Which of the following statements is true:

Which of the following statements is true:

I. The maximum value of the delta of a call option can be infinity

II. The value of theta for a deep out of the money call approaches zero

III. The vega for a put option is negative

IV. For a at the money cash-or-nothing digital option, gamma approaches zero
A . I and IV
B . III only
C . II and III
D . II only

Answer: D

Explanation:

The maximum value for delta of a call option is 1 and not infinity. The value of theta for a deep out of the money call option does indeed approach zero as the value of the option is hardly affected by the passage of time. Vega measures the sensitivity of option prices to the volatility of the underlying, an increase in vega increases the price of the option regardless of whether it is a call option or a put option. (Vega is identical and positive for both calls and puts). Gamma changes very rapidly and reaches its maximum (& not zero) close to the strike price, including for a digital option. Therefore statement II is true and the rest are incorrect.