Options Pricing

Options are derivative contracts that give the holder the right, but not the obligation, to buy or sell the underlying instrument at a specified price on or before a specified future date. Although the holder (also called the buyer) of the option is not obligated to exercise the option, the option writer (known as the seller) has an obligation to buy or sell the underlying instrument if the option is exercised. Depending on the strategy, option trading can provide a variety of benefits including the security of limited risk and the advantage of leverage. Options can protect or enhance an investor's portfolio in rising, falling and neutral markets. Regardless of the reasons for trading options or the strategy employed, it is important to understand the factors that determine the value of an option. This tutorial will explore the factors that influence option pricing, as well as several popular option pricing models that are used to determine the theoretical value of options. The following is intended as a review of basic option terminology, which can be used as a reference as needed: American Options - An option that can be at any point during the life of the contract. Most exchange-traded options are American. At-the-Money - An option whose strike price is equal to the market price of the underlying security. Call - An option that gives the holder the right to buy the underlying security at a particular price for a specified, fixed period of time. Contract - An option that represents 100 shares of an underlying stock. Covered Call - An option strategy in which the writer of a call option holds a long position in the underlying security on a share-for-share basis. Covered Put - An option in which the writer of a put option holds a short position in the underlying security on a share-for-share basis. Covered Writer - An option seller who owns the option's underlying security as a hedge against the option. Derivative - An investment product that derives its value from an underlying asset. Options are derivatives. Early Exercise - The exercise of an option before its expiration date. Early exercise can occur with American-style options. European Options - An option that can only be exercised during a particular time period just before its expiration. Date - The date that an option becomes void. For listed stock options, it is the Saturday following the third Friday of the expiration month. Holder - An investor who purchases an option and who makes a premium payment to the writer. In-the-Money - An option that has an intrinsic value. A call option is considered in-the-money if the underlying security is higher than the strike price. LEAPS (Long-term Equity Anticipation Securities) - LEAPS are publicly traded options that have expiration dates longer than one year. Listed Option - A put or call option that is traded on an options exchange. The terms of the option, including strike price and expiration dates, are standardized by the exchange. Naked Option - An option position in which the writer of the option does not have an offsetting position in the underlying security, thereby having no protection against adverse prices moves. Open Interest - The total number of outstanding option contracts in the exchange market on a particular day. Option - A financial derivative that gives the holder the right, but not the obligation, to either buy or sell a fixed amount of a security or other financial asset at an agreed-upon price (the strike price) on or before a specified date. Out-of-the-Money - An option with no intrinsic value that would be worthless if it expired on that day. A call option is out-of-the-money when the strike price is higher than the market price of the underlying security. A put option is out-of-the-money when the strike price is lower than the market price of the underlying security. Over-the-Counter - An option that is not traded over an exchange. An over-the-counter option is not subjected to the standardization of terms such as strike prices and expiration dates. Premium - The total cost of the option. An option holder pays a premium to the option writer in exchange for the right, but not the obligation, to exercise the option. In general, the option's premium is its intrinsic value combined with its time value. Put - An option that gives the holder the right to sell the underlying security at a particular price for a specified, fixed period of time. Strike Price - The agreed-upon price at which an option can be exercised. The strike price for a call option is the price at which the security can be bought (prior to the expiration date); the strike price for a put option is the price at which the security can be sold (before the expiration date). The strike price is sometimes called the exercise price. Terms - The collective conditions of an options contract that denote the strike price, expiration date and the underlying security. Underlying Security - The security that is subject to being bought or sold upon the exercise of an option. Writer - An investor who sells an option and who collects the premium payment from the buyer. Writers are obligated to buy or sell if the holder chooses to exercise the option. The price, or cost, of an option is an amount of money known as the premium. The buyer pays this premium to the seller in exchange for the right granted by the option. For example, a buyer might pay a seller for the right to purchase 100 shares of stock XYZ at a strike price of $60 on or before December 22. If the position becomes profitable, the buyer will decide to exercise the option; if it does not become profitable, the buyer will let the option expire worthless. The buyer pays the premium so that he or she has the "option" or the choice to exercise or allow the option to expire worthless. Premiums are priced per share. For example, the premium on an IBM option with a strike price of $205 might be quoted as $5.50. Since equity option contracts are based on 100 stock shares, this particular contract would cost the buyer $5.50 X 100, or $550 dollars. The buyer pays the premium whether or not the option is exercised and the premium is non-refundable. The seller gets to keep the premium whether or not the option is exercised. An option premium is its cost - how much the particular option is worth to the buyer and seller. While supply and demand ultimately determine price, other factors while we discussed, do play a role. he two components of an option premium are the intrinsic value and the time value. The intrinsic value is the difference between the underlying's price and the strike price. Specifically, the intrinsic value for a call option is equal to the underlying price minus the strike price; for a put option, the intrinsic value is the strike price minus the underlying price Intrinsic Value (Call) = Underlying Price – Strike Price Intrinsic Value (Put) = Strike Price – Underlying Price By definition, the only options that have intrinsic value are those that are in-the-money. For calls, in-the-money refers to options where the exercise (or strike) price is less than the current underlying price. A put option is in-the-money if its strike price is greater than the current underlying price. In-the-Money (Call) = Strike Price < Underlying Price In-the-Money (Put) = Strike Price > Underlying Price Any premium that is in excess of the option's intrinsic value is referred to as time value. For example, assume a call option has a total premium of $9.00 (this means that the buyer pays, and the seller receives, $9.00 for each share of stock or $900 for the contract, which is equal to 100 shares). If the option has an intrinsic value of $7.00, its time value would be $2.00 ($9.00 - $7.00 = $2.00). Time Value = Premium – Intrinsic Value In general, the more time to expiration, the greater the time value of the option. It represents the amount of time that the option position has to become more profitable due to a favorable move in the underlying price. In general, investors are willing to pay a higher premium for more time (assuming the different options have the same exercise price), since time increases the likelihood that the position can become profitable. Time value decreases over time and decays to zero at expiration. This phenomenon is known as time decay. An option premium, therefore, is equal to its intrinsic value plus its time value. Option Premium = Intrinsic Value + Time Value