Questions tagged [estimation]
The calculated approximation of a result which is usable even if input data may be incomplete or uncertain.
102
questions
2
votes
0answers
48 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 ...
1
vote
0answers
43 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:
$$S_\mathrm{new} = S + k (S_b − S)...
0
votes
1answer
94 views
maximum likelihood pdf
I am looking at the topic maximum likelihood, and I cannot understand why we set the pdf of $y_{t}$ equal to 1. It is with regards to a OLS example.
The information i got is this:
Model: $y_{t}=\...
3
votes
1answer
87 views
Is there an issue with estimating future returns from autocorrelated returns?
I have a time series $X_t$ generated from a standard GBM
$$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}{...
0
votes
0answers
39 views
how can I get the P-value and simulate the vasicek model in Excel?
I use the solver in Excel to estimate the parameter, the out put is b=0.001153,a=0.095516,sigma=0.0013. I follow the steps at https://www.youtube.com/watch?v=X17cpkkwG_4
The method is the Maximium ...
4
votes
1answer
203 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 ...
0
votes
0answers
57 views
4
votes
0answers
156 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
...
0
votes
0answers
64 views
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 ...
2
votes
0answers
54 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:
$$y_t = \mu + \phi_1 y_{t-6} + \phi_2 y_{t-8} + \theta_1 \...
3
votes
1answer
135 views
Mean-variance portfolio optimization: methods for superior estimates of returns
Leaving aside the aspects related to the estimation of the variance component (all the latest techniques to compute a stable covariance matrix of a given set of assets such as simple shrinkage, Ledoit-...
1
vote
0answers
16 views
fiscal period end date
If a quarterly report is released tomorrow, is there any way to figure out the date the quarterly period ended without manually researching? Such as an API?
I think there is a deadline of 35/60 ...
4
votes
1answer
138 views
Neural Networks for Estimation of Unmarked Private Asset Returns from Market Data
Let's assume it is March and my illiquid private assets portfolio is only 50% marked for 12/31, but I want to get the most accurate estimate of my final return for the quarter ended on 12/31.
What is ...
0
votes
1answer
1k views
MLE error in R: initial value in 'vmmin' is not finite
I am trying to fit an ARIMA(1,1)-GARCH(1,1) model. I changed the starting values a lot but still its returning the same error.
Below is my code which contains two functions ...
1
vote
0answers
82 views
Estimating an GARCH(1,1) model? Long hand method
I am really trying to invest some time to estimate a GARCH(1,1) method, I know there is many statistical packages that will do this for me (Eviews, MATLAB, R), but I am trying to do this by hand, so ...
3
votes
0answers
87 views
How rapidly should estimated volatility and volume change for estimating market impact in small markets?
The cost of market impact is usually modeled as:
$$
\Delta{P} = \delta \sigma (\frac{Q}{V})^{1/2}
$$
Where:
$ \Delta{P} $ is the change in price of the asset caused by the transaction size $Q$
$\...
1
vote
0answers
25 views
Sample distribution of cross-sectional statistics of returns
Currently doing an application of VaR on sample of industry portfolios in the US. I have a matrix of $n$ industry portfolios with $m$ time-series observations. I calculate cross-sectionally (for each ...
1
vote
0answers
253 views
How accurate are Black-Scholes estimates of Vega, Volga, Vanna
Wikipedia provides analytical formulas for calculating Greeks. I can get Delta, Gamma, Theta all from Bloomberg. I need Vega, Volga, Vanna for my research. Should I use these analytical formulas for ...
2
votes
2answers
144 views
Estimating realised gains given growth rate and churn
If one can estimate that the value of an investment portfolio will grow at $g$% per annum, and can estimate that approximately $c$% of that portfolio will be churned each year (sold and reinvested), ...
3
votes
1answer
595 views
How to have an unbiased estimation of the standard deviation when using rolling returns?
I want to estimate the weekly standard deviation of a lognormal process in a usual setup.
$$
\frac{dS}{S} = (\dots) dt + \sigma dW
$$
where $\sigma$ is a constant and $W$ a brownian motion.
The ...
2
votes
1answer
244 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 ...
0
votes
1answer
356 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?
...
1
vote
1answer
694 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 ...
1
vote
0answers
338 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 ...
3
votes
2answers
435 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 ...
6
votes
0answers
110 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
votes
1answer
196 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 ...
2
votes
0answers
454 views
Estimating parameters of the Cox-Ingersoll-Ross model using CLS in R
I'm working on a project where I need to estimate the parameters of the CIR model. In the particular case, the CIR model is used to model cumulated capital calls for a private equity fund.
The data ...
2
votes
0answers
30 views
Understanding pooled VAR model
I encountered a paper by Vuolteenaho (2002) in which he uses pooled VAR model. I have some troubles understanding the idea. He uses firm level variables (log returns, ROE, etc.) and ultimately he ...
3
votes
1answer
94 views
Bond yield to maturity vs current interest yield
How close is yield to maturity usually to current interest yield? Can I use yield to maturity to approximate current interest yield of a bond index?
I am trying to calculate bond index price returns ...
1
vote
0answers
49 views
How to estimate bond price returns via an index?
Let's say I have a corporate bond, for which I know current yield, modified duration, coupon and maturity. I want to estimate how it would have performed under certain market conditions by looking at ...
1
vote
2answers
307 views
How do I estimate the volatiliy of my portfolio with an estimator that requires High, Low, Open, etc
I have obtained the daily returns of my portfolio $R^{port}_t$ using a certain strategy.
Now I want to estimate the realized volatility $\sigma^{port}_t$ using the past 60 days. An obvious way to do ...
0
votes
0answers
118 views
Monte Carlo volatily
I was wondering if we could do a forecast on volatility using monte carlo on an underlying asset. For example EUR/USD :
Simulating a lot of possible paths on 1 year
then calculate the volatilty for ...
1
vote
1answer
168 views
Estimate American-style option delta from similar options
I have a data set which looks something like this, referring to American-style put and call options:
...
1
vote
1answer
360 views
Joint estimation of GARCH models with ARMA terms in the conditional mean: a necessity?
Supposing I am using the following models to forecast conditional volatility of index returns, whereby In-sample data is 1996-2007 and out of sample data is 2007-2012, using GARCH type models.
I have ...
3
votes
1answer
247 views
Estimating implied volatility of an index component with no vanilla options market
There are liquid vanilla options trading on an index of 20 equity components.
The question is how to price an option on one of the index components, knowing that there are no options trading on that ...
0
votes
0answers
94 views
Approximating an SDE for Volatility Estimation
Consider the SDE
$$
dT(t) = ds(t) + a(s(t) - T(t))dt + \sigma dW(t)
$$
where $s(t)$ is a deterministic function that turns out to be the long-term mean (this SDE is used to model daily temperature, so ...
2
votes
1answer
710 views
How to approximate the Carr-Madan decomposition formula?
I have came across the excellent answer.
I'm looking for a dicrete approximation of the Carr-Madan decomposition formula of the function $f(F_T)$ of the terminal futures price by taking a static ...
1
vote
1answer
210 views
Combine EWMA or ARCH model with estimator other than squared returns
Currently I use the EWMA model with the squared logarithmic returns as proxy estimator for the volatility, in order to forecast the volatility one step ahead in an intraday scenario (time frame is a ...
1
vote
1answer
183 views
What volatility estimator for continuous data and small time window?
I want to know which volatility estimator should I use for the following scenario:
I am implementing a market making bot and therefore I need to make estimations of the volatility of the price in ...
3
votes
2answers
357 views
How to estimate the variance of this stochastic process?
I have an unobservable stochastic quantity $\lambda(t)$, which I analytically know the variance of, that is
$$\text{Var}(\lambda(t))= \frac{\theta \sigma^2}{2\kappa}$$
My goal is to get an estimate ...
2
votes
1answer
132 views
Streaming update of the GARCH(1,1) model
Given the estimate of GARCH(1, 1) model parameters I observe the new price. How to update the estimate with this new information.
Let's assume I know the coefficients that maximize the likelihood ...
3
votes
4answers
277 views
Compare two time series with different frequencies
Lets say I have two time series $X_t$ and $Y_{t,q}$. As an examples, lets say $X_t$ is a series that measures year over year changes in the level of output of a good (say number of widgets). So $X_t = ...
1
vote
0answers
235 views
Relationship between in-sample and out-sample periods length
I have two general questions regarding "in-sample fitting vs. out-of-sample backtesting" kind of analyses. Is there any relationship between the length of the data collected for in-sample fitting ($a$)...
1
vote
1answer
676 views
What is Estimation Risk - VAR Backtest
Simple Question. Can someone explain please: What is Estimation Risk in Value at Risk Backtesting
1
vote
1answer
2k views
Package for multivariate Garch Vech model for R?
I`m new to programming and searching a package for R which inherents the estimation for a Vech Garch(1,1). This is a multivariate Garch model which forms the residuals and the covariance matrix from a ...
3
votes
2answers
1k views
Degrees of freedom in calculating significance of GARCH coefficients
I am trying to determine the significance of coefficients of a GARCH model by calculate the p-values using the following Matlab formula:
pvalues = 2*(1-tcdf(abs(t),n-v)),
where $t$ is the t-stat, $...
2
votes
0answers
766 views
How to fit exogenous + GARCH Model In Python?
I am studying a textbook of statistics / econometrics, using Python for my computational needs. I have encountered GARCH models and my understanding is that this is a commonly used model.
In an ...
2
votes
1answer
423 views
GJR-GARCH with $\alpha = 0$ as parameter estimate
I am estimating a GJR-GARCH(1,1) model with variance targeting in R. As data I am using returns on some stock indices. While calculating the GARCH models I obtain $\alpha=0$ for some indices. From ...
1
vote
0answers
1k views
Skewed Generalized Error Distribution's (SGED) pdf
I want to use the SGED distribution of Theodossiou for GARCH estimation, however, I am struggling to understand which is the correct pdf function of the distribution. Let me just say that the ...
