The paper is focused on numerical approximation of early exercise boundary within American put option pricing problem. Assuming non-dividend paying, American put option leads to two disjunctive regions, a continuation one and a stopping one, which are separated by an early exercise boundary. We present variational formulation of American option problem with special attention to early exercise a...

Abstract: The virtue of an American option is that it can be exercised at any time. This right is particularly valuable when there is model uncertainty. Yet almost all the extensive literature on American options assumes away model uncertainty. This paper quantifies the potential value of this flexibility by identifying the supremum on the price of an American option when no model is imposed on...

Option trading forms part of our financial markets. A traded option gives to its owner the right to buy (call option) or to sell (put option) a fixed quantity of assets of a specified stock at a fixed price (exercise or strike price). There are two major types of traded options. One is the American option that can be exercised at any time prior to its expiry date, and the other option, which ca...

American options are different to European style options in that the contract buyer has the right to exercise the option at any time on or before maturity . The freedom to exercise an American option whenever the holder wishes, introduces a boundary problem to solving the Black-Scholes equation popularly used to price the European options. The contract holder will ideally, of course, only exerc...

While American calls on non-dividend-paying stocks may be valued as European, there is no completely explicit exact solution for the values of American puts. We use a technique called randomization to value American puts and calls on dividend-paying stocks. This technique yields a new semiexplicit approximation for American option values in the Black-Scholes model. Numerical results indicate th...