I'm confused as to how a method that values securities purely on their expected return works in the real world if it doesn't take into account the fact that investors demand a higher return for greater variance in expected return.
1 Answer
The price of a derivative does not explicitly depend on the expected return of the underlying, however the price change or return of the derivative depends on the return of the underlying. Hence the expected return of the derivative depends on the expected return of the underlying, which is what matters.
Also remember that the price is a function of the spot of the underlying, and this is what a pricing formula does: establishes how the derivative is priced relative to the underlying price. A derivative inherits all risk from the underlying, it does not have its own risk, so to speak. If the underlying becomes very risky, then its price will fall to offer higher expected return in the future; the derivative price will also change to reflect that.