OAS - not getting the intuition behind it

CFA Level II Fixed Income
#1

“If interest rate volatility increases, the OAS for the callable bond will decrease”

Looking at curriculum, see the text, see the chart, but deep inside can not get the intuition WHY?..

Where am I wrong or what would be a better way to think about it?

Volatility UP -> call UP -> callable bond DOWN, so holding price constant, rates which we use for discounting, should go UP.

#2

Value of the Callable = Value of the Straight bond - Value of the Call Option. Volatility makes the value of the call increase, so the callable bond must decrease. That’s the intuition. The spread is applied to the interest rate tree, so it’s not quite the same as a z-spread.

#3

With all due respect, you’re talking about something completely different than what the OP asked in his question.

#4

The key to understanding this is the realization that irrespective of the volatility assumption in your tree, the market price of the callable bond doesn’t change: the market price is the market price. The market doesn’t know what volatility you have in your tree, and if it did know, it would have the good sense not to care.

With that in mind, here’s what’s going on:

When you increase the volatility assumption in your binomial tree:

  1. The high interest rates in the tree will be higher, and the low interest rates in the tree will be lower.
  2. The lower the low interest rates, the higher the present value of the remaining cash flows.
  3. The higher the present value of the remaining cash flows, the more likely it is that the bond will be called.
  4. When the bond is called, the lower the cash flow at that node, so the lower the average cash flows for the entire tree.
  5. The lower the average cash flow, the lower the average discount rate needed _ to get to the same present value _.
  6. The lower the average discount rate, the lower the required spread (OAS).

By the way: this isn’t intuition; it’s analysis.

#5

Magician is too far in the trees :wink: …

  1. Z spread for callable bond = risk free rate + OAS (which is spread for straight, option free bond) + value of call

  2. If volatility rises the value of the call increases. Normally the Z spread would increase, but that would mean the value of the callable bond would fall (rate rise = bond value falls)

  3. But here it’s stipulated that the price of the callable bond stays the same, i.e. the Z spread stays the same…so what gives?

  4. The increase in the value of the call (due to volatility increase) pushes the OAS spread down (note the risk free rate will stay pretty much constant so it’s not the component that’s giving)

#6

OK, then.

At least what I wrote is correct.

The z-spread _ is not _ the risk-free rate + OAS + value of call. It’s roughly the OAS plus the value of the call option; the risk-free rate doesn’t enter into it.

The key here is that when the volatility increases the average cash flow decreases, so a lower spread is needed to arrive at the (same) market price.

#7

Right right. So total rate = Rf + OAS + option; whereas Z spread = OAS + option.

Why would cash flows decrease when Vol increases? The price of the bond stays the same.

#8

CF would decrease because if someone calls the bond (higher probability due to the higher volatility) you will have less cashflow. Then to get the same market price (but with lower cashflow) you will need a lower discount rate, so a lower OAS. S2000magician doing the same analysis with the interest tree but in the case of a puttable bond, will the increase in volatility bring a higher probability of putting the bond? But what happens then?

#9

Thanks!

#10

When the volatility increases it’s more likely that the issuer will exercise the call option. The decision rule that CFA Institute uses in its examples is that they exercise the call option when it is in the money: the call price is lower than the (then) present value of the remaining cash flows.

Think of it this way: issuers call bonds when it’s in their best interest to do so: it costs them less to call it than to continue to pay coupons on it. Lower cost to them is less cash flow to the bondholders.

#11

That’s correct.

For a putable bond you look at the top of the tree: the higher interest rates will be higher, so the PV of the remaining cash flows will be lower, so the bond is more likely to be put (when the put price is higher than the PV of the remaining cash flows), so the average cash flow is higher, so the average discount rate has to be higher, so the OAS is higher.

#12

thanks magician, I asked you because I did the same analysis but I was unsure about the higher average cash flow. why is it higher If I am going to put the bond (giving it back) ? Because I am going to substitute this bond with another one with higher cash flows?

This is the only thing I am missing. For a callable bond, if called I will have less cashflow (“I loose the bond”) but what if I put it?

Thanks

#13

If you were a bondholder, why would you exercise your put option if it were going to result in you getting less money?

#14

:slight_smile: I got the point, obviously I would not put it. I don’t know why I was relating the cashflows with the put option.

thanks!

#15

You’re quite welcome.