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

A share is Rs 80 and will pay a certain dividend of Rs 4 in six months. The risk-free force of interest is 8% per year (e^-0.04 = 0.9608; e^-0.08 = 0.9231). A one-year European call has strike Rs 75. Which is the lower bound for the call price?

The bound is about Rs 6.92. Subtract the present value of the Rs 4 dividend, about 3.84, and the discounted strike, about 69.23, from the share price of Rs 80. Ignoring the dividend would give Rs 10.77, which overstates the bound.

  1. ARs 5.00
  2. BRs 10.70Correct
  3. CRs 6.92
  4. DRs 10.15
  5. Rs 6.70

Explanation

Lower bound = S - PV(dividend) - K e^{-rT}. PV(dividend) = 4 x 0.9608 = 3.843. K e^{-rT} = 75 x 0.9231 = 69.23. Bound = 80 - 3.843 - 69.23 = 6.93, which is about Rs 6.92 to 6.93, so check: 80 - 3.84 - 69.23 = 6.93. Hence the matching option is Rs 6.92.

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