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Questions tagged [moments]

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asymptotic behavior of the pdf constraints due to Roger Lee

In a beautiful paper, http://math.uchicago.edu/~rl/moment.pdf, Roger Lee (2004) shows that implied variance is bounded above by a function linear in the log-strike k. Does anybody know how it ...
stackoverflower's user avatar
5 votes
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394 views

Fourth moment of ARCH(2)

I am studying the ARCH(2) process given by $$X_t = \sqrt{h_t} \varepsilon_t$$ where $$h_t = \alpha_0 + \alpha_1 X_{t-1} ^2 + \alpha_2 X_{t-2} ^2$$ and $\varepsilon_t$ follows $N(0,1)$. ...
KaRJ XEN's user avatar
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Relationship between Implied Volatility Curve Derivatives and the Underlying's Moments

Very probably this question has been posed before, so if someone can pose the link to the relevant question, it would be appreciated. What is the relationship between the implied volatility skew and ...
Hans's user avatar
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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{\...
sets's user avatar
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1 vote
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Comparing standard error asymptotics of standard deviation and mean absolute deviation estimators

I was reading Chapter 4 of Jean-Philippe Bouchaud's book "Theory of Financial Risk and Derivative Pricing: From Statistical Physics to Risk Management" and in section 4.2.2 author was ...
pierce's user avatar
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Saddlepoint approximation when CGF is approximated

According to the saddlepoint approximation, if the cumulant generating function $K(t) = \log E[e^{tX}]$ of the distribution of the random variable $X$ exists and is known, then the density $f(x)$ of $...
Frido's user avatar
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1 vote
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Asian option analytical approximation

I'm trying to approximate the price of an Asian option via the Black-Scholes formula by considering the discrete arithmetic average as a log-normal distribution. $$ A_{T}(n):=\frac{1}{n} \sum_{i=1}^{n}...
Asopanap's user avatar
1 vote
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using moment matching to price spread options (multi asset)

this is my very first question in this forum, after having been a greed follower since a few years, feeling that I need your help in a topic. I need to price a multi asset option that has the ...
TraderBruceWayne's user avatar
1 vote
0 answers
105 views

Analytical formula for the moments of SABR model?

Do analytical formulae exist for the central moments under the SABR model? Assuming dynamics for the forward rate $\{F_t, t \geq 0\}$ under a shifted SABR model. How do we derive $\mathbb{E}[X(T)^n]$ ...
Cavents's user avatar
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Using GO GARCH to optimize a yearly-rebalanced portfolio based on daily data

Is it reliable to optimize portfolio weights on a yearly-rebalanced portfolio based on the Generalized Orthogonal GARCH (GO-Garch) covariance, coskewness, and cokurtosis matrices with the rmgarch R-...
Chen's user avatar
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Is there a modified Bachelier's futures spread option model with adjustments for skew and kurtosis?

I'm looking at pricing a very large deal and while the distribution is kind of "normal," there's quiet a bit of skew and kurtosis that isn't being considered when I use the normal Bachelier'...
Matt's user avatar
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Power options for pricing European claims

I have the following question: Why would somebody be interested in the expression $E[S^\theta]$ for $\theta$ between zero and one. The only thing I know is that this then can be somehow used to ...
Oli Bernet's user avatar