In a one-period binomial model, assume that the current stock price is $100, and that it will rise to $110 or fall to $90 after one month. What is the delta of a 99-strike one-month put option?
A) $- 0.50$
B) $- 0.45$
C) $+ 0.45$
D) $+ 0.50$

Question

Quizplus · Accepted Answer

Delta measures the rate of change of the option's price with respect to changes in the underlying asset's price. For a put option in a binomial model, delta can be calculated as: $\Delta = \frac{V_{up} - V_{down}}{S_{up} - S_{down}}$, where $V_{up}$ and $V_{down}$ are the option values in the up and down states, respectively, and $S_{up}$ and $S_{down}$ are the stock prices in the up and down states, respectively.Given a 99-strike put option, if the stock price rises to $110, the option's value is $max(K - S_{up}, 0) = max(99 - 110, 0) = 0$, because the option is out of the money and would not be exercised. If the stock price falls to $90, the option's value is $max(K - S_{down}, 0) = max(99 - 90, 9) = 9$, because the option is in the money and would be exercised for a value of $9.Thus, $\Delta = \frac{0 - 9}{110 - 90} = \frac{-9}{20} = -0.45$.

In a One-Period Binomial Model, Assume That the Current Stock −0.50- 0.50−0.50

In a One-Period Binomial Model, Assume That the Current Stock $- 0.50$