This paper proposes a price model for financial assets using the supply demand relationship, referred to as a supply-and-demand based price (SDP) model. The model demonstrates that stock price volatility is characterized by the downward-sloping demand curve and volume fluctuation rather than another stochastic volatility process often employed in security markets. In particular, we find that the flatter demand curve using an inverse Box-Cox transformation with a positive parameter causes asymmetric volatility, ie, the negative price return-volatility correlation often observed in security markets. The model can also classify this asymmetric volatility into the leverage and feedback effects by examining the relationship between expected price return and volatility. We then characterize the time-varying market price of risk based on the SDP model. Empirical studies using data from a recent decade for many asset classes show that stock market indexes, freight indexes and carbon assets possess positive inverse Box-Cox transformation parameters, resulting in asymmetric volatility, while commodity-related assets tend to have negative parameters, resulting in inverseleverage effects. In contrast, using the long-run data from 1950 to 2009, we illustrate the inverse-leverage effects in security markets as longstanding price-volatility relationships. Finally, we show that the positive risk and return relationship holds if the expected return is positive, regardless of the asset class.