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

A European call and a European put on the same non-dividend-paying share have the same strike price and the same expiry. Under no-arbitrage with a constant continuously compounded risk-free rate r, which relationship between the call price C, put price P, share price S0, strike K and time to expiry T is correct?

Put-call parity for European options on a non-dividend share states C - P = S0 - K e^{-rT}. Long call plus short put pays S_T - K at expiry, so its present value is the share price minus the discounted strike.

  1. AC - P = S0 - K e^{-rT}Correct
  2. BC - P = S0 - K e^{rT}
  3. CC + P = S0 - K e^{-rT}
  4. DC - P = K - S0 e^{-rT}
  5. C - P = S0 + K e^{-rT}

Explanation

A long call plus a short put gives payoff S_T - K at expiry, the same as a forward-style position. Its value today is S0 - K e^{-rT}. Option 1 compounds the strike forward instead of discounting it, which is the key error.

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