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Given monthly returns data, I would like to infill those to get daily returns. Roughly estimates imply that annual volatility is about 1.5x of SPY. One option that came up in my initial research was the Brownian Bridge method.

It seems like I will be able to maintain the performance (using the monthly data points). And the risk profile would need to be modeled properly (let's assume we need to generate 1.5x volatility of SPY and the series should have a correlation of 1 with SPY). Can anybody help with implementation of this? Links to resources would also be highly appreciated!

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  • $\begingroup$ Perhaps it could be done in 2 steps: (1) Compute log(SPX) and then take first differences, multiply them by a 1.5 scaling factor (2) Use these numbers (as if they came out of a random number generator) to drive a Brownian bridge that links the log(XYZ) at end of previous month to its value at end of current month, take exponential to recover the simulated stock price XYZ. $\endgroup$
    – noob2
    Sep 23 at 7:37

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