What does the Black-Scholes-Merton stock option pricing...

Name: Problem 1, Chapter 15: Options, Futures, and Other Derivatives
Uploaded: 2024-03-10T19:16:10-08:00
Channel: James Kiss
Description: What does the Black-Scholes-Merton stock option pricing model assume about the probability distribution of the stock price in one year? What does it assume about the probability distribution of the continuously compounded rate of return on the stock during the year?

What does the Black-Scholes-Merton stock option pricing model assume about the probability distribution of the stock price in one year? What does it assume about the probability distribution of the continuously compounded rate of return on the stock during the year?

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Key Concepts

Black-Scholes-Merton Model

This model is a fundamental tool in financial economics used to price options. It is built on several assumptions, one of which is the behavior of the stock price and its returns over time. The model’s assumptions about the stock price dynamics enable deriving closed-form solutions, streamlining the complex realities of the financial markets into a tractable mathematical framework.

Lognormal Distribution for Stock Prices

Under the Black-Scholes-Merton model, the stock price in one year is assumed to be lognormally distributed. This means that while the stock prices themselves are not normally distributed, their logarithms are. This assumption captures the idea that stock prices can only be positive and that price changes compound multiplicatively, leading to a skewed distribution for actual prices.

Normal Distribution for Continuously Compounded Returns

The model assumes that the continuously compounded rate of return on the stock is normally distributed. This is a direct result of the logarithm of stock prices being normally distributed, facilitating the mathematical operations needed for option pricing. The normality of returns underlies many statistical methods in finance, simplifying the analysis of risk and return.

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