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Questions tagged [distribution]

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1answer
66 views

Distribution of simple returns vs logreturns

I understand that stock prices are conditionally modeled using a log normal distribution by the relationship $ y_t/y_{t−1}∼logN(μ_{daily},σ^2_{daily})$ $y_t∼logN(log(y_{t-1})+μ_{daily},σ^2_{...
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1answer
227 views

Distribution of realized volatility for stock prices from a GBM

If you generate random stock price paths according to a GBM with daily increments, what will be the distribution of the realized volatility? Assume that the realized volatility is measured over daily ...
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1answer
21 views

A quick and dirty loss distribution and Credit VaR

I need to create a loss distribution for a credit portfolio as the first steps to estimate the portfolio Credit VaR. I have historical monthly account snapshots (payment history) of all accounts ...
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1answer
68 views

How to price a barrier using monte carlo when return distribution is not iid?

this question is actually related to set the stop loss and stop return. Say after a liquidity shock, I want to place two stops, one being stop loss and another being stop return. If I use, say 10 ...
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1answer
242 views

Intensity of Exponential Distribution

How do I show the following: Suppose $\lambda=-\frac{S'(x)}{S(x)}$, where $S(x)=1-F(x)$ is survival probability. Show that $\lambda$ is the intensity of the exponential distribution with cdf $F(x)=1-e^...
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1answer
102 views

Why do I get this error using ghyp-distribution function?

I want to fit multivariate GH distribution on my data, and then generate simulations for that distribution. Using the instructions given in ghyp package, I wrote following lines of code in R. ...
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1answer
69 views

How to compute Pr(S>100) when S follows Geometric Brownian Motion?

I have been trying to resolve this problem, under (b), but I cannot find the correct answer. For i=1, my ultimate answer (P=1) deviates from the correct answer (P=0.7580). Please let me know whether ...
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0answers
147 views

Arbitrage free smoothing of volatility smile - cubic spline - implementation procedure

I am studying the paper Arbitrage-Free Smoothing of the Implied Volatility Surface, from Matthias R. Fengler (https://core.ac.uk/download/pdf/6978470.pdf). The problem I want to solve is much simpler ...
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0answers
912 views

Fitting Student t-distributions to log-returns

It seems that some tail-risk centric groups are bent on using Paretian and t-distributions to account for tail risk when fitting log-returns. It has been observed, however, that with and without ...
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0answers
74 views

Alternative Method for Determining Option-Implied pdf

As I am refining a pricing model to incorporate skew, and not just ATM volatilities, I need to create random realizations of the underlying consistent with the skew-implied pdf. When searching, one ...
3
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0answers
87 views

Bivariate risk neutral distribution through copula

I want to build a bivariate risk-neutral distribution from two liquid assets (A and B) through the use of a copula. As A and B are liquid, I have the marginal distributions from the market. All I have ...
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0answers
138 views

What is the relation between return volatility and return rank volatility, and how can I control the latter?

I have no experience in finance, but I've been playing around with a virtual portfolio. I'm trying to control the "rank volatility" distribution - that is, the volatility of a stock's daily rank in ...
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0answers
22 views

Convolution of generalized hyperbolic distribution

I have a question concerning the convolution of generalized hyperbolic distributions. Proposition 6.13 of McNeil, Embrechts, Frey states the following: If $X$ has a $d$-dimensional generalized ...
2
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0answers
64 views

$\int_{0}^1W_x(t)dW_y(t)/(\int_{0}^1W_x^2(t)dt)^{1/2}$ normally-distributed?

I have came across the following stochastic integrals: $$\frac{\int_{0}^1W_x(t)dW_y(t)}{(\int_{0}^1W_x^2(t)dt)^{1/2}}$$ which was claimed to be standard normally distributed ($W_x$ and $W_y$ are ...
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0answers
109 views

Gaussian Copula with t margins

I am trying to fit a Gaussian Copula with t margins to my data (log returns of two stocks). It has already worked for a Gaussian Copula with normal margins with: normcopula_dist = mvdc(copula=...
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0answers
21 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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0answers
30 views

Finding the distribution and moments of returns with GARCH models (in R if possible)

I understand the GARCH type models and I know how to fit a model to a time series. But, there is a paper which calculates the moments of the distribution of returns (Variance, Skewness, and Kurtosis) ...
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0answers
54 views

Probability of outlier events for laplace distribution

I've read that the laplace distribution is better for forecasting purposes than the normal distribution due to it better accounting for fat tails. However, when I run the numbers in matlab, laplace ...
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0answers
35 views

Bootstrapping to Judge the Fit of a Sampled Return Distribution

Consider the following: I have sampled yearly stock returns from a specified distribution. What I want to do is compare how well my sampled distribution fits the empirical distribution of yearly ...
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0answers
17 views

Question about Paul Kupiec's “concentrated Bond loss rate distribution”

I wonder if anyone here has read the following paper by Paul Kupiec in which he approximates a loss rate distribution for a portfolio composed of (possibly) concentrated bond positions. https://www....
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0answers
264 views

Probability Integral Transform: Standardisation

I've been applying the probability integral transform as shown here to standardise date for input into a neural network: https://math.stackexchange.com/questions/592076/mapping-cdfs-to-each-other?...
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0answers
146 views

Expected shortfall of stable distribution by Stoyanov

I've been working on calculating parametric ES assuming the returns follow Paretian stable law. Given the four parameters - $\alpha, \beta,\sigma,\mu$- Stoyanov introduces closed form solution of the ...
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0answers
83 views

Interpretation of Skew and Kurtoisis - strategy backtesting

I am working on my dissertation and i would like to provide a nice interpretation of two tables which i will present below. I have 10 portfolio buckets which i sort on 6 different attributes. One of ...
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0answers
66 views

student-t asset path

I am trying to simulate an asset path based on a t-distribution. I found a lot of ressources and the fact that it will be difficult to do a path. But now I changed my Geometric Brownian Motion ...
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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 ...
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0answers
78 views

Cross-sectional moments

I got a seminar topic named Forecasting risk from cross sectional moments? Could at least someone tell me what should I write about and if there is any paper that I could read. Thank you very much in ...
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0answers
87 views

How to choose a window for curve fitting and prediction?

I am using Pareto distribution to fit a serie of survival rates (with least square). My ultimate goal is to use this fitting curve for prediction. Thus I would mainly focus on the tail of the ...
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0answers
30 views

How does CVaR change when the mean and variance of the loss distribution change?

I have a CVaR constraint in my optimization problem and I want to change the mean and standard deviation of loss distribution during each iteration. How can I get the new CVaR based on the old CVaR ...
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0answers
38 views

History to use to fit a gaussian mixture distribution?

I have to model the distribution of past returns for several time horizon using a gaussian mixture distribution. I first build my time series of past returns thanks to a rolling sum of my past log ...
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0answers
255 views

Large deviations theory and extreme value theory

I'll enter into details of both, sooner or later, but for the moment I'm concerned about the differences (and relationships, if any) between these two theories. Can someone give me a brief, but still ...