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If the prices were not equal, there would be an immediate arbitrage opportunity as you can lock in the forward rate today. Hence the law of one price holds.


There is no conflict here. In the identity, \begin{align*} \frac{1}{(1+r_{02})^2} = E\left(\frac{1}{1+r_{12}}\right)\frac{1}{1+r_{01}}, \end{align*} the expectation is under the year-1 forward measure. However, in the identity \begin{align*} (1+r_{01})E(1+r_{12})=(1+r_{02})^2, \end{align*} the expectation is under the year-2 forward measure. For ...


$$\frac{1}{(1+r_{02})^2} = E\left(\frac{1}{1+r_{12}}\right)\frac{1}{1+r_{01}}$$ Indeed, in the pricing measure, the distribution of $r_{12}$ has to be such that this relation holds. If you look at drift derivations for the LIBOR market model, a lot of work goes into making this sort of equation hold.


you don't need the risk-free rate, it's just the way it's been implemented. It will cancel out when you take the ratio of the forwards.


If you are using Bloomberg then you can pull prices adjusted for corporate actions such as splits, dividends, and other capital adjustments, assuming this meets your needs (i.e. momentum based quant strategies). If you know which global equity indices to track then you can pull the historical constituents to minimise survivorship bias. In Bloomberg, MSCI ...

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