Question

When valuing European Vanilla Options in the Black-Scholes-Merton Model, there is one source of uncertainty. What is this uncertainty?

There are 2 possible answers:
-one is the change of the stock price.
-another one is volatility.

Which of the answer is correct? Could you please provide a detailed explanation? Thank you.

Answer 1

In valuing european vanilla options using the black scholes model the only uncertainty is the change is the price of the underlying asset, ie the change is the stock price.

Most simple options are exposed to a single source of uncertainty, but those that are exposed to more than one are also called the rainbow options. the option in the given question is a plain vanilla option.

the black- scholes -merton model assumes that the option is held until maturity and the stock does not pay any dividends.as the value of the option depends on he price of the stock on which the option is bought, if the price of the stock increases, the call option increases in its value and the put option value falls and if the value of the stock falls, then the value of the call option falls and put option rises. volatility is the measure of the dispersion of the asset price from its mean value and the black- scholes- merton model assumes that volatility is constant.