Overview

The most basic option with a non-linear payoff are the plain vanilla calls and puts. The original Black-Scholes framework was designed to price these basic types.

Call

A call on an asset (such as a stock) is a contract where the purchaser has the right to purchase the asset at some future date (the maturity) at a specified price (the strike price).

As an example, a call might be the right purchase a stock at $100 1 year in the future. If the stock is currently trading at $100, the payoff of the call in 1 year would look like. If the asset falls below $100, the call expires worthless, and the payoff is a negative amount (the upfront price paid for the option). Otherwise, the payoff is equal to

Put

A put is similar to a call, but instead of allowing the holder to buy the underlying asset at the given strike price, it allows the holder to sell the asset at the strike price. Of course, at maturity, the put is only valuable if the underlying asset price is higher than the strike.