THE EARLY EXERCISE BOUNDARY FOR THE AMERICAN PUT NEAR EXPIRY: NUMERICAL APPROXIMATION

ABSTRACT. It is well known [11] that the early exercise boundary for the American put approaches the strike price at expiry with infinite velocity. This causes difficulties in developing efficient and accurate numerical procedures and consequently trading strategies, during the volatile period near expiry. Based on the work of D. ˇ Sevčovič [10] fortheAmerican call with dividend, an integral equation is derived for the free boundary for the American put which leads to an accurate numerical procedure and an interesting, and accurate, asymptotic solution for the early exercise boundary near expiry. 1. Introduction. Many different