A TRADER WRITES THE FOLLOWING 1-YEAR EUROPEAN-STYLE BARRIER OPTION...

17.

A trader writes the following 1-year European-style barrier options as protection against large movements in

a non-dividend paying stock that is currently trading at EUR 40.96.

Option

Price (EUR)

Up-and-in barrier call, with barrier at EUR 45

3.52

Up-and-out barrier call, with barrier at EUR 45

1.24

Down-and-in barrier put, with barrier at EUR 35

2.00

Down-and-out barrier put, with barrier at EUR 35

1.01

All of the options have the same strike price. Assuming the risk-free rate is 2% per annum, what is the

common strike price of these options?

a.

EUR 39.00

b.

EUR 40.00

c.

EUR 41.00

d.

EUR 42.00

Correct Answer: b

Rationale:

The sum of the price of an up-and-in barrier call and an up-and-out barrier call is the price of an other-

wise equivalent European call. The price of the European call is EUR 3.52 + EUR 1.24 = EUR 4.76.

The sum of the price of a down-and-in barrier put and a down-and-out barrier put is the price of an otherwise

equivalent European put. The price of the European put is EUR 2.00 + EUR 1.01 = EUR 3.01.

Using put-call parity, where C represents the price of a call option and P the price of a put option,

C + Ke

^-r

= P + S

K = e

^r

(P + S – C)

Hence, K = e

^0.02

* (3.01 + 40.96 – 4.76) = 40.00.

Section:

Financial Markets and Products

Reference:

John Hull, Options, Futures, and Other Derivatives, 9th Edition, chapter 26, “Exotic Options.”

Learning Objective:

Identify and describe the characteristics and pay-off structure of the following exotic options:

Chooser and barrier options

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2015 Financial Risk Manager (FRM®) Practice Exam