A message from our CEO about the future of Stack Overflow and Stack Exchange. Read now.

# Questions tagged [variance]

The tag has no usage guidance.

142 questions
Filter by
Sorted by
Tagged with
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 ...
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.
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?
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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).
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 ...
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 ...