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# P1.T3.730. Chooser and barrier (exotic) options (Chapter 26 cont.)

#### Nicole Seaman

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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:

730.1 A non-dividend paying stock is currently trading at a price $35.00 when its volatility is 30.0% and the riskfree rate is 3.0%. Consider a chooser option with a strike price of$30.00 that gives the holder the right to choose (a call or put option) in three months and the chosen option, at that point in time, will have a remaining time to maturity of nine months; i.e., T1 = +0.25 years and T2 = +1.0 years. The price of this chooser is $7.710. Which of the following changes, ceteris paribus, will INCREASE the value of this chooser? a. Dividend increase to 4% b. Volatility decrease to 20% c. Stock drops to$30.00
d. Increase T1 to six months

730.2 Consider a one-year barrier call option on a non-dividend-paying stock with a volatility of 30.0% per annum when the stock's price is $25.00 and the option's strike price is$20.00. The risk-free rate is 3.0%. The price of a regular call (i.e., without the barrier) in this case is $6.32. This barrier option has a barrier at$18.00 such that, if it is a knock-in (aka, down-and-in) its price is only $0.22. Each of the following statements is true (or at least plausible!) EXCEPT which statement must be false? a. The corresponding knock-out (aka, down-and-in) must have a price of about$6.10
b. If the barrier is increased to $22.00, then the price of this knock-in must be higher than$0.22
c. If the barrier is increased to $22.00, then the price of the corresponding knock-out must be lower than$6.10
d. If the barrier is increased to $28.00, then the price of this knock-in will be$6.32 and the price of the corresponding knock-out will be zero

730.3. A non-dividend-paying stock with a current price of $40.00 and a volatility of 30.0% per annum when the risk-free rate is 4.0%. Consider a one-year barrier option with a barrier, H =$43.00, and a strike price, K = $45.00. Please note that the corresponding regular (i.e., without the barrier) put option price is$6.75. Which of the following instances of this barrier option has the LOWEST price?

a. Knock-in call
b. Knock-out call
c. Knock-in put
d. Knock-out put