Questions tagged [estimation]
The calculated approximation of a result which is usable even if input data may be incomplete or uncertain.
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Estimating instantaneous forward rate without continuous formula
I'm trying to use Hull-White - Vasicek extension short-rate model (1994a).
I need the market forward rate $f^{M}(t)$ which is used in $\theta(t)$, $A(t,T)$ and $B(t, T)$. But data is not continuous: ...
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Stochastic Approximation of CVaR / VaR mini-batch
I know that minimizing MSE in stochastic gradient descent is done by minimizing the MSE estimated from a mini-batch of observations. This implies minimizing the MSE of each observation (I think of a ...
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Estimating Zero Coupon Curve using only Fixed-Coupon bonds available
Today I have been struggling with something that someone here for sure has already encountered. I have a corporate issuer with a set of fixed coupon bonds (maturities between 1.5 to 20+ Years, luckily ...
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Estimating the relationship between short-term intretes rates and 10Y bond yields
On the 16th of March 2020, the Polish Central Bank announced its first-ever round of Quantitative Easing. I am conducting an event study on how this announcement impacted the term structure.
The main ...
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2
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Estimating historical volatility from inconsistent time intervals
Given historical asset prices at consistent time intervals, one can estimate annual volatility as:
SampleStDev(log(Si/Si-1)) / sqrt(interval)
What's the correct way to do this when the time intervals ...
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Estimate market positioning from flow data
I have a set of time series data from a bank that is transaction data from all its clients on a particular currency.
From that data, I attempt to estimate the current "position" of all ...
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2-step system-GMM for static panel models?
Could we use the 2-step system generalized method of moment (GMM) for static regression models? As I know, 2-step system GMM is designed for dynamic panel data models but I see many papers use it for ...
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Market Sentiment Concept Question
I came across an interesting concept question and was curious what other people thought:
Let's say some commodity has a certain return distribution. Now, if one knows that over the next five days, ...
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Find Financial Estimates for NYSE stock from SEC filings?
I want to know in which SEC filing does companies provide their financial estimates for upcoming results?
I am unable to find it in 10-Q/K and 8-k filing.
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How to annualize kurtosis of returns (in simple terms)?
I'm confused by this post on how to annualize kurtosis. I don't understand how to apply it to annualize the kurtosis for my data. In other words, if I evaluated the kurtosis of, say, monthly returns (...
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A Bayesian-Stein based expected return estimator by J.P. Morgan
Please consider the following estimator for the expected returns specified in the paper "Improving on risk parity: Hedging forecast uncertainty" by Peter Rappoport, J.P. Morgan, October 2012....
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Correct terminology - estimate or model?
I am doing some academic work and I'd like to summarise the picture around volatility models. As such, I'd like to refer to several ways of estimating volatility and I'd like to use proper terminology....
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Calibrating OU parameters using AR(1)
I have a mean reverting time series and want to find the Ornstein-Uhlenbeck (OU) parameters of it. I researched the internet and found that we can calibrate the model as a simple AR(1) process,
$$\...
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2
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Estimating the variance of returns with aggregated data
Say I have an asset return time series:
Jan2020: -5%
Feb2020: +5%
Mar2020: -5%
Apr2020: +5%
May2020: -5%
Jun2020: +5%
Q3 2020: +20%
Oct2020: +5
Nov2020: -5
Dec2020: +5
Note that 3 months of data is an ...
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How does yahoo calculate Growth Estimates
Does anyone know how yahoo calculates Growth Estimates for the Next 5 Years (per annum)? For example, I can see 12.64% for AAPL as reporetd in Yahoo finance in https://finance.yahoo.com/quote/AAPL/...
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Mean estimate in portfolio optimization (Markowitz) [duplicate]
The Markowitz mean-variance portfolio optimization problem is to find the optimal allocation, $w_{optimal}$ by solving:
\begin{equation}
w = \mathrm{argmax} \ \mu_{t}^Tw - \frac{\gamma}{2}w^{T}\...
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Entropy-implied volatility requires itself to be calculated?
\begin{align}
H &= \frac{1}{2} \ln (2\pi\sigma^2) + \frac{1}{2}\\
&= \frac{1}{2} \ln (2\pi e \sigma^2)
\end{align}
is the analytical solution for the entropy of a Gaussian random variable, ...
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Estimating constant and local volatility based on passage times
Consider a Brownian motion B_t with constant instantaneous volatility σ and zero drift
where ...
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Do portfolio mean and portfolio variance have probability distributions?
If $X$ is a $T\times N$ matrix of multivariate asset returns,
and $w$ is some optimal portfolio weight vector,
then the portfolio return series is $r_p = X w \in\mathbb{R}^{T}$. This return series ...
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A simple question about VaR estimation
"A 99% VaR using 1,000 (simulation) replications should be expected to have only
10 observations in the left tail, which is not a large number. The VaR estimate
is derived from the 10th and 11th ...
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Question on the use of a limit in a proof
I ran into a step in an argument that I can't quite figure out. It's basically how they use a limit that I don't seem to understand. The context is local-to-unity asymptotics in vector autoregressions,...
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Do EWMA weights remove autocorrelation in asset returns?
I know that the exponentially weighted moving average (EWMA) volatility estimator drapes a decaying weight function over historical returns in order to weight the past according to the decay of their ...
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Why is asset volatility easier to estimate than the asset mean if it contains the mean?
It is well known that the variance of asset returns, $\sigma^2$ (whose square root is volatility), is easier to estimate than the asset mean $\mu$ (also known as expected return) because the mean of ...
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Do the weights of the exponentially weighted moving average (EWMA) have to sum to 1?
I am currently trying to calculate a volatility by using the EWMA model because it is said to yield better results than just using an equal weighted calculation approach. However I am a bit confused ...
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Can you approximate stochastic volatility processes using GARCH processes?
Let me specific. Suppose that you have the following process:
\begin{align}
z_t &= \sigma_t \epsilon_t \\
\sigma_t &= \sigma \exp \left( \frac{v_t}{2} \right)
\end{align}
where $v_t$...
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Correcting high AR(1) coefficients in dynamic Gordon model
I have just finished my thesis on a heterogeneous dividend expectations model applied to the COVID-19 crisis. However after receiving some feedback there is one last issue I want to resolve. I'm using ...
4
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Change of measure
I am looking at the derivation of the Hill estimator. It is $ \bar{F}(x) = 1 - F(x)$ the right tail of the distribution. In the derivation they use the equation
$$ \frac{1}{\bar{F}(u)}\int\limits_u^\...
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Are asset return means difficult to predict because they have no lower bound?
In finance, it is widely known that the volatility of asset returns ($\sigma$) are easier to predict than the expected value of asset returns ($\mu$) , otherwise known as the average return or mean.
...
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Are intraday volatility estimators useful for close-to-close predictions
I am interested in predicting the PnL of a gamma scalping strategy which trades only once per day. For simplicity, let's say we can always trade at the daily close. So, what I need to predict are the ...
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How to predict realised variance?
I am trying to predict the realised daily close to close variance of an equity index.
I checked the literature on volatility forecasting and tried a bunch of things on a dataset for the S&P 500....
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realized correlation estimation
I'm trying to implement the Hayashi - Yoshida estimator for correlation (T. Hayashi, N. Yoshida: On covariance estimation of non-synchronously observed diffusion processes, 2005) and there's something ...
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Beta estimates of Regressions on AR(1) Process
I am currently working through the paper The Myth of Long-Horizon Predictability [1] and I got stuck in reproducing the empirical results in Section 1.4.
It is my understanding that time series of ...
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Maximizing a GARCH likelihood: Good practice on constraining solutions and initial values
I am currently working on option pricing model and I'd like to include a method for maximizing the likelihood of returns under the P measure. I am using the Heston and Nandi (2000) model:
\begin{align}...
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GARCH(1,1)-M MLE optimization with fmincon in R
I've searched thru dozens of papers and did not find in any of them satisfying and enough theoretical answers to my concerns. So I've combined everything what I found below. Please indicate if my ...
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How is it possible that the measurement uncertainty in Kalman Filter is less than 0?
In Euan Sinclair's Option Trading, Pricing and Volatility Strategies and Techniques, it mentions that the true value of the price can be estimated via Kalman Filter:
$$S_\mathrm{new} = S + k (S_b − S)...
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maximum likelihood pdf
I am looking at the topic maximum likelihood, and I cannot understand why we set the pdf of $y_{t}$ equal to 1. It is with regards to a OLS example.
The information i got is this:
Model: $y_{t}=\...
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Is there an issue with estimating future returns from autocorrelated returns?
I have a time series $X_t$ generated from a standard GBM
$$dS_t = \mu S_t dt + \sigma S_t dW_t$$
If I take the log returns over a rolling window of length $l$
$$r^{(l)}_i = \log \left( \frac{S_i}{...
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Arithmetic Brownian Motion in Market Making papers
We often consider high-frequency market maker and suppose that the reference price is the arithmetic Brownian Motion:
$dS_{t} = \sigma d W_t$
What is the difference $t_n - t_{n-1}$ in this case? Is ...
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mean reversion model estimation - what method?
how can I estimate this model for mean reversion?
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ARMA-GARCH estimation with EGB2 distribution
I want to estimate a ARMA-GARCH model by using the EGB2 distribution instead of the normal distribution. The model I want to estimate is:
$$y_t = \mu + \phi_1 y_{t-6} + \phi_2 y_{t-8} + \theta_1 \...
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Methods for superior estimates of returns in m.v. portfolio optimization
Leaving aside the aspects related to the estimation of the variance component (all the latest techniques to compute a stable covariance matrix of a given set of assets such as simple shrinkage, Ledoit-...
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fiscal period end date
If a quarterly report is released tomorrow, is there any way to figure out the date the quarterly period ended without manually researching? Such as an API?
I think there is a deadline of 35/60 ...
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Neural Networks for Estimation of Unmarked Private Asset Returns from Market Data
Let's assume it is March and my illiquid private assets portfolio is only 50% marked for 12/31, but I want to get the most accurate estimate of my final return for the quarter ended on 12/31.
What is ...
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MLE error in R: initial value in 'vmmin' is not finite
I am trying to fit an ARIMA(1,1)-GARCH(1,1) model. I changed the starting values a lot but still its returning the same error.
Below is my code which contains two functions ...
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Estimating an GARCH(1,1) model? Long hand method
I am really trying to invest some time to estimate a GARCH(1,1) method, I know there is many statistical packages that will do this for me (Eviews, MATLAB, R), but I am trying to do this by hand, so ...
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How rapidly should estimated volatility and volume change for estimating market impact in small markets?
The cost of market impact is usually modeled as:
$$
\Delta{P} = \delta \sigma (\frac{Q}{V})^{1/2}
$$
Where:
$ \Delta{P} $ is the change in price of the asset caused by the transaction size $Q$
$\...
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Sample distribution of cross-sectional statistics of returns
Currently doing an application of VaR on sample of industry portfolios in the US. I have a matrix of $n$ industry portfolios with $m$ time-series observations. I calculate cross-sectionally (for each ...
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How accurate are Black-Scholes estimates of Vega, Volga, Vanna
Wikipedia provides analytical formulas for calculating Greeks. I can get Delta, Gamma, Theta all from Bloomberg. I need Vega, Volga, Vanna for my research. Should I use these analytical formulas for ...
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Estimating realised gains given growth rate and churn
If one can estimate that the value of an investment portfolio will grow at $g$% per annum, and can estimate that approximately $c$% of that portfolio will be churned each year (sold and reinvested), ...
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How to have an unbiased estimation of the standard deviation when using rolling returns?
I want to estimate the weekly standard deviation of a lognormal process in a usual setup.
$$
\frac{dS}{S} = (\dots) dt + \sigma dW
$$
where $\sigma$ is a constant and $W$ a brownian motion.
The ...
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