###### Analyzing Insurance Companies

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The option-adjusted spread (OAS) depends on the interest rate volatility assumption. For a callable bond, the OAS decreases as the interest rate volatility increases, and vice versa.

A high volatility assumption generates a higher value for a call option, while the calculated value of the option-free bond remains unaffected. The calculated value of the callable bond will decrease, moving closer to the bond’s market price.

This implies that the constant spread (i.e., the OAS) added to the one-year forward rates to equate the calculated value to the market price of the callable bond will be lower.

On the other hand, the OAS of a putable bond increases as the interest rate volatility increases, and vice versa. This is because a higher volatility rate generates a higher value for the put option, while the calculated value of the straight bond remains constant.

The calculated price of the benchmark putable bond will be higher, moving away from the market value. This means that the additional constant spread required to equate the calculated value will be higher.

## Question

All else equal, as the interest rate volatility increases, the OAS for a putable bond

most likely:

- Decreases.
- Increases.
- Remains unchanged.

Solution

The correct answer is B.As the interest rate volatility increases, the OAS for a putable bond increases.

This is because higher interest rate volatility generates higher put option value, increasing the price of the putable bond, meaning that its price moves further away from its actual market price.

A higher OAS will thus be required to equate the bond’s value to its market price.

Reading 30: Valuation and Analysis of Bonds with Embedded Options

*LOS 30 (h) Explain how interest rate volatility affects option-adjusted spreads.*