###### The Information Content of Dividend Ac ...

Modigliani and Miller assumed that both inside and outside investors have similar information... **Read More**

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.

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.

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:

- increases.
- decreases.
- 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.*