Define delta and explain how it relates to the sensitivity of an option's price to the underlying asset.

• A. Delta is the time decay of the option price.
• B. Delta is the rate of change of the option price with respect to changes in the underlying price; for a typical long call delta ∈ (0,1) and for a long put delta ∈ (-1,0).
• C. Delta measures how sensitive an option's value is to changes in interest rates.
• D. Delta is the second derivative of the option price with respect to the underlying.

Answer: (B)

Delta measures how much an option’s price changes when the underlying asset’s price moves. It is the first derivative of the option’s value with respect to the underlying price. For a typical long call, delta lies between 0 and 1, meaning the option’s value rises as the underlying goes up, but not more than one-for-one. For a long put, delta lies between -1 and 0, so the option’s value tends to fall as the underlying rises. In practical terms, if the underlying increases by $1 and the option has a delta of 0.6, the option’s price would increase by about $0.60 (ignoring other effects). Delta changes as the underlying moves and as time to expiration changes, a property captured by gamma. Delta is also used for hedging: a position with delta 0.5 would require about 0.5 shares to hedge small moves in the underlying. The other options describe different ideas—time decay (theta), sensitivity to interest rates (rho), and the second derivative with respect to the underlying (gamma)—not how option value responds to moves in the underlying itself.