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Question Directory
Digital Option II
Suppose we have an in-the-money European digital option which pays one if the spot price stays in a specific range $[K_1, K_2]$, and zero otherwise. What sign does Vega have?
Clearly, if the option pays off if the underlying stays within a specific price range, then increasing volatility will decrease the probability of the option expiring in the money. As a result, Vega must always be negative.