# Option cost as a %

Can anyone suggest an intuitive way to think of the option cost as a % for fixed income securities?

Is it similar to the risk of an option being exercised… for example, in an MBS, a very large Z spead but a small OAS , meaining there is a larger option cost and more risk of prepayments?

Price of bond with option - Price of bond without option = Cost of option.

You can think of % cost as Cost of option / Par value or Cost of option / Price of bond without option.

If you had a Bond with a large Z spread and a smaller Option cost than the embedded option should be one that benefits you, like a put option. A bond with a prepayment option for the issuer should increase the spread over a standard Z spread, because you (the bond holder) are facing all the risk if interest rates decline.

So think about the formula Option cost = Zspread - OAS. So in the case of the issuer having a prepayment option, the option cost is going to be negative. So options that benefit the borrower(issuer) will be negative in the formula because they are paying us (bond holders) for them via higher yeilds.

I was confused by this for a while, then it came up in another thread where it got cleared up. I’ll see if I can find the link.

Thanks for the Answers! What i had in mind was…is the magintude of the Option cost in any way related to the probability that the option is exercised?

Most definitely. If we adjust the future volatility assumptions in our binomial model to price the OAS, then the future shifts in interest rates will be wider, and therefore more opportunities for the bond to be called will arise. Which will result in a lower PV of future payments (or Higher Yield).

Say under our initial volatility assumptions Interest wouldn’t shift far enough for the bond to be called for atleast another 3 years. Then we adjust the volatility assumptions and now the first scenario where the bond is called happens next year. So under the new vol assumptions there are more scenarios where the bond is called, and less future interest payments to discount back to PV, lowering the total present value of the bond.