# Volatility Risk in Bonds with Embedded Options

Bonds with embedded options such as call options and put options also have volatility risk. This happens because any factor that affects the value of the embedded option will also impact the value of the bond. We earlier learned that interest rates affect embedded options. When interest rates rise, the price of the embedded call option declines. Therefore, the overall effect on the decline in the price of the bond is less. Apart from interest rates, there are other factors that affect the price of the embedded options. One such factor is expected volatility. For bonds this is called expected yield volatility.

In general, the higher the expected yield volatility, the greater is the value of the option.

Let’s review how the price of a call option is affected by the embedded option.

Price of Callable Bond = Price of Option-free Bond – Price of Call Option

So, how will the bond price change when volatility increases? When volatility increases, the price of the call option increases. This will result in a decrease in the price of callable bond. In callable bonds, therefore, the volatility risk arises from an increase in volatility.

The opposite is true for puttable bonds.

Price of Puttable Bond =  Price of Option-free Bond + Price of Put Option

When volatility increases, the price of put option increases, and hence the price of puttable bond will also increase. In puttable bonds, therefore, the volatility risk arises from a decrease in volatility.