# Stock option trader black scholes calculator

By using the Black Scholes pricing model, it's possible, theoretically, to determine whether the trading price of an option is higher or lower than it's true value: The Black Scholes pricing model is based on a mathematical formula and that formula uses a number of variables or inputs to calculate a fair value for an option. These variables are known as the inputs to the model and they are as follows:. The model also relies on several underlying assumptions for it to work.

These assumptions are as follows:. It should be reasonably obvious that some of these assumptions aren't always going to be valid, and it's very important to recognize this because, it means that there is a distinct possibility that the theoretical values calculated using the Black Scholes model may not be accurate.

There can be no doubt that the development of the Black Scholes pricing model helped make options trading more viable in the eyes of investors, because it helped to change the idea that valuing options was little more than a guessing game. However, there are a couple of key points you should be aware of. First, it isn't absolutely necessary to fully understand the mathematical formula behind the pricing model to be successful at options trading and it's not even necessary that you use it at all.

If you do wish to use it though, you will probably find it easier to use one of the many Black Scholes model calculating tools on the internet rather than carrying out the calculations yourself. You will find that a number of online brokers include such a calculating tool for their customers to use. Second, it should be noted that it should never be considered a precise indicator of the true value of an option, because there are some problems with the assumptions that underpin the model. For example, it assumes that interest rates and the volatility of the underlying security will remain constant during the period of the contract, and this is unlikely to be the case.

It also doesn't take into account the fact that some stocks pay dividends, nor the extra value that American style options have because the holder of them is able to exercise them at any point.

There are, however, variants of the Black Scholes model that can be applied to factor in such issues. If you do plan on using the model as part of your trading strategy, then we strongly suggest that you don't rely upon it to return exact values, but rather theoretical values. These theoretical values can then be used for the purposes of comparing options to assist you in determining what trades you should be making.

However other researchers have added various methods for valuing options with dividends. Usage — The original usage of the model was to calculate a fair value for a call option. The practitioner would plug in a value for each of the main parameters of the model and it would calculate the fair value. The key to using the model has always been to come up with a good estimate of future volatility. The goal of a trader is to buy an option below its fair value and sell it if it is above.

Key Model Assumptions — One important assumption made in the Black Scholes model is that the stock price path follows a log normal random walk. To a large extent this price distribution is a fair model of stock price behavior. However many have pointed out the the distribution of the tails of the stock price changes are fatter than the tails of the log normal.

Estimating Volatility — Most practitioners estimate volatility by calculating the log normal standard deviation of the stock over some recent time period. Then they take the recent volatility and extrapolate it going forward. Some make adjustments based on whether they believe volatility will rise or fall in the future. Most options traders have heard of the Black Scholes Model but few really know much about it. Following are some key bullet points about the model, its use and history:.

Merton published a follow up paper further expanding the understanding of the model. Merton and Scholes received the Nobel Prize for their work. Fisher Black was ineligible because Nobel prizes are not awarded posthumously. Main Contribution — The main contribution of the Black Scholes model was the recognition that two parties with different expectations for the performance of a stock could still agree on a fair price for the option given that it was traded.

The key factor in the valuation was the volatility of the stock. Expectation does not enter into it. Of the listed factors, only Volatility is not known with a high degree of certainty. Volatility is also the most important factor. It should also be mentioned that for stocks which pay dividends the dividends and ex-dividend date are also factors which effect the valuation of options.