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2
votes
2answers
51 views

Problem with obtaining densities

For my research I need to obtain a series of densities, however, I am encountering some problems. The first problem is perhaps very simple, but the answer eludes me. Let's say I have an observation ...
0
votes
0answers
35 views

Skewed Generalized Error Distribution in GARCH modelling

I am trying to estimate GARCH models with the use of Theodossiou's (2000) Skewed Generalized Error Distribution. I am modifying matlab's ARMAX-GARCH-K toolbox to calculate this model. I am calculating ...
6
votes
1answer
165 views

Density forecast of a GARCH model

I am currently working on developing a series of density forecasts and I am encountering some problems. I am working on weekly S&P 500 returns and the returns process is described as $r_{t} = ...
2
votes
1answer
104 views

Density of Geometric BM via Fokker-Planck

Attempting to derive density of a GBM (which we know is log-normal) the long way, using the Fokker Planck-equation. Can't figure out where I went wrong - would appreciate a few sets of extra eyes! ...
5
votes
0answers
119 views

“Extract” the density of the underlying, given the implied volatility “surface”

Suppose given implied volatility quotations $\widehat{\sigma}(T_i,K_j)$ of call options on an underlying $S$ for various expiries $T_i$'s and strikes $K_j$'s. I am interested in the following problem ...
3
votes
4answers
1k views

Copulas simply explained

I try to understand the basic idea of copulas, however I am still struggling and hope that someone can help me. I understood that in general a copula is a function which links several marginal ...
0
votes
1answer
35 views

y-axis unity of density probability function

What is the unity/interpretation of the y-axis of a density distribution function? The X-axis is the values of the random variable, the area is the probabilty what about the y-axis ?
2
votes
1answer
522 views

Implied probability density (Question 2 - Applications and Interpretation)

Using the second derivative of the Call-Option-Price one can try to recover the pricing density. Formally: Assuming a constant interst rate $r$ and also not making any assumptions on the model ...