The stock price is $30.The strike price of a three-month European put option is $32.If the put option is priced at $5,and the risk-free rate of interest is 2%,and the stock pays no dividends,then the insurance value of the option is
A)1.84
B)2.00
C)3.16
D)4.96

Question

Quizplus · Accepted Answer

The insurance value of the option is calculated as the difference between the strike price and the stock price, discounted back at the risk-free rate for the period until expiration. Here, the strike price is $32, and the stock price is $30, so the difference is $2. However, we need to discount this $2 back for three months at a 2% annual rate. The formula for the present value is PV = FV / (1 + r)^t, where FV is the future value ($2 in this case), r is the annual interest rate (2% or 0.02), and t is the time in years (3/12 or 0.25 years). So, PV = $2 / (1 + 0.02)^0.25 ≈ $1.98, which is not an option provided. The mistake here is in the interpretation of the insurance value in the context of the question. The insurance value is actually the intrinsic value of the option, which is the max(Strike Price - Stock Price, 0) = max(32 - 30, 0) = $2. However, none of the options match this calculation directly, and the explanation provided was to clarify the common misunderstanding. The correct approach to find the insurance value directly from the given options was not applied correctly in this explanation. The insurance value, in simpler terms, should be directly the difference between the strike price and the stock price when the option is in the money, which is $2. However, the detailed calculation involving the option's price and the risk-free rate was unnecessary for determining the insurance value as defined. The correct answer should reflect the intrinsic value or the immediate payoff if exercised, not requiring discounting. My explanation mistakenly attempted to apply financial formulas not directly relevant to the question's simpler ask.

The Stock Price Is $30