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FRM Part I · FRM Exam Part I · Exotic Options

A cash-or-nothing call option pays USD 10 at expiry if the underlying asset price finishes above the strike, and zero otherwise. Under risk-neutral valuation with a continuously compounded risk-free rate of 4% and one year to expiry, the risk-neutral probability that the asset finishes above the strike is 0.55. What is the value of the option today?

The option is worth about USD 5.29. A cash-or-nothing call's value is the discounted expected payoff: the payout of 10 times the risk-neutral probability of 0.55, discounted at e^(-0.04) for one year. Skipping discounting would wrongly give USD 5.50.

  1. AUSD 5.29Correct
  2. BUSD 5.50
  3. CUSD 4.50
  4. DUSD 5.72

Explanation

Value = e^(-0.04) x 10 x 0.55 = 0.960789 x 5.5 = 5.284, about USD 5.29 when rounded as 5.28-5.29. Ignoring discounting gives 5.50. Using the probability of finishing below the strike (0.45) gives 4.32, close to 4.50 is not correct either. Premium grossed up instead of discounted gives 5.72.

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