Answer-first summary for fast verification
Answer: + $1.00
Use **put-call parity** for a non-dividend-paying stock: \[ c - p = S - Ke^{-rT} \] When time to expiration changes from 0.5 to 1.0 year: \[ \Delta c - \Delta p = \big(S - Ke^{-r(1.0)}\big) - \big(S - Ke^{-r(0.5)}\big) \] \[ \Delta c - \Delta p = K\left(e^{-0.03\cdot 0.5} - e^{-0.03\cdot 1.0}\right) \] \[ = 30\left(e^{-0.015} - e^{-0.03}\right) \approx 30(0.985112 - 0.970446) \approx 0.440 \] Given \(\Delta c = 1.440\), solve for \(\Delta p\): \[ \Delta p = \Delta c - 0.440 = 1.000 \] So the nearest increase in the put value is **+$1.00**.
Author: Manit Arora
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Q-725.3. The risk-free rate is 3.0% while the price of a stock is $30.0030.00$. Let $c = $ value of the call option and $p = $ value of the put option. If nothing else changes except the options' terms double from six months to one year, then value of the call option increases by +$1.44`0. Put simply,
What is nearest to the increase in the value of the corresponding put option on the same stock, if its time to expiration similarly doubles from six months to one year; i.e., what is
A
$0.35B
$1.00C
$1.27D
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