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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? | Financial Risk Manager Part 1 Quiz - LeetQuiz

Explanation:

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%.

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