American Option Definition
An American option refers to an option (either put or call option) that can be exercised before and at its expiration date. Usually, options have maturity dates at which they can be exercised by holders, both the European and American options are good examples.
Unlike the European option which holders can only exercise at maturity dates, the American options can be exercised before the maturity date and at the time of maturity. In most options, the option price is determined by the price movement of the underlying asset which can be upward or downward movement. If a holder feels exercising option at a time before its maturity is the best decision, it is permissible in the American option.
A Little More on What is an American Option
An American option is a derivative contract where the contract can be redeemed or exercised during the life of the option or at its maturity time. This means that an option holder or investors have the right to exercise the option at any time before and at the expiration date. Typically, American options are given more value than the European counterpart, which can only be exercised at the maturity time. When investors choose to exercise their options early, they pay a premium.
Oftentimes, people mistake American and European options for geographic locations, it is important to know that these names are unrelated to geographical locations.
American Call Option
The American Call Option allows an investor to exercise the option at any time, up to the maturity date. This means the investor is left to decide the most favorable time that the option should be exercised. For instance, investor A purchased a call option on Company XYZ, if the expiration date is October 2019, the investor has the right to exercise the option at a date prior to October and in October. This right helps investors avoid their call option from being worthless or out-of-the-money.
American Put Option
An American put option is the opposite of the call option. However, in both options, holders have the right to exercise the option before or at the expiration date. An investor that purchases a put option is not required to wait till expiration before exercising the option as obtainable in the European option.
When to Exercise Early
Naturally, exercising an option at its expiration date is cost-effective because investors are not required to pay a premium before exercising the option. In an American Option, however, investors that choose to exercise early need to pay a premium. This premium makes early exercising of options less rampant in the American option.
There are two major situations that make investors exercise early, these are;
- When a call is an in-the-money option.
- When a put is an in-the-money put.
Reference for “American Option”
Academics research on “American Option”
Efficient analytic approximation of American option values, Barone‐Adesi, G., & Whaley, R. E. (1987). Efficient analytic approximation of American option values. The Journal of Finance, 42(2), 301-320. This paper provides simple, analytic approximations for pricing exchange‐traded American call and put options written on commodities and commodity futures contracts. These approximations are accurate and considerably more computationally efficient than finite‐difference, binomial, or compound‐option pricing methods.
The pricing of the American option, Myneni, R. (1992). The pricing of the American option. The Annals of Applied Probability, 1-23. This paper summarizes the essential results on the pricing of the American option
American option valuation: new bounds, approximations, and a comparison of existing methods, Broadie, M., & Detemple, J. (1996). American option valuation: new bounds, approximations, and a comparison of existing methods. The Review of Financial Studies, 9(4), 1211-1250. We develop lower and upper bounds on the prices of American call and put options written on a dividend-paying asset. We provide two option price approximations, one based on the lower bound (termed LBA) and one based on both bounds (termed LUBA). The LUBA approximation has an average accuracy comparable to a 1,000-step binomial tree with a computation speed comparable to a 50-step binomial tree. We introduce a modification of the binomial method (termed BBSR) that is very simple to implement and performs remarkably well. We also conduct a careful large-scale evaluation of many recent methods for computing American option prices.
An analysis of a least squares regression method for American option pricing, Clément, E., Lamberton, D., & Protter, P. (2002). An analysis of a least squares regression method for American option pricing. Finance and Stochastics, 6(4), 449-471. Recently, various authors proposed Monte-Carlo methods for the computation of American option prices, based on least squares regression. The purpose of this paper is to analyze an algorithm due to Longstaff and Schwartz. This algorithm involves two types of approximation. Approximation one: replace the conditional expectations in the dynamic programming principle by projections on a finite set of functions. Approximation two: use Monte-Carlo simulations and least squares regression to compute the value function of approximation one. Under fairly general conditions, we prove the almost sure convergence of the complete algorithm. We also determine the rate of convergence of approximation two and prove that its normalized error is asymptotically Gaussian.
Operator splitting methods for American option pricing, Ikonen, S., & Toivanen, J. (2004). Operator splitting methods for American option pricing. Applied mathematics letters, 17(7), 809-814. We propose operator splitting methods for solving the linear complementarity problems arising from the pricing of American options. The space discretization of the underlying Black-Scholes Scholes equation is done using a central finite-difference scheme. The time discretization as well as the operator splittings are based on the Crank-Nicolson method and the two-step backward differentiation formula. Numerical experiments show that the operator splitting methodology is much more efficient than the projected SOR, while the accuracy of both methods are similar.