hard · Quantitative Finance derivatives
An arbitrageur observes a six-month European call struck at 50 trading for 4.50 and a six-month European put struck at 50 trading for 2.50. The stock price is 51 and the risk-free rate is 4%.
According to Put-Call Parity (C - P = S_0 - Ke^-rT), is there an arbitrage opportunity?
- No, because C - P should equal S_0 - K, and 2.00 = 51 - 50 is close enough.
- Yes, because the call price should always be at least 5 higher than the put price when the stock is at 51.
- No, because the difference of 0.01 is too small to be an arbitrage.
- Yes, because the synthetic stock price C - P + Ke^-rT ≈ 51.01 is higher than the actual stock price.
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