Autoregressive trending risk function and exhaustion in random asset price movement

In this article, we look again at the derivation of Black¿Scholes option value equation. The risk function involved, as we discussed, if looked at more closely, is more complicated than the standard deviation function that people are used to. This observed risk function implies interesting properties of asset price movements in real-world situations and it seems to have the ability to indicate when price move in one direction is `exhausted¿ and a reverse of trend should take place. Therefore, a model based on random walk theory may derive autoregressive trend reversing indicator at particular moments of asset price movements.