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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Summarizing the Volatility Skew as a Single Number

Related questions to this topic/subject: Expressing Volatility Smile as One Number Volatility skew and how to capture it? In both posts, the authors/respondents recommend using the second derivative ...
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Variance Swap Valuation

I am trying to find the future volatility of a variance swap. I have a trade which has already commenced and i am valuing it midway. I can observe the past variance till my valuation date but i am not ...
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Emanuel Derman Volatility Approximation [closed]

Can someone please explain Emanuel Derman's volatility approximation as given below? Under Linear Skew If skew is assumed to be linear, at least for strikes relatively close to the money, then Derman’...
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pricing option with two volatility regimes

How would I price a 1-year ATM European call option, given I know that for the first 6 months, the realized volatility will be 20% and the latter six months, the realized volatilty will be 90%? One ...
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Volatility surface for futures options

When looking at futures options such as CME's Gold options or many equity index futures options, the underlying is not the index but to be precise the closest to delivery futures contract. That means, ...
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How to conclude which option is overpriced (by using implied volatility)

I have a small question regarding how to conclude which option is more overpriced? See the following table Option Theoretical Value Option Price Option Implied Volatility 7.00 8.00 26% 6.00 6.75 28%...
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Calibrating Hull White volatility on swap rate volatility

I'm strugling with the Hull-White 1F model. I'am trying to calibrate the volatility with the swap rate volatility. Here is the model I'am curently working on : $$ \begin{align} dr_t = a(b-r_t)dt + \...
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Multivariate Markov Regime switching GARCH in R

I am looking for R package handling Multivariate Markov Regime switching GARCH models, but MSGARCH package only work for univariate time series. Any suggestion would be welcomed, thanks!
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How to calculate historical returns and variance for a non-BAH trading strategy?

Suppose i have a strategy that is not buy-and-hold type of strategy. It can have unique entry timing and unique exit timing for a single asset and both long and short positions will be allowed, and ...
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GARCH before and after a shock. How to test if volatilities are different?

I have an intraday dataset with minute returns for a bond. At a specific point in time, say 10:30, there is an external shock (in my case an auction where that bond is traded). I want to know whether ...
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Implied forward volatility definition

What is the rigourous definition of the 'implied forward volatility' and how is it calculated? I couldn't find a rigorous definition as would be the case for 'implied volatility'. Also, could anyone ...
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Question about marginal risk contribution / portfolio volatility decomposition

I am trying to understand the rule where you add a new asset to a portfolio if its Sharpe ratio is greater than the product of the portfolio sharpe ratio and the correlation between the portfolio and ...
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How should I go about computing the 30-day model free implied volatility (MFIV) daily?

As the title suggests, how can I calculate the MFIV daily (for a market index)? My MFIV follows the procedure described in DeMiguel et al. (2013) Improving Portfolio Selection Using Option-Implied ...
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Are there standardized measures to characterize the volatility skew?

Might be too simple a question, but I saw in Gatheral & Jacquier (2014) that commonly used features to match volatility skews are (and then I subsequently ChatGPTed some commonly used industry ...
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Cross corridor var swap

How should I think about replicating a cross corridor variance swap like breaking into strips of calls and puts and an over hedge that I can rebalance at some frequency? Given the earnings move, I can ...
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What are state-of-the-art methods for forecasting of rates and volatilities?

Usually forecasting is based on a model for the evolution of a value $x(t)$ based on some parameters ${\beta}$ that can then be estimated using various statistical means. For yield curves and ...
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Libor Market Model

I try to simulate forward rates with the Libor Market Model (LMM). Unfortunately, I just have data for normal vols instead of lognormal vols which are assumed in the LMM. Is there a way I can adjust ...
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Why do unleveraged VIX ETPs have large beta relative to VX futures, with much faster decay?

I hope the title explains it fairly adequately. To add a little more detail, it's my understanding that VIX ETPs such as VXX and VIXY hold VX Futures as their underlying assets. I believe that this is ...
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Master Thesis about Heston vs. Duan option pricing model

I would like to write my master's thesis on volatility in option pricing. My idea was to compare the stochastic volatility model of Heston 1993 with the GARCH option pricing model of Duan 1995. For ...
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How to calculate the spot variance from the TSRV (Two-Scale Realized variance)

If the TSRV is given by: $$TSRV = \frac{1}{K} \sum_{i=K}^{n} (S_i - S_{i-K})^2 - \frac{\bar{n}}{n}\sum_{i=1}^n (S_i - S_{i-1})^2 $$ where $\bar{n} = \frac{n - K + 1}{K}$, with $n$ is the number of ...
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Forward Rate Volatility Calculation - Caps

I am trying to calculate the forward rate volatilities from cap volatilities using Rebonato`s volatility model. Unfortunately, my approach always results in unrealistic forward rate vols. Furthermore, ...
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Standard deviation of large equal-weighted portfolios

Say I've got a portfolio of shares with the following parameters: Let $n$ be the number of shares in the portfolio, let $\bar\sigma$ be the average standard deviation (volatility/risk) for each share, ...
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Deriving eq. 5 in Carr & Madan 1998

I don't understand this derivation from Carr & Madan (1998), specifically the derivation of the third term on the left (left-most term on the bottom line). My attempt Let $h(t, F_t) := V(F_t, t; \...
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Vol Smile Call/Put Wing calibration

Is call/put wing volatility smile calibration approach used in practice? To calibrate an index (SPY) using only more liquid OTM calls/puts, to kind of use an "if" condition on K to S0 to ...
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How do options traders capture volatility?

Let's say I'm an options trader, and I want to go long volatility on a particular underlying. How do I capture this volatility mispricing? How do I convert my forecast into a bet with a cash payoff. ...
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Volatility of a stochastic Process given by an SDE

I am currently working on this thesis: http://arks.princeton.edu/ark:/88435/dsp01vd66w212h and i am stuck on page 199. There we have a portfolio $P=\alpha F+\beta G $ with $\alpha +\beta =1$ and ...
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Vol-Vol Breakeven (MC Estimation)

I am currently reading the paper Computation of Break-Even for LV and LSV Models. This paper defines the vol-vol breakeven \begin{align*}\tag{1} B_t(T,K,T',K') &\ :=\ d\langle \ln \sigma^{T,K}...
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the pre-averaging function in Jacod et al

In the paper of jacod et al the authors used the pre-averaging function to deal with microstructure noise. They suggest the easiest function which is $$\bar{Z_i} = \frac{1}{kn} \left( \sum_{j=kn/2}^{...
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Arbitrage-Free implied/local volatility surface with Cubic Spline Interpolation

I am trying to create a local volatility surface using a cubic spline interpolated implied volatility surface. In other words, I have a function $\sigma(T,K)$, that is arbitrage-free $\forall T,K$ (...
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Modeling mean-reversion for different volatility regimes

Motivation: Half-life (HL) period shows how long it takes for a mean-reverting process to return halfway to its mean after a deviation. Most commonly, an Ornstein–Uhlenbeck (OU) process is applied to ...
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Delta on x-axis in Volatility smile

I want to ask a perhaps simple question: Why do we use delta on the x-axis instead of the strike price when discussing volatility smile or volatility surface? In the book I'm currently reading, it is ...
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Measure of the behavior of Swaption surface

I'm looking to find a different measure than average shift move to explain the behavior of the IR VOL products say Swaption. I know it's a very open question not only touching upon IR VOL scope. Let ...
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We can forecast the direction of (constant maturity) implied vol of various indices well. Is that useful?

We've been financial building ML models for years, and have multiple portfolios live - but we're new to the volatility space, none of us are options traders. How could we effectively use implied vol ...
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Instrument volatility scaling as a function of sample rate

Question: I did some experimentation today to see if volatility changes as a function of the sample frequency. Prior to starting this experiment, I believed that volatility was a function of sample ...
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Do options/prop trading firms put any effort into predicting (the direction of (implied)) volatility?

What are the "best practice" models that quant firm that trades options would use to "predict" (let's say SP500) implied vol, that they integrate into their decision making? Do ...
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Option price calculation using Local Volatility and Monte Carlo

The below formula is used to convert the implied vol into the local volatility, my question is, once I have converted it into the LV ( and have built the full surface), what models do I use to ...
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Creating Implied Volatility surface using log moneyness [closed]

When creating the implied volatility surface using $\left(T,log\left(\frac{K}{S_0}\right)\right)$ as $(x,y)$ axis, do the inputs for the implied vol calculation need to be logged too? In other words, ...
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Volatility is not becoming sigma in simulated GBM [closed]

I am trying to simulate GBM using values for sigma and then after calculating the price, calculate the log of returns and the associated volatility. I was expecting the calculated volatility of log ...
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Volatility Tax/Variance Drag and Drawdowns/Breakevens

been reading about Drawdowns and respective returns to get back to breakeven as shown below: Many cite this as an evidence of the well publicized Vol Tax Formula (Geo Mean = Arithmetic Mean - 0.5*...
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Connection between the $\sigma$ parameters of the spot price and the forward price

It is well known, that under the Black-Scholes framework: $$F\left(t,T\right)=\exp\left(r\left(T-t\right)\right)S\left(t\right),$$ where $S\left(t\right)$ is the spot price of an asset at time $t$, $F\...
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Distribution of Geometric Brownian with time-dependant volatility

The process $S(t) =\exp\left(\mu.t + \int_0^t\sigma(s) \text{d}W(s) - \int_0^t \frac{1}{2}\sigma^2(s)\text{d}s\right)$ where $\sigma(s) = 0.03s$ is log-normally distributed, but i'm not sure about the ...
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Optimal Price Metric for High-Frequency Volatility: Executed Price, Mid Price, or Weighted Mid Price?

In the context of high frequency trading, I'm exploring the application of the mean absolute deviation estimate for high-frequency volatility calculation. What would be the optimal choice for this ...
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Why do the Greeks not converge to the strike as the volatility tends to zero? [closed]

So, I was playing around with the Greeks in Python with some made up data for a European call option assuming the Black-Scholes model. I plotted the graphs to see what happens to the Greeks when ...
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High/Low range under GBM - Analytic solution?

Does anybody know of an analytical solution to the expected high / low range for an asset that follows a GBM process over sampling frequency dt? I have ran numerical simulations and find that the ...
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implied volatility for close to expiry ATM options vs VIX

All throughout my MFE I was told that implied volatility for close to expiry ATM options is a reasonable estimate for current volatility and tracks realised vol pretty well. Then why does VIX measure ...
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How to adjust an assets position to target volatility in a long-short portfolio?

I have a portfolio of weights $\mathbf{x}$ where some positions in $\mathbf{x}$ are short s.t. $\Sigma_i x_i=0$ (dollar neutral). The standard way to estimate the volatility contribution per asset is ...
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Implied vs. Realized Vanna in Risk Reversal

I am trying to understand how to build an implied-to-realised Vanna trade using a risk reversal, as shown in the Hull's paper: https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3968542 I have some ...
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Implied volatility greater than realized volatility at all strikes?

It is usually stated that the implied volatility is statistically generally --- not always --- greater than the realized volatility. It seems this statement is made with regard to the implied ...
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For each day I have volatility for country A and B. How to test if volatilities are different? [closed]

I have a dataset with 10Y benchmark government bond volatilities of two countries. So, my data looks like this: Date, Volatility5day_A, Volatility5day_B The volatility measure itself is from Bloomberg ...
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0DTE volatility and greeks

When european stock options have very little time until expiration (less than 2-3 hours), they can exhibit extreme sensitivity to changes in the underlying asset's price. This behavior leads to ...
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