Exponential Probability Distribution Function for Asset Value Difference

This paper presents mathematical formulation for the probability distribution function of asset value difference using canonical ensemble framework. For asset value significantly smaller than the total market value, the distribution is given by exponential function, which depends on market-eta 𝜂. Market-eta is a quantity, which is inversely related to market volatility 𝜎. It is proposed to use range of market-eta values to attain probabilities of profit return, which is always bounded in the range {𝑃_𝑋,𝜂1≤𝑃_𝑋≤𝑃_𝑋,𝜂3}, where 𝑃_𝑋 is the probability of profit returns. This exponential distribution can be efficiently used by traders and firms dealing with small proportion of total market value for risk assessment and hedging.