Option adjusted spread and Interest rate volatility

It is written that, if interest rate volatility goes up for callable bond, then option asjusted spread goes down. My question is that if Volatility goes up> price of call option goes up > value of callable bond goes up… Then OAS should go up to match with the new value of callable bond as they are inversly related. My second question is: “The convexity of call option is negative when it is in the money & Positive when it is out of the money. On the other hand, the convexity is always positive for put option.” Is my above statement is correct?

  1. As volatility goes up, call option value goes up, so callable bond value goes down, so it gets closer to its real price, so the OAS needed for adjustment is lower

  2. Yes, however, i do not think that the convexity is ALWAYS negative when the call option is in the money. I’d say the probability of the convexity to be negative increases as the call option gets deeper in the money. If someone could agree with me, it’d be swell.

I thought am oas means a, spread without the effects of an option?

Suppose that the market price of a callable bond is $985.03. We build an interest rate tree with 10% volatility and estimate the OAS as 57bp: the spread we need to add to each (forward) rate in the tree to get a price of $985.03.

Now we increase the volatility of our tree to 15%. The high interest rates in our tree are now higher and the low interest rates are now lower (than in the 10% volatility tree). The likelihood of the option being exercised is higher. When it is exercised, the cash flow is lower, so, overall, the average cash flow in our tree is lower (than in the 10% volatility tree). We have to discount those new cash flows to get . . . and here’s the important point . . . a price of $985.03. (The market price doesn’t change because we changed the volatility in our tree. The market doesn’t know about the volatility in our tree, and if it did know, it wouldn’t care.) As we’re discounting lower cash flows to get the same market price, the discount rates are lower, so the OAS is lower, say, 43bp.

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Rahat a callable bond goes down in value when the call option goes up in value, because a callable bond = value of straight bond - value of call. The call is a benefit to the issuer, not the investor.

This explanation has been extremely useful for me to understand the OAS correctly. Let me write the process but for a putable bond:

If the interest rate volatility is higher, the likelihood of the option being exercised is higher (that’s why the option increases in value). Hence, for a putable bond this would mean that the cash-flow is higher when it is exercised, and so it is the average cash-flows in our binomial tree. Since the MARKET PRICE DOES NOT CHANGE, but the AVERAGE CASH FLOWS ARE HIGHER, you have to DISCOUNT AT A HIGHER RATES to match market price.

High volatility for a putable bond, means higher OAS.

High volatility for a callable bond, means lower OAS.

Is that correct?

Bingo!

Thanks one more time Sir!

You’re quite welcome.

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Just remember it by this formula

Z = OAS + OC for calls

Z = OAS - OC for puts

Keeping Z the same, higher OC would lower OAS for calls, and raise OAS for puts.

Thank you both for these explanations. What I do not understand is: why are cash flows lower when a callable bond is called, and cash flows higher when a putable bond is put?

Because value of callable bond is lower, value of putable bond is higher.

The criterion that we’ve been using to decide when a call or put will be exercised is that it well be exercised whenever it is in the money. So we assume that a call option will be exercised whenever the call price is lower than the present value of the remaining cash flows: lower cash flow. And we assume that a put option will be exercised whenever the put price is higher than the present value of the remaining cash flows: higher cash flow.

In the real world, this is certainly too simple a criterion, but it’s the one we’ve been using universally in the CFA curriculum.

Thanks!!!