An option is a derivative contract that permits, but doesn’t obligate, a trader to buy (a call) or sell (a put) a specific underlying instrument at a specific price. An option contract specifies the following:
- a type (call or put)
- the identity and quantity of the underlying security
- the strike price (the price of the underlying security), which is a floor or ceiling as to whether the contract may be exercised
- an expiration date
Exchange-traded options (also called “listed options”) have standardized contracts and are settled through a clearing house with fulfillment guaranteed by the credit of the exchange. Since the contracts are standardized, accurate pricing models are often available. Exchange-traded options, which are available from prime brokers, include:
- stock options
- commodity options
- bond options and other interest rate options
- index (equity) options
- options on futures contracts
Over-the-counter options (OTC options, also called “dealer options”) are traded between two private parties, and are not listed on an exchange. The terms of an OTC option are unrestricted and may be individually tailored to meet any business need. In general, at least one of the counterparties to an OTC option is a well-capitalized institution. Option types commonly traded over the counter include:
- interest rate options
- currency cross-rate options
- options on swaps (swaptions)
The price of an option consists of two components:
- Intrinsic value: the difference between the price of the underlying security and the strike price
- Time value: a calculated amount that decreases with the approach of the expiration date and increases with the difference between the price of the underlying security and the strike price
There are several standard formulas for calculating profits on puts and calls, depending on whether the investor is long or short an option position. A long holder pays a premium to buy an option; the investor on the short side collects the premium. A warrant is basically a call option, but it can have an longer lifetime than does a call option.
Call Option Calculation
This calculation illustrates that a call option has positive monetary value when the underlying instrument has a spot price (S) above the strike price (K). Since the option will not be exercised unless it is “in-the-money”, the payoff for a call option is
Intrinsic value = max[(S − K);0] or, more formally, (S − K) +
where :
That is, the call’s intrinsic value is the strike price less the spot price.
The profit or loss on the call option is the payoff (if any) on the option less the sum of its intrinsic value and the premium paid:
P&L = payoff – (intrinsic value + premium)
The calculation of an option’s premium is extremely complicated and beyond our scope.
Example
‘Trader A’ (call buyer) purchases a call contract to buy 100 shares of ZZZ Corp from ‘Trader B’ (call writer) at $50/share. The current price is $45/share, and ‘Trader A’ pays a premium of $5/share. If the share price of ZZZ stock rises to $60/share right before expiration, then ‘Trader A’ can exercise the call by buying 100 shares for $5,000 from ‘Trader B’ and sell them at $6,000 in the stock market. In practice, Trader A would simply sell the call to collect the payoff of $1,000, unless Trader A wanted to own the actual shares.
Trader A’s P&L can be calculated as follows:
- Sale of 100 stock at $60 = $6,000 (payoff)
- Amount paid to ‘Trader B’ for the 100 stock bought at strike price of $50 = $5,000 (intrinsic value)
- Call option premium paid to Trader B for buying the contract of 100 shares @ $5/share, excluding commissions = $500 (premium)
- ‘Trader A’ P&L = payoff – (intrinsic value + premium) = $6,000 − ($5,000 + $500) = $500
Put Option
The buyer of a put option is betting that the underlying will decrease in price. The calculation is analogous to that used for a call option, except:
Intrinsic value = max[(S − K);0] or, more formally, (K − S) +
where:
That is, the put’s intrinsic value is the spot price less the strike price.
