You have been presented with the option of investing in either Bond #1 or Bond #

Question

You have been presented with the option of investing in either Bond #1 or Bond #3 issued by the same UK corporation. Bond #1 and Bond #3 are equal in every respect (i.e. both are 3-year 6.5% coupon bonds), except that Bond #3 has a put option embedded in it. The following are the bonds’ Z-spreads over the UK term structure.

Bond #1: Z-spread = 4.65%

Bond #3: Z-spread = 4.05%

Your broker informs you that Bond #3 is a more attractive investment because, based on its option-adjusted spread (OAS), its option spread is .85% a. What are the option-adjusted spreads (OAS) for Bond #1 and Bond #3? Do you agree with your broker?

Suppose your broker informs you that the option-adjusted spreads (OAS) in part a. was computed using an assumed interest rate volatility of 10%, how would the OAS in part a. be affected if a 5% interest rate volatility is assumed?

Explanation / Answer

Option-adjusted spread (OAS) is the yield spread which has to be added to a benchmark yield curve to discount a security's payments to match its market price, using a dynamic pricing model that accounts for embedded options. OAS is hence model-dependent. This concept can be applied to a mortgage-backed security (MBS), or another bond with embedded options, or any other interest rate derivative or option. More loosely, the OAS of a security can be interpreted as its "expected outperformance" versus the benchmarks, if the cash flows and the yield curve behave consistently with the valuation model.

The OAS effectively nets out the effect of the embedded option. So just think of it as the “option-removed” spread. For a bond with no embedded option, the OAS = the Z-spread.

So Bond 1 OAS = 4.65%

For Putable Bonds

OAS = Z-spread + Option cost = 4.05% + (6.5% * 0.1) + 0.85% = 5.55%

5%

OAS = Z-spread + Option cost = 4.05% + (6.5% * 0.05) + 0.85% = 5.23%

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