quantopian (a python-powered trading platform). The two step consists of ...
0
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0answers
35 views

Integrated Volatility in Diffusion Processes vs Volatility of Discrete Processes

In a Diffusion Process of the form $$dX_t = \mu(X_t)dt + \sigma(X_t)dW_t $$ the Integrated Volatility is defined as $$IV_t = \int_t^{t+1} \sigma^2(X_s)ds.$$ In this case, the Integrated Volatilty ...
9
votes
3answers
638 views

Is the price of European put option monotone in volatility if we replace BM in Black-Scholes with a general Levy process?

Under the Black-Scholes model, we have the European put option is $\mathbb{E} [e^{-rt}(K-S_t)]$, where we take $\log(S_t)=X_t$ and $dX_t= \sigma dW_t - \dfrac{1}{2}\sigma^2 dt + rdt$. Here the option ...
2
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0answers
48 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 ...
3
votes
2answers
879 views

how do we know if the volatility which is quoted in market is Normal (Bachelier model) or log normal (Black 76)?

in market, many instruments are quoted in volatility, but how we can tell what kind of volatility is this? is it normal volatility, or lognormal volatility. because it affect our hedging positions so ...
3
votes
3answers
228 views

Could we estimate a portfolio's volatility using a GARCH on the portfolio returns?

Estimating the volatility of a portfolio is typically done by first estimating the covariance matrix. This, however, can be difficult to do accurately and predictivly. This paper gives a nice summary ...
5
votes
2answers
343 views

How to calculate volatility on intraday data?

I have several weeks of minute-by-minute stock data (start and end prices, volume). Everything I've read so far leads me to believe there isn't a standard method for volatility, which is leaving me ...
7
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2answers
576 views

Why linear interpolation not appropriate for volatility surface construction?

We know linear interpolation is not appropriate for constructing a surface, but why? In the book, "Foreign Exchange Option Pricing: A Practitioners Guide", the author writes: native linear ...
5
votes
1answer
2k views

Historical volatility from close prices (Haug pg 166)

I have implemented a function for calculating historical volatility using close the close method as described by Haug on page 166. When I implemented the formula given by Haug, it resulted in some ...
3
votes
2answers
195 views

How to get around flat likelihood function when calibrating GBM parameters?

I want to calibrate jointly the drift mu and volatility sigma of a geometric brownian motion, $$\log(S_t) = \log(S_{t-1}) + (\mu - 0.5*\sigma^2) \Delta t + \sigma*\sqrt{\Delta t}*Z_t$$ where $Z_t$ ...
2
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0answers
96 views

Callable bond price sensitivity to Hull-White volatility changes

I'm using classic Hull-White model for short term interest rate dynamic: $$dr(t)=[\theta(t)-\alpha(t)r(t)]dt+\sigma(t)dW(t)$$ (Notation is quite intuitive, anyway I am using the same as Wikipedia ...
2
votes
3answers
1k views

How to trade volatility?

I am analyzing the volatility of financial stock returns and let's say I have a pretty good model to forecast tomorrows volatility of the stock returns. So let's say for simplicity reasons I have a ...
2
votes
2answers
77 views

Volatility of Multiple Stocks

According to BSM, Stock Price follows log-normal distribution s.t. $$S(t)=S(0)*\exp(\sigma\sqrt t Z-(\sigma^2t)/2)$$ where Z is standard normal variable Then volatility of this stock is $\sigma \sqrt ...
3
votes
1answer
341 views

How to adapt a Moving Average period to market conditions?

I would like to know if there is some way to adapt the period of a moving average to market conditions like for instance the stop loss can be adapted to market conditions using the average true range. ...
4
votes
2answers
128 views

Estimating an appropriate haircut for illiquid stocks

I am trying to determine an appropriate haircut for a basket of illiquid stocks that barely traded during the year. Can someone suggest me an approach to estimate the risk? My dataset has a lot of ...
1
vote
1answer
560 views

Calculate and plot historical volatility with Python

I have downloaded historical data for FTSE from 1984 to now. What I would like to do is to graph volatility as a function of time. What I have written is: ...
7
votes
1answer
1k views

Can American options with no dividends and zero risk-free rate be treated as European?

Let's say you've got American options on a future of a stock index. There are no dividends, and no risk-free rate either (assume $r=0$). Can these options then be treated as European from the ...
5
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2answers
485 views

How to calibrate a volatility surface using SVI

I've read the following paper by Gatheral and Jacquier and have several question regarding the calibration of a volatility surface in a arbitrage free way and some theoretical aspects. Let me first ...
3
votes
2answers
158 views

How to user GARCH(p,q) to identify most volatile sector?

I would like to ask help concerning the utilization of GARCH(p,q) models to identify volatility. Suppose that I have daily closing prices of 6 financial sectors spanning several years, and I am ...
4
votes
1answer
515 views

Moving window forecasting in Python

I am looking to create some code that will out-of-sample forecast the HAR-RV model. The model itself is formulated as the following, and the betas are estimated through HAC-OLS or Newey-West. ...
3
votes
1answer
230 views

How to interpret negative asset volatility numerical results in Merton model?

I am currently working on my thesis where I discuss the Merton default probability model. I have a huge sample of US firms for the period 1990-2010. I use both numerical and complex iterative approach ...
7
votes
2answers
316 views

HFT to blame for Flash Crashes?

Some people 1, 2, 3 claim that High Frequency Trading is partly to blame for the extreme volatilities in the markets yesterday (24. August 2015). Is that true? Is the amount HFTs move even enough ...
0
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2answers
156 views

How to handle currency change in exchange rate volatility measurement

I am trying to measure exchange rate volatility in some countries and I am using their currencies against euro. Problem is that one of them is Slovakia which has changed the currency in 2009 from ...
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0answers
101 views

GARCH filtering and extreme value theory

We are evaluating a model for risk management based on extreme value theory using peaks over threshold and markov chain monte carlo methods. In doing this, we are firstly fitting a GARCH (we have ...
0
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1answer
155 views

Looking for a definition of financial entropy

In Science, Entropy is generally considered to be the irreversibility of stuff. Google defines entropy as: lack of order or predictability; gradual decline into disorder The 'gradual decline in ...
2
votes
1answer
71 views

How to measure the volatility of illiquid bond with no historical prices

The basket of corporate bonds that I am following barely traded after the issuance. Hence, there is no historical data to estimate the volatility. Can you suggest me a different approach to come up ...
5
votes
1answer
389 views

Is volatility for the next day forecastable? To any extent?

In a more general way: is there 1) a methodological approach to quantify the correctness of a model that produces a probability distribution for the, say, S&P 500 index return for the next ...
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0answers
92 views

GARCH estimation does not work, error in my returns?

Hey everyone and I hope that there are some smarter people out here that can help me out with my problem...: I have trouble with my implementation of a GARCH(1,1) model and I do not know how to move ...
0
votes
1answer
435 views

Realized Volatility vs. Standard deviation of log returns

I am interested in calculating high frequency 5-minute intraday volatility. I am going to use the standard Realized volatility which is the square root of the sum of squared log returns. Given X is ...
6
votes
1answer
226 views

How is implied volatility derived?

How to compute Implied Volatility Calculation? The above link shows that there multiple ways to calculate implied volatility. My question is that for most of the common data sources like Bloomberg, ...
10
votes
2answers
444 views

GARCH model, expectation of volatility?

Consider a time series $\{r_t\}$ following a standard GARCH(1,1) model, i.e., $$ r_t = \sigma_t \epsilon_t,$$ where $\epsilon_t \sim N(0,1)$ and are i.i.d, and $$\sigma_t^2 = \omega + \alpha_1 r_{t-1}^...
4
votes
1answer
213 views

Calculating 6-minute, 20-minute, 45-minute, and 3-hour volatility

I am looking to measure the volatility from the open of the market until a trade takes place and use that volatility in post-trade regressions to help explain transaction costs. A simple regression ...
0
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1answer
67 views

Interpreting and scaling of Realized Variance with sample data

I have some question about realized variance(RV) and I have some sample prices below to work with. You can run the R code below to build a vector of log returns. Three are 78 5-minute buckets in a ...
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0answers
50 views

Estimate volatility in forecast

I have a model with a rolling forecast. In each time step $t$, I predict the price for the next periods, e.g. $\hat{p}(t, t+1)$ and $\hat{p}(t, t+2)$. If I start in $t=0$ and arrive at $t=2$, I ...
2
votes
1answer
100 views

Garch models and assumption of stationarity ?

I found big inconsistency in the GARCH models and their underlying assumption of stationarity. GARCH models require that data must be stationary, where stationary means both mean and variance are ...