# Understanding the r/s between interest rate volatility and OAS

Dear all,

Reference to LOS 44.h: Explain how interest rate volatility affect OAS

The paragraph that follows used callable bond as an example.

As interest rate volatility increases, call option value will increase and this cause the value of the callable bond to fall.

It has been stated in the paragraph that this price will be closer to its actual market price. It states furthers that the constant spread that needs to be added to the benchmark rates to correctly price the bond will be therefore lower.

1. Question 1: Why is price closer to its actual market price?
2. Question 2: Why the OAS to be added is lower? I thought price and return are inversely related. If price of callale bond drop, the OAS that need to be added should be larger instead?

Can someone explains to me?

Thank you.

Cheers,

Ernest

Great question. In for the answer.

Good to see you post again, Ernest.

You’re confusing price with value.

How about you re-write the original paragraph?

Is this from the CFA Institute curriculum, or from Schweser or Élan?

I suspect what they’re comparing is the price of a callable bond generated from a particular binomial tree model to the market price. As you increase the interest rate volatility in the model (leaving the OAS constant), the model price of the bond will decrease, reflecting the increased value of the call option. Similarly, if you increase the interest rate volatility of the model (leaving the price constant), the model OAS will decrease, reflecting the increased value of the call option.

Hi Kos!

Haha thanks man! Let’s work hard together! Thanks S2000magician!

Yup, its from Schweser.

Can I say that the purpose of adding a constant spread (i.e. OAS) to the return is to prevent the mispricing of credit risky bond (e.g. if risk free rate is used to value the bond, the bond will be overpriced)

Thanks again.

You’re quite welcome.

Yes.

Actually, the OAS covers all risks (not just credit risk) other than:

• Option risk (which we have explicitly removed)
• Those present in comparable Treasury secuirites (which are included in the underlying Treasury yield curve)

My pleasure.

Hey S2000 Magician, This is throwing me a bit as well. I had the exact same questions Ernest had to start this thread. In you answer, “Similarly, if you increase the interest rate volatility of the model (leaving the price constant), the model OAS will decrease, reflecting the increased value of the call option.” Do you mind expanding a bit on that. In otherwords I get that we are holding the calculated model price constant and vol is shifting, by why exactly is OAS decreasing? It’s very counterintuitive for an decrease in OAS in a situation where the bond’s market value should decrease. Thanks

Remember that the OAS is equal to the z-spread less the option cost (measured in basis points of additional yield). The more valuable the option, the higher the option cost, so the lower the OAS.

If interest rates are more volatile, it’s more likely that the call option will be in the money, so it’s more likely that it will be exercised: the option is more valuable. And when the option is more valuable, its cost is higher, so the OAS is smaller.

I think I actually got it, So for a callable bond, if we increase volatility, in each node, there is a higher liklihood for the PV of cashflow to be adjusted down from a price above the call price to the call price (lets say par). If one of the PV’s of your node’s is let’s say 102 you will need to decrease that price to 100. Now to discount those NEW cashflows to the SAME model price (pv at node 0) you originally calculated, you would have to lower your discount rates, in otherwords reduce the OAS at each node. Same idea applys to a put, A put option would INCREASE price at a specific node where based on increased volatility, the bond fell below put price (lets say par). So if a bond’s pv at a node fell to 97, and the TOTAL model price is kept constant, the node’s value would move from 97 to 100, and you would have to increase the discount rate at that node to compensate for the higher price. This would be reflected in a higher OAS. S2000, you mind sanity checking that logic? Thanks

Yes, and yes.

Awesome, thanks a lot. Took a few minutes to wrap my head around the constant price. Have a good evening

My pleasure.

I know how that feels.

And you as well.