Effect of volatility and the arbitrage free value, Financial Management

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The volatility assumption has a great influence on the arbitrage free value of the bond. The higher the expected volatility, the greater the value of an option. When we assume a higher interest rate volatility for a callable bond, it means that the value of the call option increases. But the value of the option-free bond is not affected; therefore the value of the callable bond will be lower.

Let us consider that the binomial interest rate tree provides a value of $105.385 for both 10% and 20% interest rate volatility. The value of the callable bond with a volatility interest rate assumed at 20% and callable at par beginning in year-1 is $103.076 and the value of the callable bond with an assumed interest rate volatility of 10% is $103.765. We notice that the higher the assumed volatility, the lower the value of the callable bond. This is because the value of an option increases with the higher assumed volatility. Therefore, the value of the embedded option is higher at 20% assumed volatility than the value of the embedded option at 10%. When a higher value for the embedded call option is subtracted from the option-free value, the value of the callable bond would be lower compared to 10% volatility. The difference between the two values implies that the bond is cheaper by $0.689.


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