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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Volatility basics: what happens to implied volatility of stock in week of earnings and dividend payment?

Question: Imagine it is a Monday. Company A (stock you are following) has an upcoming dividend payment on Wednesday and an earnings announcement on Thursday. Company A stock is currently trading at \$...
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Infill lower frequency data: Brownian Bridge

Given monthly returns data, I would like to infill those to get daily returns. Roughly estimates imply that annual volatility is about 1.5x of SPY. One option that came up in my initial research was ...
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Price process with square root of BM

Suppose a stock price follows $dS_t=rS_tdt+\sqrt{S_t||\sigma(t)||dW_t}$ where $||\sigma(t)||=1+0.5t$. How can I find $S_t$ in a way that afterwards I generate paths based on it? I tried to use the ...
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Mathematical solution to return decay of daily leveraged products (leveraged ETFs)

Daily leveraged ETFs have an inherent path dependence. An index performing (5%, -5%, 5%) on 3 days has an overall performance of 2.9%. A -1x leveraged ETF would perform -3.1%. At a higher volatility, ...
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Annualization of discrete returns

There is a well known approach to annualize volatility of log-returns for a given frequency. Let $P(t)$ a price process and define a log return $r_l(t)$ as $$r_l(t) = \ln \left( \frac{P(t)}{P(t-1)} \...
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Why do option prices depend on volatility? [closed]

I'm thinking about option prices as the price to hedge against changes in the underlying asset's value. Suppose we assume geometric brownian motion of the underlying stock's value: $$\mathrm{d}S(t) = \...
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CMS cap has more vega exposure than CMS floor for same strike

When I priced a 10y expiry single look CMS30 ATMF CAP, I noticed that the vega exposure is higher than that of the same 10y expiry single look CMS30 ATMF FLOOR. Why is that? I have a suspicion that it ...
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Fitting ARIMA + GARCH in R

I'm forecasting Electricity consumption Data. I have data for one year , so for every 15 minutes there is an observation. My data contains seasonality and I don't know how to fit SARIMA + GARCH into R,...
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Does my caplet stripped volatility surface make any sense?

My goal is to build a volatility surface for caps on a 3M index implied from SABR model. I have a set of cap normal volatilities for a range of strikes (4%, 6%, 8%, 10% and ATM) and maturities (1, 2, ...
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Yield curve steepening/flattening using different duration treasury futures (TUT Spread) and volatility

Yield curve steepening: long 2 contracts 2 year (2 contracts due to contract size), short 1 contract 10 year Vice versa for flattening. If the 2 year note has a expected volatility of 2% per contract (...
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Spot-Vol covariance and risk reversals

I have been looking into the covariance between log spot returns and log IV returns over a variety of tenors and lookback windows. However I am not sure how these numbers relate back to the outright ...
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sizing fx futures trades by targeting volatility

If I lever up a JPY/USD futures with a 6% volatility/contract 2x to meet my 12% volatility target, how many contracts should I buy per $100,000 I have in liquidity? How do I size my position based on ...
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Are there any public implementations of realized kernels? (preferably in Python)

looking to implement a realized kernel model to forecast realized variance of around ~140 equities and indices in Python given order book data. I have read "Realised Kernels in Practice: Trades ...
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Charting Annual Volatility From Start Date In a Line Plot

I'm pretty new to python/data viz and this is my first time asking a question on here but I have a df with monthly price data back to 2016 for 6 different instruments. I just want to be able to ...
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Reduced volatility in local stochastic volatility model

in Local Stochastic Volatility models I always read or hear "first the stochastic volatility model is calibrated to reduced vols and then the local volatility model corrects it" also I head ...
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Using converted lognormal volatilities for negative rates in a lognormal Libor Market Model (LMM)

There exist formulas to convert between normal and lognormal interest rate volatilities. In the most simple form the approximation for ATM volatilities would be $\sigma_{LogNorm}=\frac{\sigma_{Norm}}{\...
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What is Nassim Taleb's Stance on Volatility

Over the years I have read all of Taleb's Incerto. I recall him more or less writing that "stock returns have no second moment". Hence stock volatilities, defined via the standard deviation ...
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Understanding out-of-sample performance metrics for Realized Volatility

I fitted several models on a realized volatility process and then proceeded to obtain out-of-sample results. I'm struggling to interpret these results apart from to tell model A seems better than ...
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Rationale for Historical Volatility definition

I think I understand the most common definition for historical volatility (standard deviation of log returns), but it has me puzzled because it conflicts with my intuitive idea of what volatility is. ...
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Vol, Gamma, Vega -- essentially all the same?

When talking to traders I hear this sentence a lot I am a buyer/seller of X where X = {vol, gamma, vega} Is X basically all the same -- they are just saying -- I think implied volatility is cheap or ...
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Maximum market volatility

I program trading algorithms that create profits from unpredictable market fluctuations. I am looking for markets with the most extreme fluctuations and I need them to fluctuate up and down in a zig-...
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Examining the dependence of the fractional difference parameter in ARFIMA(0,d,0) vs bar size for Realized Volatility

Realized volatility is a long-memory process and so I fitted an ARFIMA(0,d,0) to log(RV15) where RV15 is realized volatility calculated from 15-min bars. I proceeded to examine how changing the bar ...
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FX options: is convexity usually heavily overpriced?

I have access to daily vol quotes for EURUSD options from 2006 to today. I was playing around with them and constructed a "daily rolled backtest" for various options constructs, like ...
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Spot-Vol Correlation ITM Receiver Swaption

I am new to the term Spot-Vol Correlation. As far as I understand it describes the "relationship" between the spot rate and the implied volatility. So I heard when we are ATM it means that ...
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Introduction to volatility targeting, scaling, timing

I am a finance student, but I am quite new to the field of asset management and quantitative Finance. I have to write a literature review about volatility targeting and I am looking for good resources ...
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Computing the Variance Risk Premium

The Variance Risk Premium (VRP) is defined as: $$VRP(t,t+\Delta t) \equiv RV(t,t+\Delta t)^2 - IV_t(t,t+\Delta t)^2$$ where $RV^2$ is the realized variance between $t$ and $t + \Delta t$ and $IV_t^2$ ...
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Why calibrate volatility Models to volatility surfaces rather than underlying's historical price data?

I'm trying to grasp the rationale for calibrating stochastic volatility models (i.e. Heston model) to empirical IV data from market prices. Doesn't this assume that the options are fairly priced and ...
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Early expiry option implied volatility

I’m new to this forum so first of all I wanna welcome everyone here. I am a commodity trader, mostly covering option books (vanilla and structured one) and I would ask more expert people how they can ...
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Realised variance under simple rough volatility model

Using the Mandelbrot-Vann Ness representation of fractional Brownian motion in terms of Wiener integrals, increments of the logarithm of realized variance $v = \sigma^{2}$, under the physical measure $...
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Covariance of ARCH(2) model

I am having problems solving the following exercise: The solution is the following: I understand we are calculating E(r^2t) and E(r^2tr^2t-1) because they are part of the covariance formula, and ...
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Where can I find a source that futures traders use ATR and stock traders use log price ratio standard deviation to calculate volatility?

In the wikipedia article about the average true range, I can find the following statement: Since true range and ATR are calculated by subtracting prices, the volatility they compute does not change ...
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How to measure accuracy of SABR volatility surfaces?

I would like to test how accurate are SABR volatility surfaces with respect to historical volatility over a given time period and for a specific equity index. Reading a few papers I realised that one ...
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Industry standards for vol control index options

Consider an index of the type: $I(t)/I(t-1) = 1+ a(t) (S(t)/S(t-1)-1)+(1-a(t))r(t-(t-1))$ It is arbitrarily initialized. $r$ is the risk free rate. a(t) is determined piecewise as: $a(t)=s_{target}/s_{...
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Difference of polynomial interpolation for volatility smile

I am using 5 volatility points to build a volatility smile : put 10D, put 25D, ATMF, call 25D and call 10D. I have thus 5 pairs of data : (Delta, Vol) let's say for example (10;5.75) ; (25; 5.50) ; (...
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Sharpe Ratio of a Long-Short Portfolio

I have a portfolio High and Low (according to the highest profit). From this I have formed my long short portfolio and calculated my Sharpe Ratio. How to interpret this correctly? Does a positive ...
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If the volatility of pounds/euros = .2 do we know anything about the volatility of euros/pounds?

I think the question here is what we know about $\mathrm{Var}\left(\frac1X\right)$. Is this the right question to ask, and if so is there anything that can be said?
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Volatility targeting / sizing for option strategies

I am trying to work out how to properly size an option strategy to a given target volatility. Assuming I have \$100 capital and I would like to have a strategy's long-run daily volatility to be \$1 (e....
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Construction of vol term structure for Libor

When we want to construct Interest rate term structure we look at various market instruments like futures, swaps etc. and using ...
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GARCH(1,1) parameter estimation optimization method

In estimating a GARCH(1,1) model, $$\sigma_{t+1}^2 = \omega+\alpha \epsilon_t^2+\beta\sigma_t^2$$ Usually the parameter tuple $(\omega,\alpha,\beta)$ is estimated by the quasi-maximal likelihood. ...
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Ito's lemma results in negative volatility processes

I struggle with the interpretation of a process I derive from Ito's Lemma. Let's say I have function f(S,t) which is twice differentiable wrt S. I thus can apply Ito's Lemma to get $df(S,t)$. So far ...
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GARCH parameter estimation by linear regression?

In estimating a GARCH(1,1) model, $$\sigma_{t+1}^2 = \omega+\alpha \epsilon_t^2+\beta\sigma_t^2$$ Usually the parameter tuple $(\omega,\alpha,\beta)$ is estimated by the quasi-maximal likelihood$. Can ...
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Realized Volatility + GARCH - can I use hourly realized volatility?

I hav minute bar FX data and I am trying to fit a realized variance GARCH model using rugarch. This normally works by providing daily returns and daily realized volatility to the model. Realized ...
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GARCH calibration with overlapping time intervals

In constructing a GARCH(1,1) model over a time length $\delta$, I am considering the following procedure. The purpose of this procedure is to give more training (calibrating) samples than non-...
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284 views

Where can I find caplet implied volatility data?

I am looking for caplet implied volatility data for Libor-EUR. Is there any online data base etc. available to get such data? Does ...
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QuantlibXL - How can I define a volatility surface using moneyness instate of strikes?

I wonder if in the function qlBlackVarianceSurface() I can replace the strikes for moneyness and then price the option using the spot = 100% and the option strike = Original_Strike / Original_Spot. ...
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Contribution to Mahalanobis Distance

I am using Mahalanobis Distance to measure abnormal behavior within a portfolio consisting of a handful of general asset types, and am trying to figure out how to decompose this measurement into ...
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Delta hedge analysis - volatility rapidly growing

I'm working with a hedge expirement design, where I daily hedge with EGARCH(1,1) forecasted volatilty based on a moving evaluation of the past 126 days. However, I can't seem to understand the profit ...
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Free Arbitrage conditions in ATM swaption surfaces

I'm wondering how can we check free arbitrage conditions in ATM swaptions surfaces since we only have access to Expiry, Tenor and volatility? Can someone help me please, i didn't find any article ...
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Perfect in-sample size for out-sampling volatility prediction (EGARCH(1,1)

I have a few questions regarding in-sample size for volatility forecasting in EGARCH(1,1). I'm currently sitting with a dataset consisting of 1387 trading days of the S&P-500 index. I would like ...

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