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IAI Actuarial Core Principles · Economic Modelling · Principles of option pricing

A share pays no dividends. The share price is Rs 200, and a 6-month European call with strike Rs 210 trades at Rs 9 while the 6-month European put with strike Rs 210 trades at Rs 17. The continuously compounded risk-free rate is 4% per year. K e^{-rT} = 205.92. Which statement is correct?

C - P equals -8, whereas S0 minus the discounted strike equals -5.92. Parity fails, with the put overpriced relative to the call, so an arbitrage profit is available by selling the put and buying the call and bond-equivalent position.

  1. AParity holds exactly, so there is no arbitrage
  2. BParity is violated because C - P exceeds S0 - K e^{-rT}; sell the call, buy the put and buy the share is not appropriate
  3. CC - P = -8 while S0 - K e^{-rT} = -5.92, so the put is relatively overpriced and an arbitrage existsCorrect
  4. DC - P = -8 while S0 - K e^{-rT} = -10, so the call is overpriced
  5. C - P = 8 while S0 - K e^{-rT} = -5.92, so the put is underpriced

Explanation

C - P = 9 - 17 = -8. S0 - K e^{-rT} = 200 - 205.92 = -5.92. Since -8 is lower than -5.92, the put is too expensive relative to the call, so an arbitrage exists. Option 1 wrongly claims parity holds.

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