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IAI Actuarial Core Principles · Economic Modelling · Black-Scholes derivative-pricing model

A share currently trades at Rs 520. It will pay a single dividend of Rs 20 in exactly 3 months. A European call expires in 6 months. The continuously compounded risk-free rate is 8% per annum. Which value should be used as the share price input S in the Black-Scholes formula (to the nearest rupee, using the discrete-dividend adjustment)?

The adjusted price is the share price less the present value of the dividend: 520 minus 20 discounted for three months at 8%, about 19.60, giving roughly Rs 500.40. Rs 500 is the nearest listed value, whereas using the undiscounted dividend would give Rs 500 too closely, so check carefully.

  1. ARs 520
  2. BRs 500
  3. CRs 480
  4. DRs 504Correct
  5. Rs 510

Explanation

Subtract the present value of the dividend from the share price: PV = 20·e^(-0.08×0.25) = 20·e^(-0.02) = 20×0.98020 = 19.60. Adjusted S = 520 - 19.60 = 500.40, which rounds to Rs 500. Check: Rs 500 is option 1 and is the closest to 500.40.

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