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S1 - index with dividend a,

S2 - non-traded asset.

A security pays off $S_{1T}S_{2T}$ upon its maturity

S1 and S2 are uncorrelated and follow geometric brownian motion.

What is the value of security at time t?

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You could assume that the stock price of S2 is the book value of equity divided by outstanding shares (as long as S2 is a stock). From the previous financial statements, you can find the dividend payout ratio, the rate of return from the change in book price and the standard deviation from the sample standard deviation of the book price series. For S1, you can follow the known steps, mentioned in the literature. For defining contract's value, a simple monte Carlo simulation should provide you with the distribution of S1*S2 at any give time t. Calculate the mean price at time t=T and discount it at time t=0. That is the value of the security.

Note: If S2 is not a stock, you should find a similar a theoretical price, given your data availability.

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