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0
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1answer
49 views

Is the value also log-normally distributed?

Sorry if this is a stupid question. My book assumes many times that $log(1+R)$ is normally distributed, so R is log-normal. But does this also mean that the value process is log-normal? Since ...
0
votes
0answers
11 views

Distribution of the differences of the inverse of the integral of a Gaussian Distribution

I have a time series, $P$, undergoing geometric Brownian motion, which varies between $1$ and $1000$. I difference it $P(t) - P(t-1)$ and can see the differences are distributed according to a ...
2
votes
1answer
41 views

Variability in the Expected Shortfall estimator

Are there any results for calculating the variability in the Expected Shortfall measure. I am looking for Large sample confidence intervals under Normality for Expected Shortfall or calculation of ...
1
vote
1answer
30 views

Can Standardized unexpected earnings be considered a Z-score

According to this wikipedia: http://en.wikipedia.org/wiki/Earnings_surprise, the SUE score is a "standardized" difference between reported earnings and expected earnings. Therefore, can the SUE score ...
6
votes
2answers
210 views

Normally Distributed Returns Become Leptokurtic Due to Compounding

I was running a bunch of simple simulations in excel the other day in excel. Using the NORM.INV(RAND(),0,1) to simulate daily stock returns I noticed that the more compounded the returns, ie, the more ...
2
votes
2answers
456 views

An alternative to the Gaussian distribution to describe/fit market stock returns

After the financial crisis in 2008, many people (including me) don't really believe that stock returns can be described in terms of the normal distribution (Gaussian distribution). But besides the ...
0
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0answers
86 views

Stock Price Question

Can anyone show me how to answer this please? A stock has beta of 2.0 and stock specific daily volatility of 0.04. Suppose that yesterday’s closing price was 95 and today the market goes up by 3%. ...
0
votes
0answers
76 views

BS Implied Volatility under Normal returns

If I use theoretical prices under a normal valuation model, and I estimate their implied volatility using BLACK SCHOLES implied volatility, do I'll get corresponding log normal volatility?
2
votes
1answer
299 views

Interpretation of cross-correlation matrix when one sample distribution is not normal

I am looking at the variance of (log) price changes in securities vs. the amount of social media discussion about them. I'm not interested in building a model. I'm just looking to see if there is a ...
3
votes
1answer
155 views

What is the correct Stutzer index and Sharpe ratio relation, assuming a normal returns distribution?

Assuming the returns distribution is normal, then there is a relation between Stutzer index and Sharpe ratio. However, I found in the following paper 2 different equation: Paper I (page 10-11)‎ ...
3
votes
1answer
200 views

How to design back-testing (validation) for such modified Vasicek model?

Consider a classical Black Scholes model , $$\frac{dS}{S} = \mu dt + \sigma dW$$ , where $dW$ is a Brownian motion, that $W(t_1) - W(t_0) \sim N(0, t_1 - t_0)$. The back-testing strategy is ...
2
votes
1answer
70 views

Creditworthiness indicator for copula one-factor model

In this paper in equation 15 on page 261 dealing with one factor copula model, one is using creditworthiness indicator as one of a variables. It is defined as \begin{equation} Y_c = \sqrt{\rho_c} Z ...
3
votes
2answers
278 views

Transformation to reduce standard deviation without changing median

Consider some negative skew and high kurtosis return time-series $X_t$. I do not know the functional form of the pdf of $X_t$ and have about 150,000 data points. Suppose that I was to create an ...
4
votes
5answers
581 views

In Black-Scholes, why is $\log{\frac{S_{t+\triangle t}}{S_t}} \sim \phi{((\mu - \frac{1}{2}\sigma^2)\triangle t, \sigma^2 \triangle t)}$?

Namely, I dont understand why the mean is $(\mu - \frac{1}{2}\sigma^2)\triangle t$ and not just $\mu \triangle t$. I am aware that it is supposed to represent a lognormal distribution, but I guess I'm ...
1
vote
0answers
78 views

How to trade risk-adjusted returns?

Why does dividing daily returns by daily range eliminates fat tails and results in an (almost) gaussian distribution? And how could that distribution be exploited to enter trades?
1
vote
1answer
235 views

normalized accumulation distribution

I am looking for a way to take an accumulation/distribution indicator and normalize it so I can compare a bunch of stocks with stock prices that have no relationship with each other. EDIT: This ...
2
votes
1answer
615 views

a simpler test for normality given skewness, kurtosis and autocorrelation and size of time series

I typically do a JB (Jarque Bera) test and DW (Durbin Watson) tests for check for normality given skewness, kurtosis and autocorrelation of the data. However this requires a CHI distribution table ...
7
votes
1answer
563 views

Monte carlo portfolio risk simulation

My objective is to show the distribution of a portfolio's expected utilities via random sampling. The utility function has two random components. The first component is an expected return vector ...
1
vote
2answers
764 views

Whats the equation to calculate the area under the curve of a normal distribution, given an upper and lower standard deviation?

Lets say I want to find out the area under the graph of normal distribution curve, between X1=standard deviation of -0.5 and X2 = standard deviation of 0.5. Is there a formula for this? Case study: ...