The Critical Price Of The American Put Near Maturity In The Jump Diffusion Model

TL;DR

This paper investigates how jumps in stock prices affect the critical price of American put options near maturity, revealing that jumps can alter the convergence rate when the limit is below the stock price.

Contribution

It provides a theoretical analysis of the impact of jumps on the critical price behavior near maturity in jump diffusion models, especially when the limit is below the stock price.

Findings

Jumps influence the convergence rate of the critical price.

The limit of the critical price can be smaller than the stock price.

The behavior differs from the case where the limit equals the strike price.

Abstract

We study the behavior of the critical price of an American put option near maturity in the Jump diffusion model when the underlying stock pays dividends at a continuous rate and the limit of the critical price is smaller than the stock price. In particular, we prove that, unlike the case where the limit is equal to the strike price, jumps can influence the convergence rate.