Log-Normal Distribution

The log-normal distribution is a continuous probability distribution that is often used in finance to model asset prices. It is a skewed distribution, meaning that it has a longer tail on the right side than on the left side. This means that there is a higher probability of observing extreme values (i.e., very high or very low prices) than would be the case with a normal distribution.

The log-normal distribution is derived from the normal distribution by taking the logarithm of the random variable. This transformation has the effect of stretching out the distribution in the tails, making it more skewed.

The log-normal distribution is often used to model asset prices because it can accommodate a wide range of possible outcomes. For example, it can allow for the possibility of negative prices (which is not possible with a normal distribution) and it can also allow for the possibility of very high prices.

The log-normal distribution is also used in finance to model the returns on investments. This is because the returns on investments are often positively skewed, meaning that they have a higher probability of being positive than negative.

The log-normal distribution is a useful tool for financial analysts because it can be used to model a wide range of possible outcomes. However, it is important to remember that the log-normal distribution is only a model and it does not always accurately reflect reality.

Here are some of the key features of the log-normal distribution:

* It is a skewed distribution, with a longer tail on the right side than on the left side.
* It can accommodate a wide range of possible outcomes, including negative prices and very high prices.
* It is often used to model asset prices and the returns on investments.
* It is only a model and it does not always accurately reflect reality.