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

A European call on a share of an Indian company that pays a known dividend before expiry is priced with the basic Black-Scholes formula using the current share price S0. What adjustment is appropriate and what is the error if ignored?

Replace S0 with S0 minus the present value of the known dividend. The call holder does not receive the dividend and the share drops when it is paid, so ignoring it overstates the share input and overprices the call.

  1. AUse S0 less the present value of the dividend; ignoring it overprices the callCorrect
  2. BUse S0 plus the present value of the dividend; ignoring it overprices the call
  3. CUse S0 less the present value of the dividend; ignoring it underprices the call
  4. DReduce the strike by the dividend; ignoring it overprices the call
  5. No adjustment is needed because dividends do not affect European calls

Explanation

The call holder does not receive the dividend, and the share price falls when it is paid. So the share price input should be reduced by the present value of the dividend. Using S0 unadjusted gives too high a price, overpricing the call.

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