The delta of a put option is which of the following expressions?

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Multiple Choice

The delta of a put option is which of the following expressions?

Delta is how much the option price moves for a small change in the underlying. For a put, this change goes in the opposite direction to the underlying, so the put’s delta is negative. In the Black–Scholes framework, the call option delta is Phi(d1). Put delta relates to call delta via put–call parity: P = C + K e^{-rT} − S. Differentiating with respect to S gives delta(P) = delta(C) − 1 = Phi(d1) − 1. This can be rewritten using the identity Phi(-x) = 1 − Phi(x) as delta(P) = −Phi(-d1). So the correct expression for the put delta is negative Phi of minus d1. (Note that Phi(-d1) = 1 − Phi(d1), so this matches the alternative form Phi(d1) − 1.) As S rises, a put’s value tends to fall, reflecting the negative delta.

Delta is how much the option price moves for a small change in the underlying. For a put, this change goes in the opposite direction to the underlying, so the put’s delta is negative.

In the Black–Scholes framework, the call option delta is Phi(d1). Put delta relates to call delta via put–call parity: P = C + K e^{-rT} − S. Differentiating with respect to S gives delta(P) = delta(C) − 1 = Phi(d1) − 1. This can be rewritten using the identity Phi(-x) = 1 − Phi(x) as delta(P) = −Phi(-d1).

So the correct expression for the put delta is negative Phi of minus d1. (Note that Phi(-d1) = 1 − Phi(d1), so this matches the alternative form Phi(d1) − 1.)

As S rises, a put’s value tends to fall, reflecting the negative delta.

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