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

A forward contract on an index paying a continuous dividend yield of 2% p.a. is priced with a risk-free rate of 7% p.a. (continuous). The index is at 20,000 and the contract matures in 6 months. A Black (1976) style formula prices a European call on the index using the forward price F. What is the forward price F, to the nearest whole number?

The forward price is the index level grown at the net carry rate r minus q: 20,000 times e to the power 0.05 times 0.5, about 20,506, so 20,505 is the closest option. Using the risk-free rate alone would overstate it by ignoring the dividend yield.

  1. A20,000
  2. B20,707
  3. C20,505Correct
  4. D20,253
  5. 21,425

Explanation

F = S·e^((r-q)T) = 20,000·e^(0.05×0.5) = 20,000·e^(0.025) = 20,000×1.025315 = 20,506.3. Nearest whole number is 20,506, so the nearest listed value is 20,505. Using r alone gives 20,000·e^0.035 = 20,712, and using q alone ignores carry.

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