Suppose, if the price of a European option (say a put) can be shown to be monotone in volatility (say for any maturity), does it follow that American options has to be monotone in volatility? ...
Let us consider an American call option with strike price K and the time to maturity be T. Assume that the underlying stock does not pay any dividend. Let the price of this call option is C$^a$ today ...
Here is my question: This is a question about Black-Scholes model, but it may be applicable to more complicated models. Throughout the discussion, the strike price $K$, interest rate $r$ and ...