Optimal exercise of American put options near maturity: A new economic perspective

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

Exercise boundary of the American put near maturity in an exponential Lévy model

We study the behavior of the critical price of an American put option near maturity in the exponential Lévy model when the underlying stock pays dividends at a continuous rate. In particular, we prove that, in situations where the limit of the critical price is equal to the stock price, the rate of convergence to the limit is linear if and only if the underlying Lévy process has finite variatio...

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...

Approximate ordinary differential equations for the optimal exercise boundaries of American put and call options

We revisit the American put and call option valuation problems. We derive analytical formulas for the option prices and approximate ordinary differential equations for the optimal exercise boundaries. Numerical simulations yield accurate option prices and comparable computational speeds when benchmarked against the binomial method for calculating option prices. Our approach is based on the Mell...

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...