David Harper CFA FRM

David Harper CFA FRM
Staff member
Learning objectives: Define and contrast exotic derivatives and plain vanilla derivatives ... Identify and describe the characteristics and payoff structures of the following exotic options: gap, forward start, compound, chooser, barrier, binary, lookback, Asian, exchange, and basket options.


22.28.1. At the beginning of the fourth quarter, the price of a very speculative stock was approximately $10. Peter believed that imminent events would cause the stock's realized volatility over the subsequent quarter to greatly exceed its implied volatility, although he was unsure of the direction. He considered buying a straddle which is long volatility.

Instead, he purchased a portfolio that included two exotic options: a floating lookback call plus a floating lookback put. The maturity of both options was three months. The measurement frequency was weekly. During the options' lives, the measured prices were as follows:

October: $11, 13, 12, 14
November: $12, 9, 7, 10
December: $12, 15, 18, 14

What was the portfolio's payoff?

a. Zero
b. $11
c. $25
d. Not enough information (need strike prices)

22.28.2. While the current stock price is $47.00, Bertha considers a call option with a strike price of $50.00. However, she perceives this standard option to be a bit too expensive. For the sole purpose of reducing her initial cost, she considers a barrier option with the same strike price. Her criteria is that the barrier option must be cheaper, but it must be possible to achieve a payoff that is at least equal to (or better than) the regular call's payoff. In other words, she wants the possibility of (at least) a similar payoff but achieved with a lower initial cost. She considers the following two barrier options:
  • Knock-in: An up-and-in call with barrier H = $52.00
  • Knock-out: A down-and-out call with barrier H = $45.00
In regard to her options (pun intended!), each of the following statements is TRUE, except which is false?

a. The knock-in option fits her criteria; it is cheaper than the standard call
b. The knock-out option fits her criteria; it is cheaper than the standard call
c. As the observation frequency increases, the knock-out option becomes less expensive, but the knock-in becomes more expensive
d. She could also buy an up-and-out (knock-out) call with a barrier set below the strike prices (e.g., H = $49.00), but it will be slightly more expensive than the standard call

22.28.3. While the current stock price is $47.00, Betty is considering a regular one-year call option with a strike price of $50.00. However, the cost of this call is $6.09. Because this is a bit too expensive, she considers a compound option as an alternative. This is a call-on-a-call where T1 = 0.5 years (i.e., six months) and K1 = $7.00. She happens to have additional information that a put-on-a-call with the same strike prices has a price of $2.27.

In regard to this call-on-a-call compound option which of the following statements is TRUE?

a. The call-on-a-call will be less sensitive to an increase in the stock's volatility
b. She can also express a bullish (directional) view with a put-on-a-put, but her upside will be capped
c. Because the call-on-a-call has more leverage, its price is higher than the standard one-year call's price of $6.09
d. The price of this call-on-a-call can be obtained neither with any versions of put-call parity relationship nor Black-Scholes Merton due to its exotic and discontinuous features

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