I’m experiencing some confusion with one of the statements regarding OAS Spread - specifically related to LOS 37.h: “Explain how interest rate volatility affects option adjusted spreads.” Here is the statement form the Schweser text that is giving me problems:
“Consider a callable bond. When interest rate volatility increases, the value of the call option increases, the value of the straight bond is unaffected, and (because the issuer, not the bondholder is long the call) the computed value of the callable bond decreases. Hence when the assumed level of volatility of benchmark rates used in a binomial tree is higher, the computed value of the callable bond will be lower, and therefore closer to its actual market price. The constant spread that needs to be added to the benchmark rates to correctly price the bond is therefore LOWER”
I have no confusion understanding either of the following two point: (1) higher volatility in interest rates leads to higher call option value (2) higher call option value leads to lower callable bond value - because you subtract the value of the call option as the investor is effectively short the call. I am confused as to why the discount rate (which is the underlying spot rate plus an OAS spread) should be lower. Shouldn’t the OAS in fact be higher in order to yield a lower callable bond value (which would be reflective of the higher Call Option value), shouldn’t you want to discount cash flow MORE - thus using a higher OAS.
The same question relates to the calculation of OAS on a putable bond.
The OAS removes the value of the option; it is a spread for the underlying, option-free bond.
The price of the callable bond doesn’t change when you change the assumed volatility in your tree.
Increasing the assumed volatility increases the value of the call option. Because the price of the callable bond doesn’t change, the increase in the value of the call option increases the value of the underlying, option-free bond:
Callable bond price = Option-free bond price – Call option price
Option-free bond price = Callable bond price + Call option price
Therefore, an increase in the assumed volatility leads to:
A higher target price for the option-free bond
Lower discount rates to arrive at that target price
A lower OAS
For a putable bond, increasing the assumed volatility increases the value of the put option, decreases the value of the option-free bond, increases the required discount rates, and, consequently, increases the OAS.
Rule 6: Higher Interest Rate Volatility reduces OAS, because volatility in your model doesn’t affect the market price, but does affect your estimated cashflows. With higher volatility you always have lower cashflows (put or call) so you must decrease OAS discount rate to compensate.
Ok - thank you very much. All that I really needed to know is that the OAS is the spread on an option free bond - I can deduce the rest. That being said, that seems like a strange assumption that the OAS is the spread on the option free bond, considering the fact that the branches on the binomial tree represent payoffs of the bond with the embedded option. Could you possibly help me understand this?
Also, as an aside, could you possibly explain why the potential payoffs of bonds with embedded options are not defined as “interest rate path dependent - like an MBS” - it sure seems to me like the payoffs depend on the path the interest rates follow. (Note, if bonds with embedded options were said to be “interest rate path dependent” they wouldn’t be able to be modeled using a binomial tree)
Volatility does not affect OAS of a straight bond, assuming you are using a recombining binomial interest rate model, I hope to god I am not wrong about that.
There are two prices, I call them real price and binomial model price (of straight bond, callable or puttable). The real price is always lower than binomial model price because of liquidity risk, credit risk. That’s why the OAS is positive for all of three bonds.
For straight bond, when volatility increases, the real price is unchanged, but the binomial model price becomes smaller, that narrows the gap between real price of straight bond and binomial price of straight bond, so, decreases the OAS.
If _ actual _ volatility of interest rates increases, the value of a call option will increase, the value of the straight bond will remain unchanged, so the price of a callable bond will decrease.
If the assumed volatility (in your binomial interest rate tree) increases, the price of the callable bond remains the same, so the assumed value of the option-free bond increases.
Magician, you say that if assumed volatility in the tree increases, the price of the callable bond remains the same - is this in the market, and separate to the model value?
You say the assumed value of the option free bond increases. Does the assumed value of option free bond value not remain constant in any volatility scenario in the model?
The market doesn’t know about your interest rate tree. You’re trying to estimate the bond’s OAS based on a number of assumptions, one of which is the interest rate volatility. You’re also assuming that you’re accurately modeling the circumstances under which the option will be exercised.
It does. But you have to understand what we’re doing here.
We’re trying to estimate the OAS for a bond, and we’re given the price of a callable bond, not the price of the underlying straight bond. The market has assumed (consciously or unconsciously) a volatility for interest rates (from which it extracts a price for the call option), and we’re doing the same thing. Unfortunately, we don’t know the volatility that the market has assumed. (In fairness to us, neither does the market.) So we’re simply trying to estimate what we can (OAS) from the data we have (the market price on the callable bond).