Expressions of Market-Based Correlations Between Prices and Returns of Two Assets

TL;DR

This paper develops a comprehensive model for calculating correlations between asset prices and returns that accounts for trade volumes and past values, improving accuracy over traditional frequency-based models.

Contribution

It introduces a novel set of expressions for market-based correlations that incorporate trade volumes and historical data, addressing limitations of existing models.

Findings

Correlation expressions depend on statistical moments and trade volumes.

Traditional frequency-based models are a special case of the new model.

Using market-based correlations improves forecasting accuracy.

Abstract

This paper derives the expressions of correlations between prices of two assets, returns of two assets, and price-return correlations of two assets that depend on statistical moments and correlations of the current values, past values, and volumes of their market trades. The usual frequency-based expressions of correlations of time series of prices and returns describe a partial case of our model when all trade volumes and past trade values are constant. Such an assumptions are rather far from market reality, and its use results in excess losses and wrong forecasts. Traders, banks, and funds that perform multi-million market transactions or manage billion-valued portfolios should consider the impact of large trade volumes on market prices and returns. The use of the market-based correlations of prices and returns of two assets is mandatory for them. The development of macroeconomic models and market forecasts like those being created by BlackRock's Aladdin, JP Morgan, and the U.S. Fed., is impossible without the use of market-based correlations of prices and returns of two assets.