Sampling Future Asset Prices Conditional on Current Prices

Summary

The document frames a forecasting problem involving future prices for gold, silver, and the S&P 500. Historical observations are proposed as a basis for modeling their joint distribution, with the central question being how to sample future prices conditional on current prices rather than estimate an unconditional distribution. The author also notes that individual prices might have Pareto distributions.

It provides no fitting procedure, model comparison, or empirical evidence that current price levels predict prices several years ahead. The Pareto suggestion does not specify parameters or explain how to preserve dependence between assets. As presented, this is a research question rather than a tested method; choosing a conditional distribution would require defining the data, forecast horizon, transformations, and dependence structure.

Key ideas

• The problem is to sample a vector of future asset prices given current prices.
• Historical observations could inform a joint distribution across the assets.
• The document suggests Pareto marginals but does not define a fitting or dependence method.
• It offers no evidence that current price levels have predictive power.

Tags

# Sample conditional multivariate random variable?


# Sample conditional multivariate random variable?












There's multivariate random variable, future prices of assets, 5 years from now: $$X = [Gold, Silver, SP500]$$

There's historical prices for $X$ available for last 50 years. It's possible to fit historical prices to get multivariate probability distribution of future prices

$$P(X)$$

How to fit the multivariate conditional probability distribution? To get better prediction, as (let's suppose it is so) the current prices have predictive power for the future prices.

$$P(X|CurrentX)$$

I don't need the distribution itself, just the ability to sample $X$ given $CurrentX$. If that helps the individual prices have Pareto distribution.

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.