European versus American options

A European option can be exercised only on maturity day, while an American option can be exercised any time before or on its maturity day. Since an American option could be held until it matures, its price (option premium) should be higher than or equal to its European counterpart:

An import difference is that for a European option, we have a close form solution, that is, the Black-Scholes-Merton option model. However, we don't have a close-form solution for an American option. Fortunately, we have several ways to price an American option. Later in the chapter, we show how to use the Binomial-tree method, also called the CRR method, to price an American option.

Understanding cash flows, types of options, rights and obligations

We know that for each business contract, we have two sides: buyer versus seller. This is true for an option contract as well. A call buyer will pay upfront (cash output) to acquire a right. Since this is a zero-sum game, a call option...