Questions tagged [variance]

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133 questions
42 views

Antithetic sampling Monte Carlo

In Peter Jaeckel, Monte Carlo in Finance book, I read the following sentence: Whenever the first realised moment of the underlying variate draws $\{z_i\}$ has a strong impact on the result of the ...
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How can i fit the following regression in R? Why is the coefficient [second Columns] for R so low?

'Rwml' is the monthly log return So the first column is clear, I got nearly the same values, at least the same magnitude. But: If I regress on the variance, my input values are way too low to get a ...
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Vasicek model and spot interest rate parametrised by reversion rate

By solving an SDE I want to derive the analytical results for mean and variance of the process of extended Vasicek model. $$dr(t) = \left(\eta - \gamma r(t) \right)dt + c dX(t)$$ where $\gamma$ ...
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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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How is Kalman Filter used to estimate Term structure Models

I am implementing "The Term Structure of Variance Swap Rates and Optimal Variance Swap Investments" . This paper is using kalman filter to estimate the state and the mean variance and a parameters on ...
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Condition expectation calculation examples and theory [closed]

I want to ask you an advice about reading theory and examples of conditional expectation and conditional variance. I want to have my understanding deeper, because sometimes I can't understand ...
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Expectation and variance of standard brownian motion

Assuming that the price of the stock follows the model $S(t) = S(0) exp ( mt − (σ^2/ 2) t + σW(t) ) ,$ where W(t) is a standard Brownian motion; σ > 0, S(0) > 0, m are some ...
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Spot variance drift consequently to style drift

I am looking for some information on how to spot variance drift for a portfolio in accordance to its benchmarks, Let's say that we have returns of the portfolio $\textbf{P}=(P_1,...,P_t,...,P_n)$ and ...
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Residual Risk and Variance

I've solved part a, but am struggling with b and c. $x_m$ is the market portfolio vector, and I think $T$ should be a diagonal matrix. Any hints greatly appreciated!
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Applying portfolio variance weight based on logarithmic returns?

The expected logarithmic return of a portfolio is calculated as : $$𝐸_p = \log\left(\sum_i w_i e^{R_i}\right)$$ Therefore, I was wondering that how can I apply weight to use with the variance based ...
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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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Options on realized volatility / variance

If I'd like to price options on variance/volatility in the Heston model. Is MC simulation and/or finite difference the only way to do it? Or is there an analytical expression for the probability ...
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Usages of variance swap

I’m interested in variance swap. Considered from its feature, variance swap is used for betting the (historical) volatility of underlying asset. If we use it for hedge tool of Vega or Volga, does it ...
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Terminal Variance in the Heston Model

I am trying to understand the basics of financial models. Random Walk as a model for asset prices. We use gaussian random numbers to generate a Gaussian Random walk. The variance of the terminal ...
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How can I compute a realized variance for raw instead of log returns?

Whenever I read about calculating realized variance, people are using log returns. However, I was asking myself whether it is possible to calculate realized variance also for simple, raw returns. ...
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Criticise GARCH relative to Realized Volatility

I would like to have your opinion about a simple question. While GARCH would be useful to calculate the conditional volatility, and the RV being in some sense the "historical" volatility, what would ...
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What is the difference between volatility and variance?

How do volatility and variance differ in finance and what do both imply about the movement of an underlying?
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Determine GARCH(1,1) from a mean reverting time series recursion

Let $(v_t)$ be a discrete time series of variance obeying a mean-reverting variance process $v_t$, which is actually the discrete version of the Heston model in finance. \begin{align} x_t &= \sqrt{...
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.