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P2.T5.202. Hull's exotic options (II)

Suzanne Evans

Well-Known Member
Questions:
202.1. A certain asset starts at an intial price of $10, then increases to $15, then drops to $7, and finally settles at a final price of $9. In summary, the asset exhibits the following sequence: initial $10, 15, 7, and final $9. Consider the payoffs of all four lookback option types on this stock. In the case of fixed lookback options assume the strike price is the initial $10 (recall that floating lookback options, on the other hand, do not have strike prices). From LOWEST to HIGHEST, what is order of payoffs?

a. Floating lookback put < fixed lookback put (K = 10) < Floating lookback call < fixed lookback call (K = 10)
b. Fixed lookback put (K = 10) < floating lookback put < fixed lookback call (K = 10) < Floating lookback call
c. Floating lookback call < fixed lookback put (K = 10) < fixed lookback call (K = 10) < floating lookback put
d. Fixed lookback call (K = 10) < Fixed lookback put (K = 10) < floating lookback put < Floating lookback call

202.2. An asset-or-nothing (binary; aka, digital) call option that pays the stock price or nothing has one year (1.0) to maturity while the risk-free rate is 4.0%. The current stock price, S(0), and the strike price (K) are both $30.00. The stock has a volatility of 36.0% and pays a dividend yield of 1.0%. N(d1) = 0.60 and N(d2) = .460. What is the price of the asset-or-nothing binary call option?

a. $4.52
b. $9.15
c. $13.66
d. $17.82

202.3. A one-year Asian option pays off based on the average of each quarter's closing price, where the four observed prices are $20.00 (Q1), $25.00 (Q2), $17.00 (Q3) and $22.00 (Q4). Consider the following statements:

I. If the strike price (K) is $20.00, the payoff of a geometric average price call is greater than the payoff of an arithmetic average price call
II. If the strike price (K) is $20.00, the payoff of a arithmetic average price put is zero
III. The payoff of an arithmetic average strike call is zero
IV. The payoff of an arithmetic average strike put is zero

Which of the above is (are) true?

a. None
b. I. and III.
c. II. and IV.
d. All are true

Answers:
 
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