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There are many papers.
Here are some random examples:
Many of the papers under https://www.michaeljacobsjr.com/research-papers/
http://dx.doi.org/10.2139/ssrn.1466710 Ralf Elsas, Sabine Mielert. Rating Validation Based on Shocks to Firms’ Credit Quality
http://dx.doi.org/10.2139/ssrn.2521216 Sean Flynn, And... |
Agreed with nbbo2. I did this exact thing a while back.
[So, for example If I want to compare =10% with =15%. That means I should calculate initial option value with =10%, but then on each step: montecarlo simulation as well as 1(Δ) will use =15%?]
Calculate initial option value with vol(b) = .10, and the hedgin... |
Suppose that yesterday I shorted some call and put option contracts of an underlying and I had a neutral delta. This morning, I have a positive delta, and I want to keep my delta neutral. What do I need to do and why do I need to make this action? Should I buy or sell its underlying future contract? |
What shall I do to make my delta neutral? |
Suppose that yesterday I shorted some call and put option contracts of an underlying and I had a neutral delta. This morning, I have a positive delta, and I want to keep my delta neutral. What do I need to do and why do I need to make this action? Should I buy or sell its underlying future contract?
Below is what I ... |
There are many papers.
Here are some random examples:
Many of the papers under https://www.michaeljacobsjr.com/research-papers/
http://dx.doi.org/10.2139/ssrn.1466710 Ralf Elsas, Sabine Mielert. Rating Validation Based on Shocks to Firms’ Credit Quality
http://dx.doi.org/10.2139/ssrn.2521216 Sean Flynn, And... |
What is the optimal input and target variables for forecasting with a deep neural network on daily stock/index data? More specifically I’m training a temporal convolutional network, but a more general answer is also appreciated.
Are normalized closing prices, daily returns, or nominal daily changes better inputs? Fo... |
There are hundreds of articles online about how to forecast daily close price using some variant of machine learning, most of the are total crap.
What is it exactly you want to predict? do you understand the dynamics of the problem at hand? machine learning is plain useless without understanding of the fundamentals,... |
Suppose we have the following random variables, given a fixed $t$ we define the last zero before $t$ and the first zero after $t$:
\begin{align*}
\alpha_t &= \sup\left\{ s\leq t: B(s) = 0 \right\}\\
\beta_t &= \inf\left\{ s\geq t: B(s) = 0 \right\}\
\end{align*}
Why $\beta_t$ is a stopping time but $\al... |
I have created a piecewise linear zero curve using quantlib (c++). It's a NACA, modifiedFollowing swap curve. When I extract the zero rates on the pillar dates the rates line up with what is expected but when I call zero rates in between I get a slightly different linear interpolated rate to what I'm expecting. The dis... |
I'm having a problem getting options data with IB's API. The data seems not to be correct. In my code I'm getting some 0DTE call options for the Mini SP500 March Futures contract and printing their bid, ask and delta. For this I'm using the ib_sync which simplifies development greatly. This is the code:
from dat... |
Getting incorrect options data with IB API. Missing real time market data subscription? |
I have recently read in a paper that the 25 day SMA and 36 day EWMA are equivalent for comparison in tests due to their half lives. The half life of the 25 day SMA is obviously 12.5 days and I understand the basic form of the equation to calculate the EWMA. I have been struggling trying to back out the half life from t... |
I'm new to Quantlib on Python and I'd like to use the overnight swap rate from Bloomberg to derive the swap curve discount factors.
I don't know which yield term structure I should specify?
I checked the QuantLib Python Cookbook and the QuantLib-Python Documentation https://quantlib-python-docs.readthedocs.io/en/l... |
I am pricing CDS calibrating the default probabilities intensities using CDS spreads from Markit.
Those spreads are given with a recovery.
I have two questions regarding the recovery:
1. In Option, Futures and Other Derivatives, Hull wrote that, provided we use the same recovery for calibrating default probabil... |
Apparently, you refer to this passage from Prof John C. Hull [(11th edition, 2021)][1]:
[![enter image description here][2]][2]
It's confusing because Hull is referring to the market conventions before the ["Big Bang"][3]. This is no longer true, but Hull, or, more precisely, his ghostwriters, never updated his boo... |
Apparently, you refer to this passage from Prof John C. Hull [(11th edition, 2021)][1]:
[![enter image description here][2]][2]
It's confusing because Hull is referring to the market conventions before the ["Big Bang"][3]. This is no longer true, but Hull, or, more precisely, his ghostwriters, never updated his boo... |
Apparently, you refer to this passage from Prof John C. Hull [(11th edition, 2021)][1]:
[![enter image description here][2]][2]
It's confusing because Hull is referring to the market conventions before the ["Big Bang"][3]. This is no longer true, but Hull, or, more precisely, his ghostwriters, never updated his boo... |
Apparently, you refer to this passage from Prof John C. Hull [(11th edition, 2021)][1]:
[![enter image description here][2]][2]
It's confusing because Hull is referring to the market conventions before the ["Big Bang"][3]. This is no longer true, but Hull, or, more precisely, his ghostwriters, never updated his boo... |
Apparently, you refer to this passage from Prof John C. Hull [(11th edition, 2021)][1]:
[![enter image description here][2]][2]
It's confusing because Hull is referring to the market conventions before the ["Big Bang"][3]. This is no longer true, but Hull, or, more precisely, his ghostwriters, never updated his boo... |
Apparently, you refer to this passage from Prof John C. Hull [(11th edition, 2021)][1]:
[![enter image description here][2]][2]
It's confusing because Hull is referring to the market conventions before the ["Big Bang"][3]. This is no longer true, but Hull, or, more precisely, his ghostwriters, never updated his boo... |
Apparently, you refer to this passage from Prof John C. Hull [(11th edition, 2021)][1]:
[![enter image description here][2]][2]
It's confusing because Hull is referring to the market conventions before the ["Big Bang"][3]. This is no longer true, but Hull, or, more precisely, his ghostwriters, never updated his boo... |
For an option with price C, the ΔC, with respect to changes of the underlying asset price S and volatility σ (first-order approximation), is given by
ΔC=δΔS+νΔσ,
where δ, and ν are respectively the delta, and vega greeks.
Assuming the asset S and the volatility σ as normal and indipendent, we can calculate the... |
How to derive numeric option VaR with delta-vega normal approach? |
For an option with price C, the ΔC, with respect to changes of the underlying asset price S and volatility σ (first-order approximation), is given by
ΔC=δΔS+νΔσ,
where δ, and ν are respectively the delta, and vega greeks.
Assuming the asset S and the volatility σ as normal and indipendent, we can calculate the... |
Apparently, you refer to this passage from Prof John C. Hull [(11th edition, 2021)][1]:
[![enter image description here][2]][2]
It's confusing because Hull is referring to the market conventions before the ["Big Bang"][3]. This is no longer true, but Hull, or, more precisely, his ghostwriters, never updated his boo... |
Apparently, you refer to this passage from Prof John C. Hull [(11th edition, 2021)][1]:
[![enter image description here][2]][2]
It's confusing because Hull is referring to the market conventions before the ["Big Bang"][3]. This is no longer true, but Hull, or, more precisely, his ghostwriters, never updated his boo... |
Apparently, you refer to this passage from Prof John C. Hull [(11th edition, 2021)][1]:
[![enter image description here][2]][2]
It's confusing because Hull is referring to the market conventions before the ["Big Bang"][3]. This is no longer true, but Hull, or, more precisely, his ghostwriters, never updated his boo... |
Apparently, you refer to this passage from Prof John C. Hull [(11th edition, 2021)][1]:
[![enter image description here][2]][2]
It's confusing because Hull is referring to the market conventions before the ["Big Bang"][3]. This is no longer true, but Hull, or, more precisely, his ghostwriters, never updated his boo... |
Apparently, you refer to this passage from Prof John C. Hull [(11th edition, 2021)][1]:
[![enter image description here][2]][2]
It's confusing because Hull is referring to the market conventions before the ["Big Bang"][3]. This is no longer true, but Hull, or, more precisely, his ghostwriters, never updated his boo... |
I have created a piecewise linear zero curve using quantlib (c++). It's a NACA, modifiedFollowing swap curve. When I extract the zero rates on the pillar dates the rates line up with what is expected but when I call zero rates in between I get a slightly different linear interpolated rate to what I'm expecting. The dis... |
I understand the NAV to be the sum of all assets minus the liabilities divided by the total number of shares.
Would the assets include the financial derivatives held by the ETF? And if so, how is this less than the fund's exposure? |
How do you define the NAV of a leveraged ETF? |
What is the reason for adding 0.5 variance when calculating the ATM DNS of an option? |
Apparently, you refer to this passage from Prof John C. Hull [(11th edition, 2021)][1]:
[![enter image description here][2]][2]
It's confusing because Hull is referring to the market conventions before the ["Big Bang"][3]. This is no longer true, but Hull, or, more precisely, his ghostwriters, never updated his boo... |
Apparently, you refer to this passage from Prof John C. Hull [(11th edition, 2021)][1]:
[![enter image description here][2]][2]
It's confusing because Hull is referring to the market conventions before the ["Big Bang"][3]. This is no longer true, but Hull, or, more precisely, his ghostwriters, never updated his boo... |
Apparently, you refer to this passage from Prof John C. Hull [(11th edition, 2021)][1]:
[![enter image description here][2]][2]
It's confusing because Hull is referring to the market conventions before the ["Big Bang"][3]. This is no longer true, but Hull, or, more precisely, his ghostwriters, never updated his boo... |
Apparently, you refer to this passage from Prof John C. Hull [(11th edition, 2021)][1]:
[![enter image description here][2]][2]
It's confusing because Hull is referring to the market conventions before the ["Big Bang"][3]. This is no longer true, but Hull, or, more precisely, his ghostwriters, never updated his boo... |
I am not 100% sure, but I think taking a close look at one leverage ETF, it's NAV and holdings may help.
Let's take an example: [TQQQ - UltraPro QQQ][1] (which is a 3x leveraged NASDAQ ETF)
If I [download it's NAV as of today it is][2]: $12,266,192,450.00.
Now download the holdings (pasted below).
If I ... |
Apparently, you refer to this passage from Prof John C. Hull [(11th edition, 2021)][1]:
[![enter image description here][2]][2]
It's confusing because Hull is referring to the market conventions before the ["Big Bang"][3]. This is no longer true, but Hull, or, more precisely, his ghostwriters, never updated his boo... |
Apparently, you refer to this passage from Prof John C. Hull [(11th edition, 2021)][1]:
[![enter image description here][2]][2]
It's confusing because Hull is referring to the market conventions before the ["Big Bang"][3]. This is no longer true, but Hull, or, more precisely, his ghostwriters, never updated his boo... |
Apparently, you refer to this passage from Prof John C. Hull [(11th edition, 2021)][1]:
[![enter image description here][2]][2]
It's confusing because Hull is referring to the market conventions before the ["Big Bang"][3]. This is no longer true, but Hull, or, more precisely, his ghostwriters, never updated his boo... |
I've read even in recent papers, and on page 21 of the book ["The Volatility Surface"][1] by Jim Gatheral (2006), all the debate over whether to reflect or truncate negative variances whilst simulating the Heston process and the subsequent ramifications of what doing that entails, etc.
[![enter image description her... |
This is a very basic question/comment regarding the way that the LOOP is stated in the book *"Dan Stefanica - A Primer for the Mathematics of Financial Engineering"*. The proposition goes as follows:
[![enter image description here][1]][1]
[1]: https://i.stack.imgur.com/QqLyF.png
What confuses me is that t... |
This is a very basic question/comment regarding the way that the LOOP is stated in the book *"Dan Stefanica - A Primer for the Mathematics of Financial Engineering"*. The proposition goes as follows:
[![enter image description here][1]][1]
[1]: https://i.stack.imgur.com/QqLyF.png
What confuses me is that t... |
For an option with price C, the ΔC, with respect to changes of the underlying asset price S and volatility σ (first-order approximation), is given by
$\Delta C=\delta \Delta S+\nu\Delta\sigma$,
where δ, and ν are respectively the delta, and vega greeks.
Assuming the asset S and the volatility σ as normal and i... |
Apparently, you refer to this passage from Prof John C. Hull [(11th edition, 2021)][1]:
[![enter image description here][2]][2]
It's confusing because Hull is referring to the market conventions before the ["Big Bang"][3]. This is no longer true, but Hull, or, more precisely, his ghostwriters, never updated his boo... |
As the title suggests, what is the difference between calibrating an option pricing model (say the Heston model) to market option prices instead of computing their implied volatilities using Black-Scholes and subsequently calibrating the Heston parameters to them?
I assume since "Implied volatilities behave 'better'... |
As the title suggests, what is the difference between calibrating an option pricing model (say the Heston model) to market option prices instead of computing their implied volatilities using Black-Scholes and subsequently calibrating the Heston parameters to them?
I assume since "implied volatilities behave 'better'... |
Apparently, you refer to this passage from Prof John C. Hull [(11th edition, 2021)][1]:
[![enter image description here][2]][2]
It's confusing because Hull is referring to the market conventions before the ["Big Bang"][3]. This is no longer true, but Hull, or, more precisely, his ghostwriters, never updated his boo... |
Say that I have a historical series of yields and no coupon data because these yields come from a generic government bond, hence an constant maturity interpolation.
How would I go about computing the daily returns of the bond, without having information on the coupon?
Thanks |
Can one compute the total return of a fixed-rate bond without having the coupon? |
Apparently, you refer to this passage from Prof John C. Hull [(11th edition, 2021)][1]:
[![enter image description here][2]][2]
It's confusing because Hull is referring to the market conventions before the ["Big Bang"][3]. This is no longer true, but Hull, or, more precisely, his ghostwriters, never updated his boo... |
Say that I have a historical series of yields and no coupon data because these yields come from a generic government bond, hence an constant maturity interpolation.
How would I go about computing the daily returns of the bond, without having information on the coupon? |
I am trying to understand what the "correct"/optimal way of betting is using the Kelly Criterion but for bets that don't immediately give an outcome.
For example, I have 100 dollars. I get a buy signal, I run Kelly Criterion and it says optimal is 20% bet, so I put 20 dollars on that buy signal. Now, let's say in th... |
Kelly Criterion - if I bet 20% of my bankroll, outcome is undecided and I need to make another 10% bet - is 2nd bet 10% of total or of remaining 80%? |
I was reading [this article](https://www.globalcapital.com/article/28mwrr0lap7g5gyuamznl/derivatives/option-prices-imply-a-probability-distribution), when I came across this text:
> Without using a complex options pricing model, one can use intuition
> to translate option prices into implied probabilities. For inst... |
I'm working with a multi-asset worst of model and the outputs are FV,d1,d2,g1,g2,v1,v2,cega, theta.
Its easy to assign proper delta, gamma, vega to the respective asset1 & asset2, but how would fair value, cega, and theta be properly split? Is it best to weight these parameters based off the total delta?
for exa... |
How to properly weight fair value, theta, and cega in a multi asset model? |
I am trying to solve the problem: Given two assets X and Y that follow a log normal distribution with volatility $\sigma_1$ and $\sigma_2$ respectively and with correlation $\rho$, what is the volatility of X*Y ?
I tried modelling X and Y as:
$$dX_{t} = X_{t}(\mu dt + \sigma_{1}dW_{t}^{1})$$
$$dY_{t} = Y_{t}(\mu d... |
This is a very basic question/comment regarding the way that the LOOP is stated in the book *"Dan Stefanica - A Primer for the Mathematics of Financial Engineering"*. The proposition goes as follows:
[![enter image description here][1]][1]
[1]: https://i.stack.imgur.com/QqLyF.png
What confuses me is that t... |
I am trying to solve the problem: Given two assets X and Y that follow a log normal distribution with volatility $\sigma_1$ and $\sigma_2$ respectively and with correlation $\rho$, what is the volatility of X*Y ?
I tried modelling X and Y as:
$$dX_{t} = X_{t}(\mu dt + \sigma_{1}dW_{t}^{1})$$
$$dY_{t} = Y_{t}(\mu d... |
Are you familiar with how a futures trading account works? You deposit a certain amount of cash. When you "buy" a future this does not use up any cash, nor is the future shown on your statement as an "asset". However, every day your account loses or gains cash because of mark to market P&L on the futures. To have a sen... |
> I assume since "implied volatilities behave 'better' than prices",
> that would mean that the calibrated model parameters using option
> prices would be more inaccurate?
I'm not quite sure what did you mean by that.
Speaking from a strictly theoretical Black-Scholes framework there is no difference between ca... |
Are you familiar with how a futures trading account works? You deposit a certain amount of cash. When you "buy" a future this does not use up any cash, nor is the future shown on your statement as an "asset". However, every day your account loses or gains cash because of mark to market P&L on the futures. To have a sen... |
I have been thinking about the notion of required return lately. I am not familiar with a formal definition, but I have tried to reason my way towards one. **Please let me know if my approach makes sense** and if it aligns itself with any mainstream finance theory.
* If it does, then I do not believe I am the first... |
How much intraday data do you have / want to consume?
i.e. you could do something like take a snap every d$t$ and then demand that it's monotonic, or make some slightly looser variant of that rule or something (i.e. above a certain percentage of d$t$ time periods are down moves).
You have a ton of flexibility tho... |
From my understanding, I know that we can decompose a long callable bond into a long vanilla bond and short receiver swaption. However, I do not understand, how could I separate or calculate the swaption part?
From what I have learnt, swaption is a option on a fixed-float swap. But a FRN is paying a index rate with ... |
Can someone provide me an intuitive explanation of how discount factors are bootstrapped for SOFR when Swaps are trading with payment delay/ lag (e.g. of 2 business days).
I can intuitively derive the discount factors when the payment lag is zero e.g.
|Trade Date | Value Date | Tenor | Maturity | Swap Rate | Pay... |
In the paper [Buy Rough Sell Smooth][1], on page 5 (8) they define an estimate of the volatility of volatility ν, by setting $log(ν)= β_1/2$. I would like to understand why this should be considered volatility of volatility, as $β_1$ is simply one of the regression terms in the model $log z_2 (ℓ) = β1 + β2 log ℓ ... |
I've just started studying quantitative finance and have had questions closed on this forum for being too basic; if that's the case for this one please let me know a more suitable place to ask.
Assume the lending and borrowing interest rates are both a fixed constant $r$; let $V_K(t,T)$ be the value at time $t$ of b... |
I’m trying to price a call option on EUR/GBP exchange rate and it expires in 1 year. Should I use GBP Libor as foreign risk free rate in order to apply BS formula? The pricing date is 02/21/2023 but in this date there is no 12m GBP Libor https://www.global-rates.com/it/tassi-di-interesse/libor/sterlina-inglese/sterli... |
I am found the [option pricer][1] and the [article][2] with different pricing methods for basket options. I have tried to repeate result from the article with the pricer and Python.
We define the price of a basket of
stocks as the weighted average of the prices of $n$ stocks at maturity $T$
$$
B(T) =\sum^n_{i=1}
... |
I'm starting to teach myself quantitative finance and I've got several questions (**marked in bold**) regarding the replicating portfolio of a security in the binomial model. I'm following, among others, the classical book "*Stochastic Calculus for Finance I: The Binomial Asset Pricing Model*".
First, I'll start wit... |
were wondering If anyone knows how to use rate bonds on Python Quantlib, that have
an ex-coupon period.
For example the link below shows the construction of such a bond in the c++ quantlib
using
FixedRateBond bond(settlementDays, 100.0,
schedule,
std::vector<Ra... |
In JPM's note on variance swaps, on page 29, they say **"... a long variance swap is also long volatility of volatility"**.
In Bennett's book Trading Volatility, on page 115, he says **"... a variance swap has no vol of vol risk"**.
I thought Bennett is correct, that variance swaps do not have vol of vol risk, be... |
Is variance swap long volatility of volatility? |
I'm asking for the curve construction of the discount curve in the case where payment currency and collateral currency are different.
If I refer to BBG, in the case of a USD swap collateralized in EUR, they use the curve N°400 (MBB EUR Coll For USD). How do they construct this curve ? |
pricing in the case where payment currency and collateral currency are different? |
Here are some answers, hope it helps:
Regarding question 1, *Do we need to replicate the derivative security using the underlying security $S$?* I think the answer is related to your other question: *What are the advantages of using the underlying over the rest of securities?*
The reason is that it is the underlyi... |
If both models fit their closed form formulas to market prices, why should I prefer a more complex model? ($\mathbb{Q}$ version has one extra parameter $\lambda$)
Do valuation with dynamics work better under the $\mathbb{Q}$-measure version? |
Say we have the active German government bond future, RXH3 and we wanted to calculate a series of returns for the active contract.
Would we calculate returns on the daily price difference? And if so, what would happen on the roll day? Or would be calculate returns on the Cheapest to Deliver bond?
|
How are SOFR implied vols calculated? Are they normal or log normal?
When we are pricing options with black-76 model, implied volatility must be log-normal as black model assumes log normal distribution of prices. right? Now that we have transitioned away from LIBOR, does SOFR calculates implied volatility which agr... |
How are SOFR implied vols calculated? Are they normal or log normal? |
How much intraday data do you have / want to consume?
i.e. you could do something like take a snap every d$t$ and then demand that it's monotonic, or make some slightly looser variant of that rule or something (i.e. above a certain percentage of d$t$ time periods are down moves).
You have a ton of flexibility tho... |
I believe inflation is greatly affecting my sample data, even when using percent-changes for movements. I have read [this](https://web.archive.org/web/20150112123921/http://www.herc.research.va.gov/resources/faq_a03.asp) post, which recommends the formula ((Current-Base Year CPI) * Price) / (Historical Year CPI) - an... |
In the paper [Buy Rough Sell Smooth by Glasserman and He (2018)][1], on page 5 (8) they define an estimate of the volatility of volatility ν, by setting $log(ν)= β_1/2$. I would like to understand why this should be considered volatility of volatility, as $β_1$ is simply one of the regression terms in the model $... |
In the paper [Buy Rough Sell Smooth by Glasserman and He (2018)][1], on page 5 equation (8) they define an estimate of the volatility of volatility ν, by setting $log(ν)= β_1/2$. I would like to understand why this should be considered volatility of volatility, as $β_1$ is simply one of the regression terms in th... |
Suppose I am a market maker making a market on an S&P ETF. Suppose that I have calculated a fair ETF price of $395. My market therefore is 394.90 (bid) and 395.1 (ask). After my bid is posted I got filled with 10 shares of the ETF. Now I want to hedge this exposure.
Suppose that 1 outstanding ETF share consists of ... |
Apparently, you refer to this passage from Prof John C. Hull [(11th edition, 2021)][1]:
[![enter image description here][2]][2]
It's confusing because Hull is referring to the market conventions before the ["Big Bang"][3]. This is no longer true, but Hull, or, more precisely, his ghostwriters, never updated his boo... |
In the paper [Buy Rough Sell Smooth by Glasserman and He (2018)][1], on page 5 equation (8) they define an estimate of the volatility of volatility ν, by setting $log(ν)= β_1/2$. I would like to understand why this should be considered volatility of volatility, as $β_1$ is simply one of the regression terms in th... |
In the paper [Buy Rough Sell Smooth by Glasserman and He (2018)][1], on page 5 equation (8) they define an estimate of the volatility of volatility ν, by setting $\log(ν)= β_1/2$. I would like to understand why this should be considered volatility of volatility, as $β_1$ is simply one of the regression terms in t... |
FIX has a few fields that do or could contain identifying information for equity option orders, the “[Actionable Identifier][1]” field in particular, although the OCC states [here][2] that
“It will not be visible to the contra party to the trade or any other party.“
Is that true that this field is hidden except d... |
If a market maker wanted to avoid filling option orders from a specific account, what information could they use? |
I am found the [option pricer][1] and the [article][2] with different pricing methods for basket options. I have tried to repeate result from the article with the pricer and Python.
We define the price of a basket of
stocks as the weighted average of the prices of $n$ stocks at maturity $T$
$$
B(T) =\sum^n_{i=1}
... |
The capital asset pricing model (CAPM) is based on mean-variance utility; investors choose their portfolio based only on its mean and variance.
This is an entirely different approach than expected utility maximisation.
You can express the expected utility using its Taylor approximation around the expected wealth,... |
I am preparing a financing model and in the template the EBT calculation is:
*EBT=EBIT - Interest Expense*.
However, I wonder if interest income (from keeping the money on the bank) should be added, i.e. *EBT=EBIT + Interest Income - Interest Expense*?
Many thanks for your explanation! |
Is interest income added to EBIT to calculate EBT? |
In the paper [Buy Rough Sell Smooth by Glasserman and He (2018)][1], on page 5 equation (8) they define an estimate of the volatility of volatility ν, by setting $\log(ν)= β_1/2$. I would like to understand why this should be considered volatility of volatility, as $β_1$ is simply one of the regression terms in t... |
Look at eq.(7), its RHS is explicit expansion of what is defined in LHS of eq.(2) with $q=2$. Now, look at RHS of eq.(2), it defines $E[|Z|^2] \ l^{2H}$. So, $\nu = \sqrt{E[|Z|^2]}$ is volatility by definition. Volatility of what? Right, of $ \log \sigma $.
Alternatively, just look at eq. (3)-(4). In (3) $\sigma_t$ ... |
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