Questions tagged [variance-gamma]
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To estimate the parameters when only the characteristic function is known to us
Recently I was working with a process named Variance Gamma with Stochastic Arrival (VGSA) and trying to fit this process on a given data.
To obtain VGSA, as explained in Carr et al. [2001], we take ...
11
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1
answer
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From VG and NIG processes to GBM
I would like to find out if it is possible to reduce:
the Madan-Seneta Variance Gamma (VG) model;
the Barndorff-Nielsen Normal Inverse Gaussian (NIG) model
to the standard Black-Scholes through a ...
2
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1
answer
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Characteristic function of CGMY model
I have a basic question about the CGMY model which has characteristic function
$$
\Gamma(-Y_p)\left((M-iu)^{Y_p}-M^{Y_p}\right)+\frac{C_n}{C_p}\Gamma(-Y_n)\left((G+iu)^{Y_n}-G^{Y_n}\right)
$$
whith $...
4
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Can the vega of ITM call-options be negative when the distribution of the underlyings returns is negatively skewed?
While calculating european call option prices, using the variance-gamma model formula provided by Madan, Carr & Chang (1998), I noticed that, holding all other things constant, the value of an ITM ...
8
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2
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751
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Confusion with volatility smiles implied by different models
I am reading a book "The concepts and practice of mathematical finance" by Mark Joshi. In Chapter 18 he discusses the shapes and dynamics of smiles under different models. I do not understand what is ...
0
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1
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107
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Strictly positive variance gamma process?
My goal is to obtain a strictly positive variance-gamma process for the variance process such that,
$$Y_{t+1} = Y_t + \mu\Delta + \sqrt{v_t\Delta}\,\,\varepsilon^y_{t+1}\\
\qquad \qquad\quad \,\,\...
3
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1
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438
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Cumulants of variance gamma with stochastic arrival (VGSA) model
The characteristic function of the VGSA model is defined as a specific parameterization of the characteristic function of the CIR (Cox-Ingersol-Ross mean reverting process) time-change:
$ \mathbb{E}e^...
3
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0
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312
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Risk Neutral Variance Gamma
In the risk neutral version of the Variance Gamma model the stock dynamics are
$$S_T=S_0 e^{ (r-q+\omega)t + X(t;\sigma,\nu,\theta)}$$
with
$$\omega=\frac{1}{\nu}\ln\left(1-\theta \nu - \frac{\...
3
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1
answer
112
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What is the tail index for NIG and/or VG?
...as a function of NIG (Normal Inverse Gaussian) or VG (Variance Gamma) parameters, obviously. I've read that the NIG $\alpha$ is related to the $\alpha$-stable tail parameter, which conversely maps ...
1
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Why doesn't Variance-Gamma process flatten volatility skew for short term options?
The Variance-Gamma (VG) process, from my inexpert point-of-view, seems to nearly perfectly model equity distributions.
For longer term options, there is little to no volatility, skewness, or kurtosis ...
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Closed form european option prices for a variance gamma process with a randomly distributed drift, volatility, and variance rate
Does an option pricing model with a closed form European option price exist that takes into account randomly distributed drift, volatility, and variance rate?
I prefer a modification to the variance ...
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How to simulate stock prices using variance gamma process?
I want to simulate stock prices with the variance gamma process. The model is given by:
$S_T=S_0 e^{ {[}(r-1)T + \omega + z{]}} $
where
$S_0= $ starting value
$T= $ Time
$\omega=\frac{T}{\nu}ln(1-...