18. An up and in barrier (European) call option on a non?dividend?paying underlying stock is trading at USD 10 with a strike price of USD 100, the barrier is at USD 120, and the stock is trading at USD 95. A plain vanilla European call option with the same parameters as the up and in barrier call option mentioned above is priced at USD 15. What is the price of an up and out barrier (European) call option with the same parameters as the up and in barrier call option mentioned above?

A. USD 25

B. USD 20

C. USD 5

D. Cannot be determined with the data provided

Correct answer is Cfficeffice" />

Price of European Up and In Barrier Call Option, c uin = $10

Price of American Call Option = $15

We know that for Call Options, Price of European Call Option, c = Price of American Call Option

Therefore, c =$15

For European Call Options, we have the following relationship:

c = c uin + c uout

where, c uout is the Price of a European Up and Out Barrier Call Option.

Therefore, c uout = c ? c uin = $15 ? $10 = $5

Reference: John C. Hull, Options, Futures and Other Derivatives, 5th Edition ? Chapter 19

Type: Market Risk