Option Adjusted Spread
What you'll learn
- LOS 25.gExplain the calculation and use of option adjusted spreads.
- LOS 25.hExplain how interest rate volatility affects option adjusted spreads.
So far our backward induction process has relied on the risk free binomial interest rate tree; our valuation assumed that the underlying bond was risk free. If risk free rates are used to discount cash flows of a credit risky corporate bond, the calculated value will be too high. To correct for this, a constant spread must be added to all one period rates in the tree such that the calculated value equals the market price of the risky bond.
This constant spread is called the option adjusted spread (OAS).
A $100 par, three year, 6% annual pay ABC, Inc., callable bond trades at $99.95. The underlying call option is a Bermudan style option that can be exercised in one or two years at par.
The benchmark interest rate tree assuming volatility of 20% is provided here:
Compute the OAS on the bond.
Solution
The value of the bond using the benchmark interest rate tree is $101.77, as shown here:
To force the computed value to be equal to the current market price of $99.95, a constant spread (OAS) of 100 bps is added to each interest rate in the tree, as shown here:
OAS is used by analysts in relative valuation; bonds with similar credit risk should have the same OAS. If the OAS for a bond is higher than the OAS of its peers, it is considered to be undervalued and hence an attractive investment (i.e., it offers a higher compensation for a given level of risk). Conversely, bonds with low OAS (relative to peers) are considered to be overvalued.
Consider for a moment the difference between the calculated value of a bond that we obtain from a tree and the bond’s actual market price. The greater this difference is, the greater the OAS we would need to add to the rates in the tree to force the calculated bond value down to the market price.
Suppose that a 7%, 10 year callable bond of XYZ Corp. is trading for $958.
Analyst A assumes a 15% value for future volatility in generating her benchmark interest rate tree and calculates the value of the bond as $1,050. She then computes the OAS (the increase in discount rate required to lower the calculated bond value to the market price of $958) for this bond to be 80 bps.
Analyst B assumes a 20% value for future volatility, and because of higher assumed volatility, the computed value of the bond turns out to be $992. (Note that this is lower than the $1,050 calculated by A, the higher the volatility, the lower a callable bond’s value.) The OAS calculated by B is accordingly lower at 54 bps.
Observe that for the same bond, the OAS calculated varied depending on the volatility assumption used.
When we use a higher estimate of volatility to value a callable bond, the calculated value of the call option increases, the calculated value of the straight bond is unaffected, and the computed value (not the market price) of the callable bond decreases (since the bondholder is short the option). Hence when the estimated (or assumed) volatility (of benchmark rates) used in a binomial tree is higher, the computed value of a callable bond will be lower, and therefore closer to its true market price. The constant spread that needs to be added to the benchmark rates to correctly price the bond (the OAS) is therefore lower.
Figure 25.1: Relationship Between Volatility and OAS
To summarize, as the assumed level of volatility used in an interest rate tree increases, the computed OAS (for a given market price) for a callable bond decreases. Similarly, the computed OAS of a putable bond increases as the assumed level of volatility in the binomial tree increases.