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Questions tagged [variance]

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3answers
2k views

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 ...
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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.
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1answer
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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?
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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
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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).
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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 ...
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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
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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 + \...
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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 ...
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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}} \...
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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 ...
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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 ...
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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;\...
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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
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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. ...
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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?
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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 ...
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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?
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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. ...
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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)?
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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)...
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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?
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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 ...
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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 ...
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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{\...
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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[...
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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] ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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3answers
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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 ...
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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 ...
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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.
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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^...