# Stock options math. bobbyroel.com - Welcome back to statistics class. Undoubtedly more important that understanding the.

## Stock options math. I got an offer from a late-stage (not sure if that's the right term, but they had a shipping product) non-public startup that included 10, stock options. That sounded like a lot, but I had problems evaluating that number without knowing the shares outstanding. I asked for that figure, and was told it was.

Already have an account? This is an introductory page in Options. If you are unfamiliar with any of the terms, you can refer to the Options Glossary. An option is a financial derivative on an underlying asset, and represents the right to buy or sell the asset at a fixed price, at a fixed time.

As options offer you the right to do something beneficial, they will cost money. This is explored further in Option Value , which explains the intrinsic and extrinsic value of an option. A call option gives the buyer the right to buy the asset at a certain price, hence he would benefit as the price of the underlying goes up. A put option gives the buyer the right to sell the asset at a certain price, hence he would benefit as the price of the underlying goes down.

Options can also be used to hedge against an existing position in the underlying. Options allow you to speculate on the direction and extent of price movements. This would magnify any losses or gains and losses are not limited to the value of the portfolio , which is why options are said to be risky. A call option is the right but not obligation to buy the underlying for a specified price strike price K , on a specified date expiry.

If the underlying fails to rise above the strike price before expiration, then the call expires worthless as it would be cheaper to buy the underlying directly from the market. As there is no upper bound on the price of the underlying, the potential profit of a call is theoretically unlimited.

Let's consider how a call option works. Accounting for the initial cost of the option, your net profit is. As such, all that you have lost is the initial cost premium of the option, so your net profit is. The payoffs net profit of this trade when the stock expires at different values is summarized in the following graph:. When the trade settles, what do you need to do so that you will no longer have a position?

Even though the option value will increase as the stock price increases, it is not necessarily profitable to buy calls even though you believe that the stock price will increase, unless the extent of increase is large enough to compensate for the theta that you are paying. Furthermore, in the stock market, option volatility often decreases as the stock price increases, as it reflects investor confidence in the company.

Hence, buying upside calls when the stock goes up, could still lose you money on vega and theta. Consider buying calls in the following situations: You believe that the underlying will move up more than the implied volatility. You believe that the underlying will move up and that volatility will increase. You believe that the underlying will move up more than the cost of theta. Consider selling calls in the following situations: You believe that the underlying will move down.

You strongly believe that the underlying will not move up significantly. The greeks of a call option are: A put option is the right but not obligation to sell the underlying for a specified price strike price K , on a specified date expiry. If the underlying falls to fall below the strike price before expiration, then the put expires worthless as it would be more profitable to sell the underlying directly in the market.

Since price of stocks do not fall below 0, the potential profit of a put is capped at the strike price. It is the obligation to buy the underlying stock at a specified price at a specified time It is the right to buy the underlying stock at a specified price at a specified time It is the right to sell the underlying stock at a specified price at a specified time It is the obligation to sell the underlying stock at a specified price at a specified time What is a put?

Let's consider how a put option works. As such, all that you have lost is the premium initial cost of the option, so your net profit is. Even though the option value will increase as the stock price decreases, it is not necessarily profitable to buy puts even though you believe that the stock price will decrease, unless the extent of decrease is large enough to compensate for the theta that you are paying.

Consider buying puts in the following situations: You believe that the underlying will move down significantly. You believe that the underlying will move down more than the cost of theta. Consider selling puts in the following situations: You believe that the underlying will move up.

You strongly believe that the underlying will not move down significantly. The greeks of a put option are: Waste less time on Facebook — follow Brilliant. Excel in math and science Master concepts by solving fun, challenging problems. Our wiki is made for math and science Master advanced concepts through explanations, examples, and problems from the community. Used and loved by over 5 million people Learn from a vibrant community of students and enthusiasts, including olympiad champions, researchers, and professionals.

Log in with Facebook Log in with Google or. Join using Facebook Join using Google or. Sign up with Facebook or Sign up manually. Contents Call option Put Option. The payoffs net profit of this trade when the stock expires at different values is summarized in the following graph: It is the obligation to buy the underlying stock at a specified price at a specified time It is the right to buy the underlying stock at a specified price at a specified time It is the right to sell the underlying stock at a specified price at a specified time It is the obligation to sell the underlying stock at a specified price at a specified time.

Call and Put Options. Sign up to read all wikis and quizzes in math, science, and engineering topics. This is likely due to network issues. Please try again in a few seconds, and if the problem persists, send us an email.

More...

1866 1867 1868 1869 1870