The American Put Option and Its Critical Stock Price
推导了美式看跌期权的临界股票价格表达式，从永续期权到有限期情况，利用首次通过概率和早期行权溢价，为期权定价提供精确近似。
We derive an expression for the critical stock price for the American put. We start by expressing the put price as an integral involving first‐passage probabilities. This approach yields intuition for Merton's result for the perpetual put. We then consider the finite‐lived case. Using (1) the fact that the put value ceases to depend on time when the critical stock price is reached and (2) the result that an American put equals a European put plus an early‐exercise premium, we derive the critical stock price. We approximate the critical‐stock‐price function to compute accurate put prices.