The option-adjusted spread (OAS) measures the credit risk of option-embedded bonds, including putable and callable bonds. The spread is calculated after removing any embedded options providing analysts with a spread of an option-free bond.

## What Is Option-Adjusted Spread (OAS)?

The OAS helps traders compare reference rates with the cash flow of fixed-income securities while valuing any included options against general market volatility. While analyzing the embedded option and the security into a bond separately, investors can determine if the investment is worthwhile at a stated price.

The option-adjusted spread is more accurate than just comparing the yield to maturity of a bond to a benchmark making the following necessary to understand:

- What is the option-adjusted spread (OAS)
- Options and volatility
- Option-adjusted spread vs. other spreads
- Calculating the option-adjusted spread of a bond

## Options and Volatility

The yield to maturity (YTM) of a bond is the yield or income returned on a benchmark security. This may be a Treasury security that has a similar maturity plus a spread above the risk-free rate or premium to compensate traders for the additional risk.

When a bond has options embedded, the analysis gets more complicated. These options can include put options that allow holders to sell the security back to business on specific dates and call options giving issuers the right to redeem to security before maturity at a predetermined price. The option-adjusted spread adjusts the spread, accounting for cash flow changes.

The option-adjusted spread accounts for two kinds of volatility affecting fixed-income investments having embedded options: prepayment risk and changing interest rates, something that affects all bonds. The shortfall of OAS is that the estimates are determined using historical data but are used in forward-looking models.

## Option-Adjusted Spread vs. Other Spreads

The zero-volatility spread (Z-spread) and the option-adjusted spread (OAS) are useful tools in calculating a security’s value. Spreads typically represent the variation between two measurements. The Z-spread and OAS assist investors in comparing the yield of two individual fixed-income securities that have options embedded.

### Option-Adjusted Spread

The option-adjusted spread accounts for how a bond’s embedded option can affect future cash flow and the bond’s overall value. The cost of the embedded option is determined by calculating the variation between the Z-spread and the OAS at the anticipated market interest rate. While initial calculations for each of these spreads are comparable, the OAS discounts the value of the bonds by any embedded options. This helps investors determine if a fixed-income security’s listed price is worthwhile based on the additional risks that come with the embedded options.

The option-adjusted spread is an active pricing model, significantly depending on the model being utilized since it adjusts the zero-volatility spread to include the value of embedded options. It takes historical data into consideration as the variability of prepayment rates and interest rates. Since they are attempting to model the probability of early redemption, prepayment behaviors of mortgage holders, and anticipated changes in interest rates, these calculations are very complex.

More sophisticated statistical modeling methods like the Monte Carlo analysis are typically used in predicting the probability of prepayments.

### Zero-Volatility Spread

The Z-spread gives analysts a way to evaluate the pricing of a bond. It’s the difference or consistent spread between the U.S. Treasury spot rate yield curve and the value of the present cash flow.

It’s the systematic measurement for comparing a bond’s price or current cash flow value with every point of maturity shown on the Treasury yield curve, so the cash flow of the bond is discounted based on the Treasury curve’s spot rate. This complex calculation takes the spot rate at any given point on the curve and adds it to the Z-spread without taking into consideration the value of any options embedded in the bond.

Mortgage-backed securities (MBS) typically have embedded options due to the increased chance of prepayment since mortgage borrowers often refinance mortgages when interest rates decrease. Embedded options result in anticipated cash flows that can be altered by issuers because the bond is callable. The issuer can also use embedded options if interest rates fall as they can call the unpaid debt, settle it, and reinstate at the lower interest rates allowing them to reduce the cost of capital.

### Nominal Spread

A third spread to consider is the nominal spread, which is the most basic kind of spread concept measuring the difference in basis points between a non-Treasury instrument and a risk-free U.S. Treasury debt instrument. The spread difference is calculated in basis points and provides only the measure of a single point on the Treasury yield curve resulting in significant limitations.

Investors investing in bonds that have embedded options take on additional risk since if the issuer calls the bond, the trader will most likely have to invest in different bonds, having decreased interest rates. Most bonds having call options embedded typically are charged a yield premium as opposed to bonds having similar terms. This makes the option-adjusted spread useful in understanding the current value of security debt having call options embedded in them.

## Calculating the Option-Adjusted Spread of a Bond

The OAS measures the credit risk of bonds with callable or putable options embedded in them. In order to calculate this spread, you must eliminate the value of the option, which leaves you with a spread of an option-free bond.

### Treasury Securities

Analysts value Treasury securities by discounting payments with zero-coupon Treasury rates. The two most common curves analysts use for discounting are LIBOR curves or Treasury curves. Discounting with a zero-coupon curve typically results in value extremely close to the bond’s market value.

Unfortunately, analysts aren’t able to locate a zero-coupon Treasury rate with a value calculated by using it that equals the noted market price. They can, however, quantify the variation between the market price and the discounted value by identifying how much the zero-coupon rate needs to be adjusted. Hence, the discounted value equals the market price.

This adjustment to the zero-coupon is called the zero-volatility spread for that security. A negative Z-spread indicates a security is expensive, while a positive Z-spread means a security is cheap.

### Corporate Bonds

Analysts use the same approach for corporate bonds that they do for Treasury securities. Since there is credit risk associated with corporate bonds analysts consider them less worthy compared to their Treasury bond counterparts. The Z-spread for corporate bonds reflects this, which is favorable for them. The higher the Z-spread, the higher the credit risk. The LIBOR curve is usually used as analysts consider it a better measure for calculating Z-spread and accurately reflecting the credit risk of a corporate bond.

### Option-Embedded Bonds

The Z-spread isn’t appropriate for bonds with callable or putable options as they can’t be simply be valued by discounting scheduled payments. The volatility of interest rates also plays a significant role. Analysts need to utilize a model that takes into account interest rate volatility to help account for the risk of the option embedded bond. The Stochastic Term Structure Model is one way to do this.

- Begin with a zero-coupon interest rate curve and parameters to determine the volatility of the interest rates.
- Several possible future interest rates scenarios, above and below the existing spot curve, are calculated using these inputs. They can use a rule to decide when an embedded option may be exercised.
- The value of the security is calculated by discounting the payments associated with each scenario based on that scenario’s interest rate.
- The average of all scenarios is calculated

The calculation of option-adjusted spread is relatable to the calculation of the zero-volatility spread as the OAS adjusts to zero-coupon interest rates for all scenarios. Hence, the model value or the average value of all scenarios is the same as the bond’s market price. If the bond doesn’t have an option embedded, the OAS will equal the Z-spread. However, investors need to be mindful not to confuse the option-adjusted spread with the zero-volatility spread.

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