Questions tagged [variance]
The variance tag has no usage guidance.
142
questions
-4
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3answers
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Value at Risk - Long/Short position
I have a simple question on the VaR for a portfolio that consists of a long and short position. Say I have a portfolio consisting of the following positions:
long 1000 shares of stock X
short 1000 ...
2
votes
1answer
83 views
Typical SPX variance GARCH(1,1) coefficients
Can someone provide a typical numerical values of GARCH(1,1) coefficients $(\omega,\alpha,\beta)$ for estimating SPX index variance? I will appreciate it if some references could be provided.
-3
votes
1answer
96 views
Derivation of arithmetic variation of a portfolio over multiple periods [closed]
I am very confused on how to derive the attached equation (15).
Would someone be kind enough to walk me through the proof?
1
vote
0answers
260 views
Does delta adjusted exposure make sense for an equity variance swap?
The software vendor that I am using for the calculation of the market risk exposure claim that they cannot compute the delta adjusted of the equity variance swap positions since there is no specific ...
2
votes
1answer
118 views
minimum variance hedge with stochastic processes
Problem set up:
asset S: $$\frac{dS}{S} = \mu dt+\sigma dz$$
Hedged using a forward contract: $F = F(S,t).$
Hedge portfolio: $$P = S+nF$$
I want to find the variance of $dP$, and then minimize that ...
4
votes
1answer
386 views
Portfolio diversification and Sharpe ratio
I have a given trading strategy T and say 3 assets in my universe. The hold time is one day. The trading strategy can general signals for the 3 assets in any given day (so signal can trigger for any ...
5
votes
1answer
449 views
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 ...
3
votes
1answer
208 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 ...
1
vote
1answer
104 views
Variance of returns on a portfolio
This must be very basic, but I don't seem to be able to express the variance of returns on a portfolio in terms of variances-covariance sum of returns of its constituents, which seems to be what is ...
0
votes
0answers
99 views
Units of Risk: Variance vs Standard Deviation
Suppose you are trading two mean-reverting assets, A and B, and that $Covar(A, B) > 0$. You are currently long one unit of A, and are considering buying one unit of B. Compared to the situation ...
6
votes
2answers
791 views
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 ...
0
votes
1answer
81 views
Question regarding the purchase of a Variance Swap
Imagine I price a Variance Swap for an investor and the observation date starts tomorrow and ends in 30 days. If I use dynamic replication with options to price my variance swap do I use options with ...
0
votes
0answers
174 views
Black Variance Surface
I came across black variance surface in quantlib code. For options, usually volatility surface is used for pricing. When you will use variance surface for pricing or any advantages over volatility ...
2
votes
4answers
820 views
Why is variance problematic as a risk measure?
I am looking for a simple example which explains why variance as a risk measure can be problematic (with a long-only portfolio with no options).
1
vote
0answers
245 views
Quantitative Strategy on Variance Swap (master thesis)
I am doing a master thesis on Variance Swap and my dear friend told me I could find some valuable help on the "Quantitative Finance Stack Exchange".
I would like to apologise beforehand, if my ...
1
vote
1answer
1k views
variance of log return
Suppose $C_i$ is i-day's closed price, when drift is small,
we have the close to close variance
$$\sigma^2 =\dfrac{1}{n}\sum\limits^n_{i = 1}\left(\log\left(\dfrac{C_i}{C_{i-1}}\right)\right)^2.$$
If ...
2
votes
1answer
431 views
How do you find variance of a sde?
I know how to find the mean of an SDE: write it on integral form, take derivative, solve a simple ODE.
But what to do when we want a variance?
In my case, $$X_{T + \delta t} = X_T + \int_T^{T + \...
1
vote
1answer
149 views
Minimum variance in a portfolio of call options
My apologies if this question might be better suited elsewhere, however it regards probability and mathematical finance, so I thought I would post it here.
The question is:
Assume a universe where ...
2
votes
2answers
234 views
Variance swap : ok for variance, but where's the square expectation?
Payout of a variance swap at maturity $T$ is proportional to $\left(\frac{252}{N} \sum_{i=0}^{N-1} R_i^2 \right) - \sigma_{\textrm{VS}}^2$ where $R_i \equiv \ln\left( \frac{S_{T_{i+1}}}{S_{T_i}} \...
1
vote
1answer
885 views
How variance dispersion trades become short volatility
From this document, http://quantlabs.net/academy/download/free_quant_instituitional_books_/[JP%20Morgan]%20Variance%20Swaps.pdf, on page 56, it states that
Losses from short correlation through ...
3
votes
0answers
230 views
Variance swap “fast” models
As far as I understand, Variance Swap (VS for short) function as follows :
no payment when entering the contract
at maturity the VS buyer pays a strike $K^2$ and is paid (by the VS seller) the ...
1
vote
1answer
371 views
Hedge variance swapping by vanilla option(constant vega portfolio against underlying asset)
One book said hedging variance swaps
$$I= \sqrt{\dfrac{1}{t}\int^t_0\sigma^2(S,t)}d t$$
by vanilla option，say value $V(S,E;\...
2
votes
1answer
1k views
Variance Ratio Test in R
I would like to conduct a variance ratio test for a financial time series in order to examine whether I can apply the square root rule for the variance with the software R.
I used the Automatic ...
3
votes
1answer
1k views
How to compute the variance of a Long-Short Equity Portfolio?
I am calculating the historical portfolio variance of various long-short equity portfolios. For simplicity, assume the portfolio is long stock A with weight 1.0 and short stock B with weight -0.5. ...
2
votes
2answers
78 views
Why can we neglect the mean in the variance when the time step is very small?
Can anyone tell me why we can neglect the mean in the variance when the time step is very small? See the following picture:
Usually, we choose a time step of one day. Is it small enough?
1
vote
1answer
104 views
Hedging equities portfolios with vol products
Quote
Hedging with variance is not comparable to puts
Due to the lack of convexity of a variance swap hedge, we believe it is best to compare long variance hedges to hedging with futures ...
1
vote
1answer
2k views
What does a negative coefficient of variation mean when calculated from daily returns during a period?
I was wondering what a negative coefficient of variation means when calculated from a set of daily returns for an index?
2
votes
1answer
4k views
Using CAPM to find correlation of two assets with each other
I stumpled upon an exercise in an investments book:
The data below describe a three-stock financial market that satisfies
the single-index model.
...
0
votes
1answer
365 views
Variance Futures Trading
Maybe you can help me with the question about trading on CFE.
With which broker can I trade S&P 500 Variance Futures (VA)?
1
vote
0answers
363 views
compute the risk-neutral expected variance
The formula (3.8) on page 30 of the book THE VOLATILITY SURFACE by Gatheral(2006) introduces a method for computing the expected variance under the risk neutral measure. By denoting $x_t = log(S_t/S_0)...
1
vote
1answer
3k views
What is the difference between overlapping and non overlapping returns [closed]
My prof asked me to make an Variance-Ratio test for overlapping as well as for non-overlapping returns.
What is the difference between overlapping and non-overlapping?
1
vote
2answers
865 views
Forward-Start Option Implied Volatility
I am preparing for an interview on Monday and I came across a practice question which has me stumped.
"The implied volatility of a 1 year option is 20% and the implied volatility of a 2 year option ...
2
votes
1answer
154 views
Risk, required return and expected volatility - what is the relationship?
Return required from risk averse agents from risky investments are proportional to expected return variance. That is from the textbook, you take the portfolio with the highest return to standard ...
8
votes
3answers
4k views
Variance of time integral of squared Brownian motion
I want to calculate the variance of
$$I = \int_0^t W_s^2 ds$$
I was thinking I could define the function $f(t,W_t) = tW_t^2$ and then apply Ito's lemma so I get
$$f(t,W_t)-f(0,0) = \int_0^t \frac{\...
2
votes
1answer
278 views
Variance of a straddle (Black Scholes)
I am trying to determine the variance of the payout of a straddle. For puts and calls individually:
Var[P] = E[P^2] - E[P]^2
Var[C] = E[C^2] - E[C]^2
where:
$$
E[...
8
votes
2answers
3k views
Is the VIX more similar to a volatility swap or a variance swap?
I am reading the following paragraph on the VIX wikipedia article and I find it confusing:
The VIX is calculated as the square root of the par variance swap rate for a 30-day term[clarify] ...
3
votes
2answers
342 views
How to estimate the variance of this stochastic process?
I have an unobservable stochastic quantity $\lambda(t)$, which I analytically know the variance of, that is
$$\text{Var}(\lambda(t))= \frac{\theta \sigma^2}{2\kappa}$$
My goal is to get an estimate ...
1
vote
2answers
110 views
Finding optimal drift, importance sampling, least square monte carlo
I am working with Importance sampling for Least Squared monte carlo and have now problems understanding the implementation of the Robbins-Monro algorithm for finding the optimal drift for finding ...
2
votes
2answers
2k views
GARCH variance vs standard deviation for volatility
in my series of questions related to GARCH and volatility I finally think I've got a decent grasp on it. You guys have been great help clearing up my questions for me.
My next question is just a ...
2
votes
1answer
3k views
What is the unconditional variance for a GARCH model?
I want to use a Matlab script to calculate Heston Nandi GARCH prices. I found an appropriate script online and it asks for the "unconditional variance" as an input. How do I calculate the appropriate ...
2
votes
2answers
134 views
Why would one prefer variance swaps over other instruments?
I understand that an investor who has a view on an underlying's variance would be tempted by a variance swap. But why would one prefer such a contract over another instrument whose value is based on ...
8
votes
3answers
2k views
Why is a variance swap long skew?
I can appreciate the mathematical derivation, but can anyone explain this in a more intuitive sense?
I often come across the mistaken belief that due to the replicating portfolio being long more ...
0
votes
1answer
333 views
GARCH Model Constant in Regression
When regressing a variable on a constant of 1, the coefficient of this constant is the mean. However, when I specified that the residuals follow a GARCH(1,1) model, the coefficient of the constant ...
6
votes
1answer
2k views
Static and Dynamic Hedging of Vol/Var Swaps
Why can a variance swap be perfectly statically hedged whereas a volatility swap requires dynamic hedging?
Possible reference request to the corresponding literature.
3
votes
2answers
424 views
Variance of a Stock price and relationship with volatility
A bit of background. I know that the forward price of a stock (or its expected price) is given by $\mathbb{E}[S_T]=S_te^{(r-q)(T-t)}$. Here, $r$ and $q$ are not constant, but follow a curve. I was ...
1
vote
1answer
158 views
What is the formula for variance in estimating exchange rate?
I was watching this Youtube Video. He used a exchange rates of Euro to Dollar for a few days and apply GARCH(1,1) to get the predicted price. However, I didnt understand variance that he calculates ...
1
vote
1answer
33 views
Are Variances generally stable for any given instrument?
My hesitation, as I look at getting into forecasting based on observed variances, is the nagging question - if variances are not constant per-instrument, is it any good to use the last month or year's ...
0
votes
1answer
943 views
Variance covariance matrix for a portfolio containing bonds also with other asset classes
What should we take for a bond or a zero coupon bond in order to make a variance covariance matrix?
For example:-
Equities - we take the market price
Cash - we take the spot rates
Bonds - Do we take ...
1
vote
1answer
247 views
Calculate control variate for monte carlo simulation
For an exercise I need to calculate $\mathbb{E}[X]$ with a Monte Carlo simulation. I need to use control variate $Y$ with $\text{Var}(Y)=2$ and $\text{Cov}(X,Y)=1$.
I am asked to give the optimale ...
5
votes
2answers
298 views
How to derive this approximation of the risk-neutral expectation of the variance?
On the paper Bollerslev, Tauchen and Zhou (2009 RFS) the authors say about equation (15):
The corresponding model implied risk-neutral conditional expectation
$$E^Q_t(\sigma^2_{r,t+1})=E_t(\sigma^...
