Questions tagged [distribution]
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173 questions
0 votes
0 answers
28 views
Understand fit results from a t distribution
I'm trying to understand the results of fitting a t distribution to a sample of data. For some reason the obtained parameters are decimal. Could somebody explain me what does decimal degrees of ...
0 votes
1 answer
58 views
Extension of SkewStudentT with different left and right tail exponents?
I found that daily stock prices have different left ~3 and right ~3.7 tail exponents. The $\text{SkewStudentT}(\mu,\sigma,\nu,\lambda)$ (Hansen and other variants) can't model that, it uses same tail ...
- 467
3 votes
1 answer
168 views
Hill Estimator for SkewStudentT is Biased
Why Hill Estimator for Pareto Tail exponent produces incorrect results for Skewed Student T? The true $\alpha = 4$ yet, yet it estimates left and right as 3 and 5. Or, maybe it's other way around and ...
- 467
2 votes
0 answers
79 views
Skew Student T variants: Azzalini vs Hansen vs Fernandez-Steel
There are 3 common ways to represent Skew Student T Distribution: Azzalini, Hansen, Fernandez-Steel. Are they equally good (flexible?) to represent financial data? I use Azzalini 2014 variant, but ...
- 467
2 votes
0 answers
128 views
Kolmogorov Smirnov test on derivatives market data
If I want to test market data( say volatility or liquidity spreads) for swaptions in a particular currency (eg. USD) for 2 different periods of time and ascertain whether their distribution is more or ...
- 101
1 vote
0 answers
63 views
What is the formula for value-at-risk (VaR) when the asset value follows an exponential distribution, and how can it be derived? [closed]
For example, say an asset value in 10 days follows an exponential distribution with mean $ W_{0} $. What would the formula for the value-at-risk for confidence c and reference level $ W_{0} $ for the ...
- 21
0 votes
1 answer
134 views
Probability distribution of portfolio loss
I was trying to do this exercise, and something doesn't quite add up. We need to calculate,with reference to a time horizon of one year the expected number of defaults and the probability of default ...
- 141
0 votes
0 answers
73 views
Measure to what extent the trades/profit are evenly distributed over time
current situation: I have several trading strategies which are working well. Unfortunately the trades are not evenly distributed over time. In some months I have several trades (so profit increases in ...
1 vote
0 answers
71 views
How to estimate mixture of two normal distributions? With limited data
In finance a mixture of two gaussian models sometimes used. When one normal used to capture the head of the real distribution and another the tail. $$f(x) = \lambda \cdot \mathcal{N}(x \mid \mu_1, \...
- 467
0 votes
1 answer
152 views
Relationship between Beta distribution and its inverse
I am attempting to transform a real world density into risk-neutral density via calibration through the beta distribution. Calibration in this context is transforming the rw density into the rn ...
- 31
0 votes
0 answers
122 views
Peaks and gaps in log-return of XAUUSD 1-minute log-return density
I'm tinkering around a 1-minute XAUUSD data from March 2009-December 2023 to see if I can model it with a log-normal or log-t distribution and I happen to notice some interesting properties in the log-...
0 votes
0 answers
70 views
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 ...
- 11
-2 votes
1 answer
139 views
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
1 answer
269 views
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 ...
- 11
1 vote
0 answers
93 views
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 ...
- 263