black scholes method risk adjusted probability

In other words, an unhedged option cannot be priced with no-arbitrage methods The drift term of the underlying only disappears when your net delta is zero. You only make money on a long option if volatility is higher than the initial price of the option predicted. But if you hedge the option with Apple shares, then you no longer care what the drift is. Then the only way you will profit is if Apple's drift is positive…if it drifts down, your option expires worthless. Then the only way you will profit is if Apple's drift is positive suppose Apple has very low volatility. And suppose Apple has very low volatility. Let's say you are naked long an at-the-money one-year call on Apple, and you will never hedge. The price of an unhedged derivative, for example, a naked long call, most certainly does depend on the drift of the underlying. The insight from the Black-Scholes PDE is that the price of a hedged derivative does not depend on the drift of the underlying. One of the most common mistakes that even highly experienced practitioners make is to act as if the assumptions of Black-Scholes (lognormal, continuous distribution of returns, no transactions costs, etc.) mean that we can always arbitrarily assume the underlying grows at the riskfree rate r instead of a subjective guess as to its real drift μ.

Black scholes method risk adjusted probability