In this paper, we derive a closed from solution for the value of a perpetual American option when the logreturn of a stock is driven by a fractional Brownian motion, with Hurst parameter H ↦ (0,1). A special case of our model would be the model driven by standard Brownian motion

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...