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# Interest Rate Volatility

The value of embedded options increases as interest rate volatility increases. This is because embedded options have a higher chance of being exercised when the volatility is high.

### Callable Bond

As the interest rate volatility increases, the value of a call option increases, assuming everything else remains constant. This implies that the value of the callable bond decreases.

From the formula:

$$V_{\text{Callable}} = V_{\text{Straight}}– V_{\text{call}}$$

We can deduce that as the value of the issuer call option increases, with that of the straight bond remaining unchanged, the value of the callable bond decreases.

### Putable Bond

The value of a put option rises with an increase in the interest rate volatility. This implies that the value of the putable bond also increases:

$$V_{\text{Putable}}=V_{\text{Straight}}+V_{\text{Put}}$$

From the above formula, we can conclude that as the value of the investor put option increases with the value of the straight bond being constant, the value of the putable bond also increases.

## Question

All else being equal, as the interest rate volatility increases, the value of a callable bond most likely:

1. increases.
2. decreases.
3. remains the same.

#### Solution

The correct answer is B.

\begin{align*} \text{Value of callable bond} & = \text{Value of straight bond} \\ & – \text{Value of issuer call option} \end{align*}

As the interest rate volatility increases, the value of a call option also increases, assuming everything else remains constant. This means that the value of the callable bond decreases

Reading 30: Valuation and Analysis of Bonds with Embedded Options

LOS 30 (d) Explain how interest rate volatility affects the value of a callable or putable bond.

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