The behavior of the optimal exercise price of American puts near expiry has been well studied under the Black-Scholes model as a result of a series of publications. However, the behavior of the optimal exercise price under a stochastic volatility model, such as the Heston model, has not been...

In this paper, an exact and explicit solution of the well-known Black-Scholes equation for the valuation of American put options is presented for the first time. To the best of the author's knowledge, a closed-form analytical formula has never been found for the valuation of American options of...

Accurately as well as efficiently calculating the early exercise boundary is the key to the highly nonlinear problem of pricing American options. Many analytical approximations have been proposed in the past, aiming at improving the computational efficiency and the easiness of using the formula,...

In this paper, a new analytical formula as an approximation to the value of American put options and their optimal exercise boundary is presented. A transform is first introduced to better deal with the terminal condition and, most importantly, the optimal exercise price which is an unknown...

The behavior of the optimal exercise price of American puts near expiry has been well studied under the Black-Scholes model as a result of a series of publications. However, the behavior of the optimal exercise price under a stochastic volatility model, such as the Heston model, has not been...