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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 Forecasting of VIX

Background: As we know, volatility in the long run is mean reverting. Given that volatility is mean reverting, when volatility is low, it tends to go up. When it is high and going down, it tends to ...
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volatility term structure calibration

As is well known in order to calibrate an interest rate model (i.e. hull-white, LMM) i need to use the current market yield curve and volatility. But in the case I want to calibrate the model in a ...
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Equity Options - “How do I build a forward simulation model with regards to shocks in spot pricing and IV?”

I am trying to build a "What-If" Portfolio, consisting of a total of 20 options, across different tenors, strikes (delta), but on the same security. Simply put, the objective is for me to test the ...
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Is variation in price-dividend ratios that is attributable to excess returns due to variation in returns or variation in risk free rates?

Cochrane and Fama show that "all variation in price-dividend ratios corresponds to changes in expected excess returns -risk premiums- and none corresponds to news about future dividend growth". Is ...
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227 views

Volatility of stocks small cap vs large cap

I read that small cap stocks are more volatile than large cap stocks. Now I am looking for sources (e.g research papers or similiar) with empirical evidence for this proposition but I can't find any (...
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How to generate variance impulse response function as in Hafner and Herwantz (2006)?

I am trying to generate variance impulse response functions as described by Hafner and Herwantz (2006) and in Walter Enders' book "Applied Econometric Time Series". Is there a command in R for this? ...
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VaR of future foreign currency income stream

Assume I have a series of future incomes in a single foreign currency. How do I calculate the total VaR for this forex risk using the volatility method? My first thought was that I could simply add ...
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122 views

XIV Positive Roll Yield

I understand that VIX futures are usually in contango and so a portfolio that holds futures with a weighted average expiration of 30 days will "roll" down to equal the VIX index at maturity. This is ...
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138 views

Why are some Yang Zhang constant k different from the original paper?

I've seen this in the original paper (Yang, Zhang: Drift Independent Volatility Estimation ...) (see Equation 10, Page 483) $$k = \frac{\alpha - 1 }{\alpha + \frac{ n + 1 }{ n - 1 }}$$ while there ...
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116 views

How to estimate $\sigma$ and $r$ in binomial pricing model?

I am writing a program to price American put options with binomial pricing model and to compare it with the market price. When I used made-up numbers for $\sigma$ and $r$, the price by binomial ...
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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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Realized volatility vs Fundamental volatility

What is the difference between the realized volatility (also called historical volatility) and the fundamental volatility?
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What is a good algorithm to predict volatility in metals commodity markets? [closed]

I'm trying to create a script to predict major swings in the price of Aluminium. I am trying to implement a dynamic time warping algorithm for the same. Was wondering if this really is the best ...
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183 views

Positive PnL with long volatility strategy

Suppose I was interested in longing volatility. Suppose I bought a long straddle today which expires in 3 months. Suppose that volatility was very high in those 3 months, however, the stock expires at ...
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141 views

inverse of stock price [closed]

Is there any intuition to use 1/P (inverse of the stock price) as a factor of volatility? $VOLT = \beta_1 * \frac{1}{P} + Res$ P.S: In a research paper, I found it's related to the market micro-...
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Time frame for implied vs realized vol

I've seen charts of implied vol (IV) against realized volatility? What time frames do people generally use to calculate each? For example, do people generally use ATM 1 month call options to get IV, ...
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219 views

Build Implied Volatility Smile

I am currently to create my own volatility smile for cryptocurrency options. I am basically reading the bids and offers and calculating the implied volatilities. I now want to shape and parametrise ...
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333 views

Daily Return to Approximate Annualized Realized Volatility 16 or 20?

Sometimes traders approximate realized volatility to compare it to the annualized implied volatilities in options by multiplying the 1-day daily return (as a substitute for the daily volatility since ...
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PRIIPs category 2 stress scenario methodology

recently new document has been provided by EU supervisors regarding the new PRIIPs KID methodology. (PRIIPs KID is 3page document about the fund/product that is being sold to clients. It has to inform ...
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366 views

Why is the volatility smile so important

This might seem like a dumb question. When using a volatility model, stochastic for example, we try to calibrate it so that it fits the implied volatility smile given by the market, but why is this ...
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57 views

How to extend Realized Volatilty to multiple periods

I'm trying to calculate 5-day realized volatility (as proxy for integrated volatility) using 5-min frequency data. I'm working from the paper CORRECTING THE ERRORS: VOLATILITY FORECAST EVALUATION ...
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353 views

Paradox in option expiry as volatility goes to infinity

As volatility goes to infinity, the delta of a call option goes to 1. The delta approximates the probability that the option expires in the money. So it seems that the probability of expiring in the ...
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What is 'off term' volatility and 'term' volatility?

I see these terms being used on the floor, but don't really understand precisely what is being referred to. One colleague asserted that an 'off term' volatility is for an option whose delivery date ...
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How does volatility affect price arbitrage?

Suppose I'm running automated classic price arbitrage on 3 currencies (let's ignore the unfeasibility of this in our day and age). We have currency pairs Gold/Silver, Silver/Bronze, and Gold/Bronze. ...
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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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Volatility taxonomy

I have been thinking about this for a while... I can't make my head around it because of the gap that there's still on between financial economics and quantitative finance. Usually, when a student is ...
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395 views

Probability of exercise in the Black-Scholes Model

What's the intuition behind the fact that the limit of $\mathcal{N}(d_2)$, i.e. the (risk-neutral) probability of exercise, in the Black-Scholes Model tends to $0$ when the volatility tends to ...
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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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396 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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453 views

What is the formula for Intraday and overnight volatility?

I'm a noob trying to calculate IntraDay and Overnight Volatility. For Intraday volatility we can get the annualization factor with the following: Length (hours, Open to Close): 6.5 Time frames per ...
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Estimating the historical drift and volatility

I want to forecast prices $S(t)$ of some asset based on historical daily values. I want to use the geometric Brownian motion given by an SDE: $$dS=\mu S t + \sigma S dB,$$ where $B$ is a Brownian ...
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2k views

Common Quanto adjustment

In this paper (Quanto Skew, by Jackel), on second page, the author states: a) Determine an effective volatility coeffcient $\hat \sigma$ exactly as in (2) using the forward as if the option was ...
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Replicating Log Contract - Errors Introduced by Jumps

In the GS Research Note about Volatility Swaps, it is shown that you can replicate a pure variance exposure (hedge) with only vanilla calls and puts, primarily thanks to the Carr-Madan formula of ...
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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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137 views

Intuition Behind Scaling Factor in Variance Swaps

In More Than You Ever Wanted to Know About Volatility Swaps the fair value of a future variance swap can be replicated from market prices for calls and puts. The fair put and call strike is shown to ...
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Explaining mathematically why to use the ATM vol [closed]

In this question, I got an answer that is much explaining in words what could be explained mathematically. The user who answered referenced the book "The Volatility Surface, by Jim Gatheral's". But ...
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I am trying to fit an GARCH(p,q) model to FX volatility. Should I be interested in the t-value of GARCH parameters?

So what I am trying to do is to model the volatility for different currencies by fitting a GARCH(p, q) model. I am selecting the values of (p, q) by iteratively going through p & q such that max(p,...
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What are the significant implications of the long-run average variance rate and why Engle won the Nobel Prize for ARCH model development?

In a ARCH(m) model we have $$ \sigma_n^2=\sum_{i=1}^{m} \alpha_i u_{n-i}^2 $$ where $u_i$ is defined as the continuously compounded return during day $i$ (between the end of day $i-1$ and the end of ...
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Predict probability of returns: How does changing volatility affect the return pdf?

I am trying to predict the future probability of stock returns based on the return distribution. Therefore I calculate the returns as $\frac{P(t)}{P(t-1)}$ for the whole daily data and fit a ...
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116 views

Why implicit volatility has the shape of a “smile”? [duplicate]

Two of the conditions for an asset price to have a lognormal distribution are: The volatility of the asset is constant. The price of the asset changes smoothly with no jumps. In practice, neither of ...
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219 views

Volatility considerations with interest rate derivatives

I am a bit confused about the practical use of vol surfaces used for derivative pricing. We know that the two main products that best represent market volatility are caps and swaptions, from which ...
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What is relation between option adjusted duration and volatility

I am calculating oasd using implied vol of 15%. What is relation between OASD vs Implied volatility in theory for various maturities. I am running using MMD curve. If anyone recommend any good ...
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MATLAB exercise on an European call option with time-varying volatility

I have to solve the following exercise: compute and plot the value $V = V(S, t),\ t<T$, ($T=$ maturity) of an European CALL option (with arbitrary $t$, $T$, $K$ (strike price), $r$ (risk-free ...
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397 views

Why is the ATM vol kind of an average volatility

In this question I asked about the mathematical rationale of using the ATM vol to price quanto options. One of the reasons pointed (as an answer) was, as expected, that the ATM volatility is kind of ...
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471 views

How can I compare 30 day implied volatility forecasts with GARCH forecasts?

I'm trying to understand whether there is a good way to compare forecasts for volatility from different sources i.e., implied volatility and GARCH. I'll outline a few statements that I believe and if ...
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283 views

Approximations for Quanto Options pricing

On page 4 of this paper, the auhor provides two good approximations for quanto options pricing: $V^d_{black}$ and $V^d_{blackATM}$. These approximations consist of using the ATM and/or stike ...
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The Heston Solution For European Option - Jim Gatheral

I have this equation (Eq. (2.4) "The Volatility Surface - A Practitioner's Guide" by Jim Gatheral (Ed. 2006)): $$-\frac{\partial C(v, x, \tau)}{\partial \tau}+\frac{1}{2}v \frac{\partial^2 C(v,x,\tau)}...
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137 views

What makes a realized vol estimate “tradeable”?

I'm trying to understand what makes a realized volatility estimate tradeable. Quoting from an abstract ...
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Volatility of a multiple-asset portfolio [closed]

I have N assets with their individual volatilities $\sigma_{i,t}$. I construct a portfolio using the weights $w_{i,t}$ that I obtained in a matter that is irrelevant. Now I want to determine the ...
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214 views

Volatility vs. Moving Average Distance

Currently I am designing a little market making bot for forex trading, that puts offers around the mid price. In the market I am trading it happens the order book becomes so thin that the mid price ...