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Outline some reasons why exotic derivative products have been developed.

FRM® Part I · Financial Markets and Products · Exotic Options · FRM1.FM.15.b

The idea

Exotic products exist because standard options do not fit every need. The first reason is hedging: a corporate treasurer with a specific exposure, such as monthly foreign currency receipts, can buy an average-rate option that matches it better than a single-date vanilla option. The second is cost. Many exotics, such as barrier, Asian and basket options, have lower premiums because the buyer gives up payoff in states thought unlikely, or because the underlying average or portfolio is less volatile than a single price. The third is to express a market view precisely, for example a belief that a price will rise but never touch a given level. The fourth is to work around tax, accounting, legal or regulatory restrictions. Dealers also like them because the margins are higher and the products are hard to compare. Exam answers should tie each reason to a concrete product.

A practice question

From the question bank, with the reason each wrong option is wrong.

A corporate treasurer's most direct reason for choosing an exotic option over a vanilla option is to:

  1. avoid counterparty risk, because exotics are traded and cleared on exchanges.Why not: Exotics are mostly OTC and carry counterparty exposure.
  2. match the hedge to a specific exposure, such as an average of future cash flows. - correct
  3. obtain a payoff that is always cheaper than any vanilla alternative.Why not: Not all exotics are cheaper; lookback options, for example, cost more than vanilla options.
  4. remove the need to estimate volatility when valuing the position.Why not: Exotics are priced with volatility and add model risk; they do not remove the need for it.

Exotics are developed mainly so that clients can hedge specific exposures more closely, for example average-rate options for flows spread over time, not because they are exchange-traded or always cheaper.

A harder one

A fund holds equal exposure to three equity indices. Separate at-the-money puts cost USD 4.20 million each, USD 12.60 million in total. A dealer quotes USD 8.10 million for a basket put on the combined portfolio. What is the saving, and why is the basket put cheaper?

  1. USD 4.50 million, because imperfect correlation makes the basket less volatile. - correct
  2. USD 8.10 million, because the basket put replaces all three separate puts.Why not: Reports the basket premium rather than the saving relative to the three puts.
  3. USD 4.20 million, because the basket put replaces two of the three puts.Why not: The saving is the difference between 12.60 and 8.10, not the price of one put.
  4. USD 4.50 million, because the dealer earns less margin on basket options than on single puts.Why not: The amount is right, but the cause is diversification, not a lower dealer margin.

Saving = 12.60 - 8.10 = USD 4.50 million. Gains in one index offset losses in another when correlation is below one, so the basket is less volatile than its parts and its put costs less than the sum of the individual puts.

The hardest tier

A 1-year average-price call is written on an asset with 30% annual volatility, with the average taken continuously. The variance of the average price's log change over the year is roughly one-third of the terminal variance. Which volatility is the right order of magnitude for valuing the call, explaining why it costs less than a vanilla call?

  1. About 10.0%, which is 30% divided by 3.Why not: Divides volatility by 3, but it is the variance that is divided by 3, so volatility falls by the square root of 3.
  2. About 17.3%, being 30% divided by the square root of 3. - correct
  3. About 15.0%, which is 30% divided by 2.Why not: Takes the average to halve the volatility; the variance, not the volatility, falls to one third.
  4. About 21.2%, which is 30% divided by the square root of 2.Why not: Uses a variance reduction factor of one half instead of one third.

Variance of the average = sigma² T / 3, so effective volatility = 0.30 / sqrt(3) = 17.3%. The lower effective volatility makes the Asian option cheaper than the vanilla option.

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