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# P1.T3.731. Lookback and Asian (exotic) options (Hull Chapter 26 cont.)

#### Nicole Seaman

##### Director of FRM Operations
Staff member
Subscriber
Learning objectives: Identify and describe the characteristics and pay-off structure of the following exotic options: gap, forward start, compound, chooser, barrier, binary, lookback, shout, Asian, exchange, rainbow, and basket

Questions:

731.1. Consider the price of an asset that begins and $30.00 and ends, after 20 periods, lower at$8.55. Also highlighted are its maximum ($39.23) and minimum price ($6.79) during this 20-period life: Among the following choices, which lookback option has the HIGHEST payoff if its life matches the 20-period interval shown?

a. Floating lookback call
b. Floating lookback put
c. Fixed lookback call with strike = $30.00 (matching the initial asset price) d. Fixed lookback put with strike =$30.00 (matching the initial asset price)

731.2. Consider the price of an asset that begins and $30.00 and ends, after 20 periods, higher at$76.55. During this 20-period life, its maximum ($89.55) and minimum price ($23.58) are also highlighted: Among the following choices, which lookback option has the HIGHEST payoff if its life matches the 20-period interval shown?

a. Floating lookback call
b. Floating lookback put
c. Fixed lookback call with strike = $30.00 (matching the initial asset price) d. Fixed lookback put with strike =$30.00 (matching the initial asset price)

731.3. Below is the output of a Black-Scholes (BSM) option pricing model for a one-year (T = 1.0) option with a strike price, K = $30.00, on a non-dividend-paying stock, q = 0%, when the stock price, S(0) =$30.00, with volatility, σ = 28.0%, while the risk-free rate is 3.0%. Under these assumptions, as shown, the price of a REGULAR European call option is $3.753 and the corresponding put option price is$2.866 However, assume that instead of a regular option, we are pricing Asian options under the same assumptions. In this case, there are four variations on the Asian option:
• Average price call with strike, K = $30.00 • Average price put with strike, K =$30.00
• Average strike call (does not utilize a strike price)
• Average strike put (does not utilize a strike price)
Let (N) represent the FREQUENCY of observations in order to determine the average price or strike during the life of the option; e.g., if N = 1 then there is only once observation at the end of the year, if N = 12 then there is an observation at the end of each month, if N = 52 there is an observation at the end of week, if N = 250 there is an observation at the end of each day. In regard to these Asian options, each of the following statements is true EXCEPT which is false?

a. If N = 1, then the average price call and put are, respectively, $3.753 and$2.866
b. As we increase (N) from 1 to 252, the value of an average price call decreases from $3.753 to lower values c. As we increase (N) from 1 to 252, the value of an average price put increases from$2.866 to higher values
d. As we increase (N) from 1 to 252, the value of an average strike put increases from zero to higher values