Deck 12: American Options

Question 1

Which is more valuable and American call option or a European call op- tion?

Answer 1

The posiblity of exercising in more dates gives additional value to the holder. So an American call option is worth more than an European call option.

Question 2

Why is it that as the lockout period becomes longer the price of the bond increases?

Answer 2

This happens because an increase in the lockout increases restrictions on the option, which will fall in value. As the option reduces the value of the underlying bond, a fall in its price increases the value of the bond.

Question 3

What effect does an embedded option have on a security's price?

Answer 3

An option is a security since it is a promise on contingent cash flows. This means that, under no arbitrage, its price should be incorporated into the price of the original security, thus, increasing the value of the original security for the holder of the option.

Question 4

Why is a mortgage a type of callable bond?

Question 5

What happens when the issuer of an American option does not exercise optimally?

Question 6

Using the information provided at the beginning of this chapter, price a 3-year callable bond with coupon rate 5% and strike price at par. There is no lockout period.

Question 7

Using the information provided at the beginning of this chapter, price a 3-year callable bond with coupon rate 5% and strike price at par.

Question 8

What is negative convexity?

Question 9

You are given the following interest rate tree. Use it when required in the
exercises.
What is an American Call option?

Question 10

You are given the following interest rate tree. Use it when required in the
exercises.
Does a callable bond have an American option embedded in it?

Question 11

How is it that negative convexity is present on a callable bond?

Question 12

You notice that when no lockout period is present and for coupons above 5%, the callable bond with strike at par is priced at par. What is hap- pening?

Question 13

Using the information provided at the beginning of this chapter, price a 3-year callable bond with coupon rate 5% and strike price at par. There is also a lockout period through which the option cannot be exercised until t =1.

Question 14

What is the relationship between changes in interest rates and changes in value of a Principal Only (PO) strip?

Question 15

What is the relationship between changes in interest rates and changes in value of an Interest Only (IO) strip?

Question 16

You are given the following interest rate tree. Use it when required in the
exercises.
Does a mortgage have an American option embedded in it?

Question 17

Do pass through securities have negative convexity?

Question 18

You are given the following interest rate tree. Use it when required in the
exercises.
Does a student loan have an American option embedded in it?

Question 19

Using the information provided at the beginning of this chapter, price a 3-year callable bond with coupon rate 5% and strike price at par. There is also a lockout period through which the option cannot be exercised until t =2.