Could someone please explain how this works?

I presume that by “interest rate volatility” you mean the volatility assumed in a binomial interest rate tree.

If so, it works this way:

- Increasing the volatility assumed in a binomial interest rate tree decreases the OAS on callable bonds and increases the OAS on putable bonds
- Decreasing the volatility assumed in a binomial interest rate tree increases the OAS on callable bonds and decreases the OAS on putable bonds

Thanks! Can you please explain why this is so? When interest rates go down, a bond is more likely to be called. How is this linked to OAS and interest rate volatility?

Also, what is the relationship between interest rates and volatility?

Is this the relationship: When interest rates are high, volatility is also high. So when volatility is increased, a lower OAS is required to match the current price of the callable bond. So when volatility is high, it is less likely for the bond to be called. So this is good for the investor. A lower OAS for bonds with similar credit ratings means that the bond is overvalued. Who benefits from this?

My pleasure.

In a moment.

That’s true.

It’s pretty much independent of them.

Level of interest rates and volatility of interest rates are different things altogether.

First, understand that we’re talking about the assumed volatility of interest rates that you use to create a binomial interest rate tree. Ideally, you’ll assume the actual interest rate volatility that you will experience in the future. Good luck with that.

Second, understand that the market price of the callable bond doesn’t change because you change the assumed volatility in your binomial interest rate tree. The market doesn’t know what volatility you’re assuming, and even if it did, it would have the good sense not to care.

If you increase the volatility of interest rates in your binomial interest rate tree, the low interest rates will be lower and the high interest rates will be higher. Lower low interest rates make it more likely that the bond will be called. When the bond is called, the cash flow you receive is lower than what you would receive if it were not called. (That’s the reason the issuer calls the bond: to save money.) So if it’s more likely to be called, it’s more likely that you will receive lower cash flows, so the average cash flow in your tree will be lower. To get the same market price with lower average cash flows, you need a lower discount rate, which means a lower spread: lower OAS.

Thanks so much for such a detailed response! Wow…you’re so good at explaining things

“If you increase the volatility of interest rates in your binomial interest rate tree, the low interest rates will be lower and the high interest rates will be higher”.

This makes so much sense now!

You’re quite welcome.

Glad to be of some help.