A sampling of terms defined includes: active premium, aggregation, angel financing, asset allocation, backwardation, benchmark, bridge loan, capital structure arbitrage, coefficient of determination, commodity option, convertible arbitrage, deferred futures, discretionary trading, distressed debt, enumerated agricultural commodities, extrinsic value, follow-on funding, hedge ratio, interdelivery spread, long short equity, modified value-at-risk, offshore fund, piggyback registration, social entrepreneurship, systematic trading, tracking error, underlying futures contract, venture capital method, and weather premium.

As shown above, a long options trade has unlimited profit potential, and limited risk, but a short options trade has limited profit potential and unlimited risk. However, this is not a complete risk analysis, and in reality, short options trades have no more risk than individual stock trades (and actually have less risk than buy and hold stock trades).
American options can be exercised at any time between the date of purchase and the expiration date. European options are different from American options in that they can only be exercised at the end of their lives on their expiration date. The distinction between American and European options has nothing to do with geography, only with early exercise. Many options on stock indexes are of the European type. Because the right to exercise early has some value, an American option typically carries a higher premium than an otherwise identical European option. This is because the early exercise feature is desirable and commands a premium.
A long options trade is entered by buying an options contract and paying the premium to the options seller. If the market then moves in the desired direction, the options contract will come into profit (in the money). There are two different ways that an in the money option can be turned into realized profit. The first is to sell the contract (as with futures contracts) and keep the difference between the buying and selling prices as the profit. Selling an options contract to exit a long trade is safe because the sale is of an already owned contract.
When you buy an option, the risk is limited to the premium that you pay. Selling an option is the equivalent of acting as the insurance company. When you sell an option, all you can earn is the premium that you initially receive. The potential for losses is unlimited. The best hedge for an option is another option on the same asset as options act similarly over time.

The less time there is until expiry, the less value an option will have. This is because the chances of a price move in the underlying stock diminish as we draw closer to expiry. This is why an option is a wasting asset. If you buy a one-month option that is out of the money, and the stock doesn’t move, the option becomes less valuable with each passing day. Since time is a component to the price of an option, a one-month option is going to be less valuable than a three-month option. This is because with more time available, the probability of a price move in your favor increases, and vice versa.
Basically, you need the stock to have a move outside of a range. A similar strategy betting on an outsized move in the securities when you expect high volatility (uncertainty) is to buy a call and buy a put with different strikes and the same expiration—known as a strangle. A strangle requires larger price moves in either direction to profit but is also less expensive than a straddle. On the other hand, being short either a straddle or a strangle (selling both options) would profit from a market that doesn’t move much.

So, call options are also much like insurance - you are paying for a contract that expires at a set time but allows you to purchase a security (like a stock) at a predetermined price (which won't go up even if the price of the stock on the market does). However, you will have to renew your option (typically on a weekly, monthly or quarterly basis). For this reason, options are always experiencing what's called time decay - meaning their value decays over time. 

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