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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43 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
150 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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114 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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102 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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52 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 ...
2
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2answers
85 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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65 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 ...
2
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1answer
111 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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61 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 ...
2
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1answer
49 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}...
4
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1answer
4k views

2-step estimation of DCC GARCH model in Python

Embedded in this thread are multiple questions. I'm currently im the process of implementing a DCC GARCH forecast model on quantopian (a python-powered trading platform). The two step consists of ...
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46 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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1answer
90 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
274 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 ...
4
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1answer
231 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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3k views

Estimating Parameters - Vasicek

The Vasicek model for the short rate $r_t$ is given by the SDE $$ dr_t = \alpha(\beta - r_t)dt + \sigma dW_t, $$ where $W_t$ is a Brownian motion under the physical measure. I'd like to compute bond ...
3
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1answer
3k views

Estimating correlation using EWMA

I am using an EWMA model to evaluate the correlation between yearly time series. I know Riskmetrics uses $\lambda=0.94$ for daily data and $\lambda=0.97$ for monthly data. Is there a value ...
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165 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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3answers
4k views

Tools in R for estimating time-varying copulas?

Are there libraries in R for estimating time-varying joint distributions via copulas? Hedibert Lopes has an excellent paper on the topic here. I know there is an existing packaged called copula but ...
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1answer
142 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-...
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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 \...
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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 ...
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1answer
2k 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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1answer
141 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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91 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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95 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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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), ...
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1answer
392 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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6k views

How can I estimate the degrees of freedom for a Student's T distribution?

I am doing research estimating the value at risk for non-normally distributed assets. I need help in the process of estimating the parameters of Student's t distribution and which method to use. I ...
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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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1answer
199 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 ...
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282 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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370 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
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1answer
596 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
264 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 ...
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2answers
503 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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2answers
372 views

How are Quandl monthly S&P500 earnings estimates derived?

Can someone explain how the monthly earnings estimates are derived for S&P500? Quandl sources multpl.com, who state: ...
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1answer
761 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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112 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 ...
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0answers
480 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 ...
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0answers
33 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 ...
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2answers
361 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 ...
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1answer
192 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: ...
3
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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 ...
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50 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 ...
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2answers
343 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 ...
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1answer
402 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 ...
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120 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 ...
3
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1answer
919 views

Log-likelihood of skew-t distribution

I am trying to estimate GARCH models with the use of Hansen's (1994) skew-t distribution. I am using matlab's ARMAX-GARCH-K toolbox, where the log-likelihood is calculated as: ...