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Although quite simple connected scatterplots can give interesting new insights on how time series perform together: http://steveharoz.com/research/connected_scatterplot/ As an example: Gold vs. S&P 500 from 1970 till today: The green point marks 1970, the red point is today. Every point is a year, moving vertically upwards means rise in the S&P ...


Let $P$ be the risk-neutral measure. We define the measure $P_S$ such that \begin{align*} \frac{dP_S}{dP}\big|_t &=\frac{S_t}{e^{rt}S_0}\\ &=e^{-\frac{1}{2}\sigma^2 t+\sigma W_t}. \end{align*} Then $\{\widehat{W}_t \mid t \ge 0\}$, where \begin{align*} \widehat{W}_t = W_t -\sigma t, \end{align*} is a standard Brownian motion under the measure $P_S$. ...

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