The six-month at-the-money European call option on a stock worth $25 is priced at $5.The rate of interest is 2%.The put is priced at $7.The dividend paid at the end of three months must be
A)1.23
B)2.26
C)3.83
D)4.77

Question

Quizplus · Accepted Answer

To find the dividend paid, we can use the put-call parity for European options, which is given by: $C + Ke^{-rT} = P + S - D$, where $C$ is the call price, $K$ is the strike price (which is equal to the stock price for an at-the-money option, so $25), $r$ is the risk-free interest rate (2% or 0.02 as a decimal), $T$ is the time to maturity in years (0.5 years for six months), $P$ is the put price, $S$ is the stock price, and $D$ is the present value of dividends paid during the life of the option. Rearranging to solve for $D$, we get $D = S + C - P - Ke^{-rT}$.Substituting the given values: $D = 25 + 5 - 7 - 25e^{-0.02 \times 0.5}$.Calculating the exponent part: $e^{-0.02 \times 0.5} ≈ 0.99005$.So, $D = 23 - 25 \times 0.99005 ≈ 23 - 24.75 = 2.25$.Given the options, the closest value to the calculated dividend is $2.26, which is option B.

The Six-Month At-The-Money European Call Option on a Stock Worth