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

Name: Problem 1, Chapter 13: Options, Futures, and Other Derivatives
Uploaded: 2024-03-10T19:16:10-08:00
Channel: James Kiss
Description: What does the Black-Scholes stock option pricing model assume about the probability distribution of the stock price in one year? What does it assume about the continuously compounded rate of return on the stock during the year?

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

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Key Concepts

Normal Distribution of Log Returns

The model assumes that the continuously compounded (or logarithmic) rate of return on the stock is normally distributed. This normality assumption allows for the application of various statistical and analytical techniques, making it possible to derive closed-form solutions for option prices within the Black-Scholes framework.

Lognormal Distribution

Under the assumption of geometric Brownian motion, the future stock price is modeled as being lognormally distributed. This means that while the stock price itself is skewed and bounded below by zero, the logarithm of the stock price follows a normal distribution, which simplifies mathematical treatment in options pricing.

Geometric Brownian Motion

This is the stochastic process that underpins the Black-Scholes model. It describes the evolution of stock prices by combining a deterministic trend with a random component, ensuring that the stock price remains positive over time. It forms the basis for the derivation of both the lognormal distribution of future stock prices and the normal distribution of log returns.

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