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

A European put on a non-dividend-paying share has strike Rs 200, expiry in one year and the risk-free force of interest is 5% per year (e^-0.05 = 0.9512). The put is quoted at Rs 5 when the share price is Rs 180. Which statement is correct?

An arbitrage exists. The European put's lower bound is the discounted strike minus the share price, 190.24 minus 180, about Rs 10.24. A quote of Rs 5 is below it, so buying the put and the share while borrowing the present value of the strike locks in profit.

  1. ANo arbitrage exists because the put price is positive
  2. BAn arbitrage exists because the put is below its lower bound of about Rs 10.24Correct
  3. CAn arbitrage exists because the put exceeds the strike
  4. DAn arbitrage exists because the put is below Rs 20
  5. No arbitrage exists because the put is below the share price

Explanation

The European put lower bound is max(K e^{-rT} - S, 0) = 200 x 0.9512 - 180 = 190.24 - 180 = 10.24. Quote Rs 5 is below this, so buying the put, buying the share and borrowing the PV of the strike gives riskless profit. Rs 20 is the American intrinsic value, not the European bound.

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