The pricing of options
There are two general styles of options: European and American. A European option is an option that cannot be exercised before its expiration date. An American option can be exercised at any point before its expiration date. American options are the most common form of options traded in the market.
The pricing model of the two styles of options is significantly different. Since a European option can only be exercised at its expiration, there exists a closed form calculation for its market price. The common form of modeling for a European option is the Black-Scholes pricing model.
The pricing of American options is complicated by their ability to be exercised at any time, which prevents them having a closed-form pricing model. ...