Analysis of the optimal exercise boundary of American put options with delivery lags

A Mathematical Analysis of the Optimal Exercise Boundary for American Put Options

We study a free boundary problem arising from American put options. In particular we prove existence and uniqueness for this problem and we derive, and prove rigorously, high order asymptotic expansions for the early exercise boundary near expiry. We provide four approximations for the boundary: one is explicit and is valid near expiry (weeks); two others are implicit involving inverse function...

A New Analytical-Approximation Formula for the Optimal Exercise Boundary of American Put Options

On the Optimal Exercise Boundary for an American Put Option

An American put option is a derivative financial instrument that gives its holder the right but not the obligation to sell an underlying security at a pre-determined price. American options may be exercised at any time prior to expiry at the discretion of the holder, and the decision as to whether or not to exercise leads to a free boundary problem. In this paper, we examine the behavior of the...

Optimal exercise boundary for an American put option

The optimal exercise boundary near the expiration time is determined for an American put option. It is obtained by using Green's theorem to convert the boundary value problem for the price of the option into an integral equation for the optimal exercise boundary. This integral equation is solved asymptotically for small values of the time to expiration. The leading term in the asymptotic soluti...

Regularity of the Exercise Boundary for American Put Options on Assets with Discrete Dividends

We analyze the regularity of the optimal exercise boundary for the American Put option when the underlying asset pays a discrete dividend at a known time td during the lifetime of the option. The ex-dividend asset price process is assumed to follow Black-Scholes dynamics and the dividend amount is a deterministic function of the ex-dividend asset price just before the dividend date. The solutio...