Optimal exercise price of American options near expiry

The American put and European options near expiry, under Lévy processes

We derive explicit formulas for time decay, θ, for the European call and put options at expiry, and use them to calculate analytical approximations to the price of the American put and early exercise boundary near expiry. We show that for many families of non-Gaussian processes used in empirical studies of financial markets, the early exercise boundary for the American put without dividends is ...

Evaluating Approximations to the Optimal Exercise Boundary for American Options

We consider series solutions for the location of the optimal exercise boundary of an American option close to expiry. By using Monte Carlo methods, we compute the expected value of an option if the holder uses the approximate location given by such a series as his exercise strategy, and compare this value to the actual value of the option. This gives an alternative method to evaluate approximat...

Installment Options Close to Expiry

In the last thirty years, there has been a dramatic growth in the trading of options, which are contracts between two parties giving one party the right but not the obligation to partake in a financial transaction with the other party at or before a specified date in the future. The majority of options involve the right to buy or sell an underlying asset at a prescribed price, known as the stri...

Optimal stopping and American options

Approximating Early Exercise Boundaries for American Options

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...