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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78 views

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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79 views

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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1answer
87 views

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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2answers
64 views

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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1answer
168 views

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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1answer
129 views

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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42 views

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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100 views

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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3answers
169 views

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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35 views

Is there no fix to improving portfolio risk estimation under small sample size?

When asked if copula are needed to calculate portfolio Value-at-Risk, it is said that "You can use historical method if you have sufficiently enough data". But actually copula are also ...
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54 views

Is asset return skewness hard to estimate?

The asset mean is known to be difficult to estimate, incurring more estimation error than estimates of asset return variance. How about asset return skewness, is it hard to estimate and how can that ...
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1answer
51 views

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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1answer
79 views

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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1answer
160 views

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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2k views

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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2answers
637 views

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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58 views

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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48 views

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 ...
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1answer
160 views

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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2answers
129 views

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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128 views

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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2answers
120 views

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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140 views

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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66 views

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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1answer
81 views

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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1answer
228 views

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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76 views

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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2answers
212 views

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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1answer
106 views

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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1answer
299 views

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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71 views

mean reversion model estimation - what method?

how can I estimate this model for mean reversion?
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265 views

Model-Free Option Pricing

From Breeden and Litzenberger (1978) and subsequent work, we may find the risk-neutral density $q_{S_T}$ of $S_T$ from European option prices - assuming there are enough traded options (e.g. SPX) via ...
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70 views

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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1answer
213 views

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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17 views

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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1answer
149 views

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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1answer
3k views

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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115 views

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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1answer
156 views

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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25 views

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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402 views

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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2answers
145 views

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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1answer
624 views

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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1answer
377 views

How to compute a single Value-at-Risk (a single quantile) of portfolio returns taking into account correlation between individual returns?

Introduction My goal is to retrieve a single Value-at-Risk (VaR) of a N(0, H) random variable $X$ at the $\alpha \in (0,1)$ confidence level where H is a known d-dimensional positive definite matrix ...
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1answer
487 views

Which program for a DCC-MIDAS model?

for a thesis research, I plan to use a DCC-MIDAS model. The program I was working with (STATA) is not able to run this. Do you have any suggestions as to which program is best for this analysis? ...
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1answer
968 views

How to estimate lambda for Jump-Diffusion Process from Empirical data?

So, I have really no idea how to go about this, but how would I go about choosing sensible parameter values for a basic jump-diffusion simulation, namely $\lambda$ ? For example, getting the average ...
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464 views

Fama French- typical time lag

I have daily prices of 400 stocks for the last 10 years. I have to create each month a portfolio of 20 stocks that minimizes variance with 2 approaches: 1) Estimate volatility with a GARCH(1,1) model ...
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2answers
683 views

Estimation Risk-Neutral Variance of Returns

I am trying to find a method which allows me to estimate $Var_{\mathbb{Q}}\left(\frac{S_{t_{i+1}}}{S_{t_i}}\right)$ where $S$ denotes the price process of an underlying stock (which has to be assumed ...
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114 views

Estimation of right truncated poisson process

I have following problem: Imagine I generate large number of homogenous poisson process sample paths (by sample path I mean a sequence of arrival times $\tau_i$ all with the same intensity. However ...
3
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1answer
209 views

Electric power price parameter estimation

currently I am working through the paper of Tino Kluge "Pricing Swing Options and other Electricity Derivatives" to get a better understanding about the power markets. The author establishes methods ...