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FRM Part I · FRM Exam Part I · Properties of Options

A trader notes that a European call on a stock is priced at 6.00 while the stock is at 40, the strike is 38, and the option expires in 6 months with a continuously compounded rate of 5%. The stock pays no dividends. Which statement is correct about the call price?

The call satisfies the lower bound. The bound is the stock price minus the discounted strike, 40 minus 38 times e to the power minus 0.025, about 2.94. A price of 6.00 is above that and below the stock price of 40, the upper bound.

  1. AIt violates the lower bound because the bound is 2.95
  2. BIt is below the lower bound of 3.00
  3. CIt satisfies the lower bound of about 2.95Correct
  4. DIt violates the upper bound because the call exceeds the strike

Explanation

Lower bound = S0 - K e^{-rT} = 40 - 38 e^{-0.025} = 40 - 38 x 0.975310 = 40 - 37.062 = 2.94, about 2.95. The price of 6.00 exceeds this and is below the upper bound of the stock price 40, so no violation exists.

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