FRM Part I · FRM Exam Part I · Exotic Options
A trader holds an arithmetic-average price Asian call option on a stock with strike 50, averaging daily prices over the whole life of the option. Compared with an otherwise identical European call on the same stock with strike 50, the Asian call will normally be:
The Asian call is normally cheaper than the European call. Averaging prices over time lowers the volatility of the variable that determines the payoff, and lower volatility reduces option value. Averaging does not raise the forward price, so it does not make the option more expensive.
- ACheaper, because averaging reduces the effective volatility of the payoff variableCorrect
- BMore expensive, because averaging increases the chance of a high payoff
- CEqual in price, because the expected average equals the expected final price under any measure
- DMore expensive, because averaging raises the forward price of the underlying
Explanation
The average of prices over the option's life has lower volatility than the final price alone. Lower volatility reduces the value of optionality, so the Asian call is cheaper than the otherwise identical European call. Option B is wrong because averaging dampens extreme outcomes rather than raising them.
Did you get it right without looking?
One question tells you little. A timed set on Exotic Options shows your real accuracy, how long you take and where you lose marks.
More Exotic Options questions
- A company will grant an at-the-money European call at the end of year 1, expiring at the end of year 3 (a forward start option). Volatility …
- A trader holds a European down-and-out call on a stock with strike 50 and a barrier at 40. Compared with an otherwise identical standard Eur…
- A corporate treasurer wants a currency option whose payoff depends on the average exchange rate over the next twelve months, because the com…
- An exchange option gives the holder the right to exchange asset B for asset A at maturity, so payoff is max(A_T - B_T, 0). Under the Margrab…
- An average price Asian call has a strike of 100 and the average is computed from four quarterly observations of the stock: 96, 104, 112 and …
- A trader compares a European call option on the price of a stock at maturity with an arithmetic-average-price Asian call on the same stock, …