What is the boundary condition for a European put option?

Question

Quizplus · Accepted Answer

The boundary condition for a European put option is Max [0, K-S(T)]. This is because at maturity, if the stock price is lower than the strike price, the option holder has the right to sell the underlying asset at the strike price, resulting in a profit of K-S(T). If the stock price is higher than the strike price, there is no benefit in exercising the option and the option holder lets it expire worthless. Therefore, the minimum value of a European put option at maturity is 0, and the maximum value is K-S(T).

What Is the Boundary Condition for a European Put Option