Questions tagged [moments]

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Contribution of an asset's variance, skewness and kurtosis to its portfolio weight?

The mean-variance model is known to assign higher weights to assets with high expected returns and low volatility, meaning that there is a direct link between the asset's weight within the portfolio ...
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0answers
45 views

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 ...
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2answers
226 views

Higher moments of a straddle

Following the logic of Ben-Meir and Schiff (2012) and this question the first, second, third and fourth raw moments of a put are: Similarity, for a call it is as follows: where and ...
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2answers
83 views

Calculate moments given density values

Suppose I have given a finite number of grid values belonging to a probability density function. Moreover, I have the associated values of the density support. For instance: ...
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1answer
33 views

Does standardizing/normalizing asset returns change their skewness and kurtosis?

Asset returns are obtained by log-differencing prices. Standardizing or normalizing/scaling asset returns can be carried out by de-meaning the returns and dividing them by their standard deviation, ...
1
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1answer
67 views

Kurtosis of a straddle

I want to determine the kurtosis of a straddle. My question is closely related with the following topic here. According to the following paper of Ben-Meir and Schiff (2012) the expected value of a ...
2
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1answer
57 views

Cornish Fisher VaR Parameters Calibration

I am trying to calculate Cornish-Fisher (modified VaR), but I am in a trouble because when I am reading some articles, some authors calculate the Cornish-Fisher expansion taking parameters S and K, as ...
4
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3answers
273 views

Any portfolio models not based on asset return moments?

The mean-variance model for portfolio optimization minimizes portfolio risk (covariance matrix), which is the second statistical moment of multivariate asset returns, and sometimes simultaneously ...
2
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1answer
64 views

Show that Riemann integral over BM is gaussian process

I am looking at the process $$X_t = \int_0^tB_udu$$ I know that this is a gaussian process with variance $t^3/3$. However, I would like to manually show the first statement directly. For this, I ...
4
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1answer
129 views

Ito isometry and the covariance of an Ito process

Let $(B_t)_{t \geq 0}$ et $(W_t)_{t \geq 0}$ be two independent Brownian motions and let $f: \mathbb{R} \rightarrow \mathbb{R}$ a deterministic function of time. We define the following process: \...
2
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1answer
50 views

ARMA moments proof

Consider a standard ARMA(1,1) process such as $$x_t - \beta x_{t-1} = \theta u_{t-1} + u_t$$ where $u_t$ is i.i.d. $u_t \sim N(0,\sigma^2)$. I know how to derive mean and variance with stationary ...
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0answers
63 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 $\mathbb{E}[X(T)^n]$ ...
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1answer
232 views

Is positive skewness preferences rational or irrational?

Is positive skewness preference rational or irrational? I have a great trouble understanding why investors should prefer positive skewness over negative one. Sometimes it is argued that preference ...
4
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3answers
270 views

The possible preferences of investors for higher than first 2 moments of return distribution?

Can anyone explain in an intuitive manner a justification for possible preferences of investors for moments of return distribution beyond the first two moments (i.e. mean and variance). For example, ...
3
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0answers
186 views

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 ...
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0answers
87 views

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-...
4
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1answer
2k views

How to price this basket option?

Underlying assets are three global stock index : Eurostoxx 50, HSI, KOSPI 200 Maturity: 36 months with advanced redemption date in every 6 months if prices of indexes satisfy given conditions at each ...
2
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1answer
140 views

Second Moment of Stock Process

I have a stock process which I have decided to model as $$S_T=S_t\exp((r-q-\frac{1}{2}\sigma^2)(T-t)+\sigma(W_T-Wt))-D_T$$ where $D_T$ is a cash dividend at time $T$. This dividend is known. I then ...
4
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0answers
279 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 $N(0,1)$. ...
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0answers
241 views

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{\...