Yin‐yang volatility in scale space of price‐time: a core structure of financial market risk

Purpose - The purpose of this study is to discover and model the asymmetry in the price volatility of financial markets, in particular the foreign exchange markets as the first underlying applications. Design/methodology/approach - The volatility of the financial market price is usually defined with the standard deviation or variance of the price or price returns. This standard definition of volatility is split into the upper part and the lower one, which are termed here as Yang volatility and Yin volatility. However, the definition of yin‐yang volatility depends on the scale of the time, thus the notion of scale space of price‐time is also introduced. Findings - It turns out that the duality of yin‐yang volatility expresses not only the asymmetry of price volatility, but also the information about the trend. The yin‐yang volatilities in the scale space of price‐time provide a complete representation of the information about the multi‐level trends and asymmetric volatilities. Such a representation is useful for designing strategies in market risk management and technical trading. A trading robot (a complete automated trading system) was developed using yin‐yang volatility, its performance is shown to be non‐trivial. The notion and model of yin‐yang volatility has opened up new possibilities to rewrite the option pricing formulas, the GARCH models, as well as to develop new comprehensive models for foreign exchange markets. Research limitations/implications - The asymmetry of price volatility and the magnitude of volatility in the scale space of price‐time has yet to be united in a more coherent model. Practical implications - The new model of yin‐yang volatility and scale space of price‐time provides a new theoretical structure for financial market risk. It is likely to enable a new generation of core technologies for market risk management and technical trading strategies. Originality/value - This work is original. The new notion and model of yin‐yang volatility in scale space of price‐time has cracked up the core structure of the financial market risk. It is likely to open up new possibilities such as: a new portfolio theory with a new objective function to minimize the sum of the absolute yin‐volatilities of the asset returns, a new option pricing theory using yin‐yang volatility to replace the symmetric volatility, a new GARCH model aiming to model the dynamics of yin‐yang volatility instead of the symmetric volatility, new technical trading strategies as are shown in the paper.