Why do we assume a lognormal distribution in option pricing? Ask the class to explain the pluses and minuses to this assumption.Once the downfalls are established,probe students to find out if a better alternative exists.

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The Answer is We assume a lognormal distribution in option pricing because it is a common and convenient way to model the distribution of stock prices. The lognormal distribution is often used because it reflects the fact that stock prices cannot be negative and tend to have positive skewness. Additionally, the lognormal distribution is easy to work with mathematically and has been found to provide a good approximation for the distribution of stock prices in many cases.

However, there are some downsides to assuming a lognormal distribution in option pricing. One major drawback is that the lognormal distribution assumes that stock prices can increase without bound, which may not always be the case in reality. Additionally, the lognormal distribution may not accurately capture extreme events or "fat tails" in the distribution of stock prices, leading to potential underestimation of the risk of extreme price movements.

To address these downsides, students can be prompted to consider alternative distributions such as the normal distribution, which assumes that stock prices follow a symmetric bell-shaped curve, or the more flexible and heavy-tailed distributions such as the Student's t-distribution or the generalized hyperbolic distribution. Each of these alternatives has its own advantages and disadvantages, and the choice of distribution should be based on the specific characteristics of the underlying asset and the goals of the option pricing model. By exploring these alternatives, students can gain a deeper understanding of the assumptions and limitations of option pricing models and the importance of choosing the most appropriate distribution for the specific context.

Why Do We Assume a Lognormal Distribution in Option Pricing