# Questions tagged [distribution]

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### Distribution fitting to data with (isolated) extreme observations

Let's assume I have 2 time series of daily observations of a given experiment. The data of one time series show a very long tail (either side) and in absolute sense the difference between the lowest ...
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### Taking skewness into account when determining daily expected ranges

I use a method to determine daily expected ranges by combining both daily IV and daily realized vol. with different weights to get the expected range, and it worked pretty accurately. However I want ...
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### Probability Distribution of Stock Returns [closed]

Is there a modern theory for the probability distribution of stock returns? It is relatively easy to deduce that under idealized conditions stock returns follow a log normal distribution. One arrives ...
1 vote
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### Implied Distributions from forward prices

I understand that the common way to arrive at an implied distribution for an underlying is through the price of its call options as per the Breeden-Litzenberger formula. I am wondering if its possible ...
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### constrains of return distribution and risk return trade off

Suppose we have a portfolio $V$, we are only allowed to invest in one stock $S$, its price movement follows the geometric brownian motion, i.e. $dS=S(\mu dt+\sigma dW)$. We are allowed to choose ...
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1 vote
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### Determing "fair" implied volatilities for SPX options

I'm trying to come up with a method to calculate fair IVs for SPX options based on historical data. I can't find much information on this so here's how I've thought to do it: Determine a metric for ...
60 views

### Taking a set of normally distributed random variables as the sample space to fitting an exponential distribution

Disclaimer, this is my first question/interaction in this forum. Let's assume I have random variables that are normally distributed. Then, say I take the observations that are greater than the mean, i....
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1 vote
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### Creating a set of histories that satisfies certain statistics

I'm looking at a download of BlackRock's capital market assumptions, which gives a bunch of statistics, such as expected and quartiles for asset classes' returns for different timeframes, volatilities ...
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### Reconciling Two Claims About Volatility Under Fat Tails

I have read the Wikipedia article on volatility, and Nassim N. Taleb's Incerto, and found two statements attributed to Mandelbrot's views, which appear to be in contradiction. Taleb (who was mentored ...
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### Estimating distribution of rate of return

Let $f[t]$ be the price of a stock at time $t$. We can calculate the rolling rate of return of the stock in a window of length $n$ by computing: $$r[t] = \frac{f[t] - f[t-n]}{f[t-n]}$$ $r[t]$ is ...
572 views

### Probability Distribution at each Simulation Period using Geometric Brownian Motion

I am using the equation $S_t = S_0e^{(\mu-\frac{\sigma^2}{2})t+\sigma\epsilon\sqrt{t}}$ to simulate a financial metric at each $t$, where $t=1$ and $T=5$. Stated in plain English, I am trying to ...
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### non gaussian distributions with higher moments and time scaling properties?

If we assume a portfolio comprised of n asset classes, whose log returns can be modeled with a distribution. I am interested in finding a distribution that: incorporates higher moments (skewness and ...
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1 vote
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### How can I find the distribution function of the following random variables?

Suppose that the random variables $Z_i$ are defined as follows: $$Z_i = D(0, t_i)(R_{i-1} +c)\Delta N,$$ where $D(0, t_i)= \exp\{-\int_{0}^{t_i} r_u du\}$ for which $r_u$ ...
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1 vote
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### Taleb's Black-Swan: interpretation of the exponent

I am reading Taleb's "Black Swan" (revised 2020th edition). In chapter 16 "The Aesthetics of Randomness" he describes the meaning of the exponent in the context of extrapolation. ...
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### Which financial time series have a PDF and/or CDF?

Consider the following types of financial time series for a single publicly-listed stock: Price data Log returns Cumulative returns Each is computed from the item listed before it: log returns are ...
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### Density of a portfolio's returns is the weighted average of asset distributions?

The expected return of a portfolio can be formulated as a weighted average of the constituent assets' returns: $$r_p = w_1 r_1 + w_2 r_2 + \dots + w_N r_N + \epsilon$$ Does it also follow that the ...
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1 vote