What is the distribution of stock returns?
Stock prices are lognormally distributed, and stock returns are normally distributed. The mean of the stock price, and the mean of the returns are obviously completely different things. However, the volatility of the returns is equal to the volatility of the price. (This makes logical sense if you think about the formula for standard deviation.
What are continuous returns and discrete returns models of stock prices?
Continuous returns and discrete returns models of stock prices, An understanding of how volatility affects the net realized returns obtained by an investor, and how the ‘average’ of discrete returns over a period of time can be misleading, How the true returns obtained by an investor are driven lower by the volatility of the discrete returns,
Is the mean of the returns the same as the price?
The mean of the stock price, and the mean of the returns are obviously completely different things. However, the volatility of the returns is equal to the volatility of the price. (This makes logical sense if you think about the formula for standard deviation.
How to model stock returns over one month?
Consider a stock with a starting price of $100 that returns 10% a year, with an annual volatility of 25%. This means the stock’s returns over one month can be modeled as: where ϵ is a random draw from a normal distribution.
10.1.0 Basic Concepts
In real-life applications, we are often interested in multiple observations of random values over a period of time. For example, suppose that you are observing the stock price of a company over the next few months. In particular, let S ( t) be the stock price at time t ∈ [ 0, ∞). Here, we assume t = 0 refers to current time.
Random Processes as Random Functions
Consider a random process { X ( t), t ∈ J }. This random process is resulted from a random experiment, e.g., observing the stock prices of a company over a period of time. Remember that any random experiment is defined on a sample space S. After observing the values of X ( t), we obtain a function of time such as the one showed in Figure 10.1.
What are the two assets that depend on the valuation of a stock?
The two assets, which the valuation depends upon, are the call option and the underlying stock . There is an agreement among participants that the underlying stock price can move from the current $100 to either $110 or $90 in one year and there are no other price moves possible.
Why is Black Scholes used in pricing options?
In a competitive market, to avoid arbitrage opportunities, assets with identical payoff structures must have the same price. Valuation of options has been a challenging task and pricing variations lead to arbitrage opportunities. Black-Scholes remains one of the most popular models used for pricing options but has limitations. 1
Introduction
It would be great if we can precisely predict how stock prices will change in near or far future. We would be rich, but it is almost impossible to create exact predictions. There are so many factors involved in the movement of stock prices that are hard to model. Human psychology is one of them.
Content
I use E.ON’s stock prices as an example throughout the article when explaining the related concepts. E.ON is an electric utility company based in Germany and it is one of the biggest in Europe. I retrieve its stock prices (in Euros) from Xetra Exchange through Python package of Quandl.
Conclusion
In this article, we learned how to build a simulation model for stock prices using Geometric Brownian Motion in discrete-time context. Below is the full code. When you put your authorization token taken from Quandl after your registration and install the required Python packages, you can use the code right away.