Conversion arbitrage from a parity violation

At the $100 strike (1-year expiry) a European call trades at $8, the put at $4, and the stock at $100. The risk-free rate is 5% continuously compounded. Put-call parity is violated. How much riskless profit (per share, locked in today) can you capture? (in dollars, to 2 decimals)

Show hints (2)+
  1. Protective put (S+PS+P) vs fiduciary call (C+Ke−rTC+Ke^{-rT}) - same payoff, so equal cost.
  2. Profit = the price gap between the two portfolios.

Answer

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0.88 (± 0.02)

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