delta of put option

The delta if an in-the-mpney put option is always less than -0.5 a. Always True b. Always false c. Could be, but does not have to be

a) Delta of at-the-money put is -0.5. As option goes in-the-money, the absolute value of its delta grows (gets closer to -1).

It’s C. Consider an extreme case where rates are 20%, dividends are 0%, and a 1-year put is 1% in the money. So, the forward is 19% out-of-the-money, hence delta > -0.5.

Answer C. the delta can be graphically represented by the tangent line. If you figure the payoff diagram of a put option, the the delta for StX. Problem is that the graph of an option is not exactly a straight line but more some sort of an hyperbole with the tangent line less steep for St

C. Even if we take a B-S risk free rate, values of puts that are barely “in-the-money” will have a delta > -0.5 if the time till expiration is very large (big T-t), and/or if the volatility is high. The “+/- 0.5” is just an approximation, not a rule. Volatility and long time till expiration are good if you are deep out of the money, yet they are not if you are just in-the-money.