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FRM Part I · FRM Exam Part I · Exotic Options

A trader compares a European arithmetic-average price Asian call option with a otherwise identical standard European call option on the same stock, same strike and same maturity. Which statement is correct?

The Asian call is generally cheaper than the standard European call, because averaging prices over the life of the option lowers the effective volatility of the underlying variable, and lower volatility reduces the value of an option.

  1. AThe Asian call is generally cheaper because averaging reduces the effective volatility of the payoff variableCorrect
  2. BThe Asian call is generally more expensive because averaging increases the chance of a large payoff
  3. CThe two calls have identical values because the expected average equals the final price
  4. DThe Asian call is worth more only when the stock pays no dividends

Explanation

The average of prices over the option's life has lower volatility than the final price alone. Lower effective volatility reduces option value, so the Asian call is typically cheaper. Option B reverses this effect. Option C is wrong because the average and the terminal price have different distributions.

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