Answer-first summary for fast verification
Answer: 4.61%
For a non-dividend-paying stock, put-call parity gives: \[ c - p = S_0 - Ke^{-rT} \] Substitute the values: \[ 5.00 - 3.86 = 50 - 50e^{-r(0.5)} \] \[ 1.14 = 50(1 - e^{-0.5r}) \] \[ 50e^{-0.5r} = 48.86 \] \[ e^{-0.5r} = 0.9772 \] \[ -0.5r = \ln(0.9772) \] \[ r \approx 0.0461 = 4.61\% \] Therefore, the implied risk-free rate is **4.61%**.
Author: Manit Arora
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Question-181.3. Put-call parity
The price of a non-dividend-paying stock is $50.00. The price of a six (6)-month European call option on the stock with a strike price of $50.00 is $5.00. The price of a six (6)-month European put option on the stock with a strike price of $50.00 is $3.86. What is the implied risk-free rate?
A
3.58%
B
4.22%
C
4.61%
D
5.00%
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