A thermodynamical view on asset pricing

The dynamics of stock market systems was analyzed from the stand point of viscoelasticity, i.e. conservative and nonconservative (or elastic and viscous) forces. Asset values were modeled as a geometric Brownian motion by generating random Wiener processes at different volatilities and drift conditions. Specifically, the relation between the return value and the Wiener noise was investigated. Using a scattering diagram, the asset values were placed into a ‘potentiality–actuality’ framework, and using Euclidean distance, the market values were transformed into vectorial forms. Depending on whether the forthcoming vector is aligned or deviated from the direction of advancement of the former vector, it is possible to split the forthcoming vector into its conservative and nonconservative components. The conservative (or in-phase, or parallel) component represents the work-like term whereas the nonconservative (or out-of-phase, or vertical) component represents heat-like term providing a treatment of asset prices in thermodynamical terms. The resistances exhibited against these components, so-called the modulus, were determined in either case. It was observed that branching occurred in the values of modulus especially in the modulus of the conservative component when it was plotted with respect to the Euclidean distance of Wiener noise, i.e. Wiener length. It was also observed that interesting patterns formed when the change of modulus was plotted with respect to the value of Wiener noise. The magnitudes of work-like and heat-like terms were calculated using the mathematical expressions. The peaks of both heat-like and work-like terms reveal around the zero value of Wiener noise and at very low magnitudes of either term. The increase of both the volatility and the drift acts in the same way, and they decrease the number of low heat-like and work-like terms and increase the number of the ones with larger magnitudes. Most interestingly, the increase either in volatility or in drift decreases the heat-like term but increases the work-like term in the overall. Finally, the observation of the golden ratio in various patterns was interpreted in terms of physical resistance to flow.