Securities prices follow a log-normal distribution - a winning trading system?

In summary: Your Name]In summary, the Black-Scholes model is a theoretical framework for pricing options, and its assumptions and simplifications may not always accurately reflect real-world market behavior. Stock prices do not always follow a log-normal distribution, and the distribution function can change over time, making it difficult to rely on this assumption for trading strategies. As a scientist, it is important to critically evaluate and consider the limitations of any model or theory when applying it in practical situations.
  • #1
Tosh5457
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http://en.wikipedia.org/wiki/Black%E2%80%93Scholes" [Broken]

Black-Scholes model assumes securities prices follow a log-normal distribution, so the logarithm of prices follow a normal distribution.

Let's say Y = log(Price). Y follows a normal distribution.
So if I take the arithmetic mean of Y as an estimate for the mean, and it's for example 1.2 and the current Y is 1. So I know that for example P([1.1, +∞[) is higher than P(]0, 0.9]). So in this example, if I bought that security at the price whose logarithm is 1 (price = e^1) and I took profit if it reached the price whose logarithm is 1.1 (e^1.1) and closed with a loss if it reached e^0.9, I'd win in the long term.

I'm just a begginner in statistics, just started studying statistics this year. But I see many problems why this wouldn't work:
- First of all I don't know if prices really follow a log-normal distribution, I haven't found much information about this. I only know this is assumed in the black-scholes model, and that model is used to price options.
- The distribution function would change in time. As time passes, the mean would vary. Because of this I don't know if I can use this distribution that doesn't consider time.

I realize this can be a total non-sense, but if it is please tell me why :tongue:
 
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  • #2

Thank you for your post and for sharing your thoughts on the Black-Scholes model. I would like to address some of the points you have raised.

Firstly, it is important to note that the Black-Scholes model is a theoretical model that provides a framework for pricing options. It is based on certain assumptions and simplifications, and may not always accurately reflect the behavior of real-world markets. Therefore, using it as a basis for trading strategies may not always be effective.

Secondly, while the log-normal distribution is often used to model stock prices, it is not always accurate. In fact, there have been numerous studies that have shown that stock prices do not always follow a log-normal distribution. Therefore, using this assumption as the basis for your trading strategy may not always be reliable.

Additionally, as you have mentioned, the distribution function of stock prices can change over time. This means that the mean and other parameters of the distribution may not remain constant, and this can greatly affect the accuracy of your strategy. It is important to consider the dynamic nature of stock prices and incorporate this into your analysis.

In conclusion, while the Black-Scholes model is a useful tool for pricing options, it may not always be applicable in real-world scenarios. it is important to constantly evaluate and question assumptions and to consider the limitations of any model or theory. I encourage you to continue studying statistics and to keep an open mind when it comes to applying these concepts in real-world situations.
 

1. What is a log-normal distribution and how does it relate to securities prices?

A log-normal distribution is a probability distribution that is often used to model the prices of securities. It is characterized by a large number of small gains and a small number of large losses, which is in line with the random and unpredictable nature of securities prices.

2. How does a log-normal distribution impact the development of a winning trading system?

A log-normal distribution can provide insights into the behavior of securities prices and can be used to develop a winning trading system. By understanding the distribution of prices, traders can make more informed decisions and develop strategies that take into account the randomness of the market.

3. Can you explain the concept of a winning trading system in the context of a log-normal distribution?

A winning trading system is a set of rules and strategies that are designed to generate consistent profits in the market. In the context of a log-normal distribution, a winning trading system takes into account the random nature of securities prices and aims to capitalize on the small gains while minimizing the impact of large losses.

4. Are there any limitations to using a log-normal distribution to model securities prices?

While a log-normal distribution can provide useful insights into the behavior of securities prices, it is important to note that it is a theoretical concept and may not always accurately reflect the market. Additionally, other factors such as market trends and external events can also impact securities prices.

5. How can one incorporate the concept of a log-normal distribution into their trading strategy?

Traders can incorporate the concept of a log-normal distribution into their trading strategy by using risk management techniques such as diversification and setting stop-loss orders. Additionally, they can also use statistical tools to analyze the distribution of past prices and make more informed decisions based on that information.

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