[According to the PRMIA study guide for Exam 1, Simple Exotics and Convertible Bonds have been excluded from the syllabus. You may choose to ignore this question. It appears here solely because the Handbook continues to have these chapters.]
Which of the following statements is true:
1. Knock-out options start lifeless and convert to a plain vanilla option when the barrier is hit
II. Barrier options are cheaper than equivalent vanilla options
III. Average price options are more expensive than equivalent vanilla options
IV. Digital options have a high gamma close to the strike price
Knock-out options start as plain vanilla options and are 'knocked-out', ie cease to exist, when the barrier is hit. Knock-in options start lifeless and 'kick-in', ie come into play as plain vanilla options when the barrier is hit. Therefore statement I is not correct.
Barrier options are certainly cheaper than equivalent vanilla options because vanilla options have a larger range of prices over which they pay out. Therefore statement II is correct.
Statement III is not correct. Average price options, also called Asian options, are less attractive to a buyer of options and therefore they are cheaper and not more expensive than vanilla options. This is because average prices are less volatile, and also when compared to a strip of equivalent vanilla options, some of the individual vanilla options in the strip may pay out whereas on the average nothing may pay out.
Digital options have a very high gamma close to the strike price as the option payout becomes uncertain and fluctuates sharply between 0 and 1. Therefore statement IV is correct.