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Monte Carlo simulation returns not normal distributed

I am generating 100,000 paths of SPX out to 1 year using Euler discretization. I look at how S is distributed for 100,000 paths at the 1 year point and I find it is lognormally distributed. I look at ...
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Stock prices and probability

Lets say that the current price of a security is £245 , $\mu =5%$ and $\sigma=32%$ Assume that the natural logarithm of $\frac{S_{t +\delta t}}{S_t}$ is approximately normally distributed with mean ...
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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?
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Use orthogonal decomposition to compute the optimal return for a CARA investor

Question from Back, 5.8. If all returns are joint normally distributed, then $R_p$, $e_p$, and ε are joint normally distributed in the orthogonal decomposition R= $R_p$ + $be_p$ + ε of any return R ...
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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 ...
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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%. ...
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94 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?