Assume a financial instrument which has a (roughly) log-normal price distribution and behaves like a random walk. I would like to generate some possible scenarios for where the price might be tomorrow.
Knowing that the prices are log-normally distributed (and hence skewed, i.e. an increase in price is usually greater in magnitude than a decrease in price), would it be more correct to generate asymmetric scenarios (with equal probability) around today's market price, for ex. by estimating a log-normal distribution based on the historical data? Or would it be more correct to generate symmetric scenarios around today's market price (in a way assuming that the log-returns are normally distributed and hence symmetric)?
Does generating asymmetric scenarios in any way bias my future view of the market, by making me believe that one direction is "more likely" than the other?