Relationship between Option Adjusted Spread and Interest rate

CFA Level II Fixed Income
#1

Volatility increases - OAS falls - for callable bonds
Volatility increases - OAS increases - for putable bonds

Can anyone explain the reason behind this?

#2

Is this in the Level II curriculum?

If the bonds are priced fairly, a change in volatility shouldn’t affect the OAS.

#3

Call and put options increase in value if volatility increases.

This is an over simplication of what you are getting at

Roughly we have
Z-spread = OAS +/- option value

For callable bond the option is a risk to the investor. They have written/are short the call option.
Z-spread = OAS + call value
7% = 5% + 2%
Volatility increases (all else equal) call value increases
The return investors require for the risk of the call option increases
If the z-spread has not changed the implied OAS drops
7% = 4% + 3%

For putable bond the option is a beneift to the investor. They are long the put option.
Z-spread = OAS - put value
7% = 9% - 2%
Volatility increases (all else equal) put value increases

If the z-spread has not changed the implied OAS drops
7% = 10% -3%

You can also demonstate this using the binomial models.

#4

OAS = Z spread - Option Cost

if vol increases Option cost increases
OAS falls.

OAS = Z spread + Option cost

if vol increases Option cost increases
OAS increases.

#5

I think you find it easier to think option value that cost.

With callable and putable bonds the option is with different parties.

Callable bond the issuer has the benefit of the option. Bond holders demand extra yield (than other risks as measured by tthe OAS whould suggest), issuers must pay bond holders for this option.

Putable bonds the investors has the option. They accept a lower yield (than other risks as measured by tthe OAS whhould suggest) becuase they have the option.

You measure the credit, liquity etc (exluding option risk) of an issuer.

You calculate/determine judge that this should be 5% = the OAS (no options involved)

The company issue 3 bonds
Callable
Putable
Bond with no options.

You would expect yields
Callable z-spread > OAS as the investor gets extra yield due to options
Putable z-spread < OAS as the investor has the benefit of the option
Bond with no options. z-spread = OAS no options.

#6

Why does OAS fall?

Why does OAS increase?