Sizing a put–call parity mispricing

A $50-strike call and a $50-strike put on a $52 stock both expire today (interest ≈0\approx0). The call trades at $4.00 and the put at $1.50. A riskless arbitrage exists - how much can you lock in per share (in dollars, to two decimals)?

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  1. Put–call parity: C−PC-P should equal S−KS-K when interest ≈0\approx0.
  2. Fair C−P=52−50=2C-P=52-50=2; the quotes give 4.00−1.50=2.504.00-1.50=2.50; the arb is the $0.50 gap.

Answer

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0.5

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Asked at: Timed Mental-Math & Sequences, Options Market-Making

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