Questions tagged [moments]

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2
votes
3answers
153 views

Any portfolio theories 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 ...
1
vote
1answer
53 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
votes
1answer
92 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
votes
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 ...
1
vote
0answers
61 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 $\mathbb{E}[X(T)^n]$ ...
4
votes
1answer
224 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
votes
3answers
248 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
votes
0answers
178 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 ...
1
vote
0answers
84 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
votes
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
votes
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
votes
0answers
278 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 $N(0,1)$. ...
3
votes
0answers
235 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{\...