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# P2.T5.413. Exotic options: barrier, binary, and lookback

#### Nicole Seaman

##### Director of FRM Operations
Staff member
Subscriber
AIMs: Identify and describe the characteristics and pay-off structure of the following exotic options: barrier, binary, and lookback

Questions:

413.1. Let (p) be the value of a standard (non-exotic or vanilla) put option with a strike price of $16.00, where the underlying current underlying stock price, S(0), is$18.40. Consider an exotic knock-in barrier put option (aka, down-and-in put) also with a strike price of (K) of $16.00. Each of the following it true about the down-and-in put, EXCEPT which is false? a. If the barrier (H) is$17.00, then the value of this down-and-in put option, p(di), is equal to the value of the vanilla put option; p(di) = p
b. If the barrier (H) is $14.00, then the value of this down-and-in put option, p(di), is equal to the value of the vanilla put option minus the value of an equivalent down-and-out put; p(di) = p - p(do) c. The vega of the down-and-in put, p(di), is generally lower than the vega of the corresponding vanilla put; vega(di) < vega (p) d. As we increase the frequency with which we observe the the asset price in determining whether the barrier is reached, the value of the down-and-in put increases 413.2. Assume an underlying non-dividend-paying stock has a current price of$40.00 with volatility of 25.0% per annum while the riskfree rate is 4.0% per annum. The price of a six-month, at-the-money (maturity = 0.5 years, strike = $40.00) call option on the stock is$3.20 where N(d1) = 0.580 and N(d2) = 0.510. Which is nearest to the price of a binary asset-or-nothing call option with the same strike price and maturity?

a. $3.20 b.$20.00
c. $23.20 d.$40.00

413.3. Assume a stock the starts the year priced at $50.00, then drops to a low of$39.00, then subsequently increases up to a high of $61.00, before dropping to finish the year at$53.00; i.e., S(0) = 50 and S(1.0) = 53 with interim low of 39 and high of 61. Now consider four lookback options with lives corresponding exactly to the year: each option life begins when the stock trades and $50.00 and expires when the stock trades at$60.00. Two of the options are floating lookback options, which do not require strike prices; the fixed lookback options have strike prices equal to the initial \$50.00. Which lookback option has, respectively, the lowest and highest final payoff?

a. Fixed lookback call (lowest payoff) and floating lookback put (higest payoff)
b. Floating lookback put (lowest) and floating lookback call (highest)
c. Floating lookback call (lowest) and floating lookback put (highest)
d. Fixed lookback call (lowest) and fixed lookback put (highest)