Consider a down-and-out call and a down-and-in call with a current stock price $S$ ,barrier $H H$ .When does the knock-out option increase in price and the knock-in decrease in price? A)When the stock price increases. B)When the volatility increases. C)When the barrier increases. D)When the strike increases.

Question

Consider a down-and-out call and a down-and-in call with a current stock price $S$ ,barrier $H < S$ ,and strike $K > H$ .When does the knock-out option increase in price and the knock-in decrease in price?
A)When the stock price increases.
B)When the volatility increases.
C)When the barrier increases.
D)When the strike increases.

Quizplus · Accepted Answer

When the stock price increases, the down-and-out call option (which gets knocked out if the stock price falls below a certain level) becomes more valuable because it's less likely to hit the barrier and get knocked out. Conversely, the down-and-in call option (which only becomes active if the stock price falls below a certain level) becomes less valuable as the likelihood of it getting activated decreases with the increasing stock price.

Consider a Down-And-Out Call and a Down-And-In Call with a Current