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FRM Part I · FRM Exam Part I · Exotic Options

A gap call on a non-dividend stock has S0 = 50, payoff strike K1 = 47 and trigger K2 = 50. The maturity is one year and the risk-free rate is 4% (continuous). Using K2 in the d1 and d2 calculations gives N(d1) = 0.60 and N(d2) = 0.50. Using the gap option formula S0N(d1) - K1e^(-rT)N(d2), what is the value of the option?

The gap call is worth about 7.42. The value is 50 x 0.60 = 30 less the discounted payoff strike term, 47 x e^-0.04 x 0.50 = 22.58. The payoff strike of 47 is used in the formula's second term. The trigger of 50 is used only in d1 and d2.

  1. A7.42Correct
  2. B5.98
  3. C6.50
  4. D2.91

Explanation

e^-0.04 = 0.960789. K1 discounted = 47 x 0.960789 = 45.157. Times 0.50 = 22.579. S0N(d1) = 30. Value = 30 - 22.579 = 7.42. Using the trigger of 50 in the second term gives 5.98. Skipping discounting gives 6.50. Using N(d1) on both terms gives 2.91.

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