Valuing Bonds With Embedded Options, Part 2

Option values are positively related to the volatility of their underlying. Accordingly, when interest rate volatility increases, the values of both call and put options increase. The value of a straight bond is affected by changes in the level of interest rates but is unaffected by changes in the volatility of interest rates.

When interest rate volatility increases, the value of a callable bond (where the investor is short the call option) decreases and the value of a putable bond (where the investor is long the put option) increases.

Level of Interest Rates

As interest rates decline, the short call in a callable bond limits the bond’s upside, so the value of a callable bond rises less rapidly than the value of an otherwise equivalent straight bond.

As interest rates increase, the long put in a putable bond hedges against the loss in value; the value of a putable bond falls less rapidly than the value of an otherwise equivalent straight bond.

Call option value is inversely related to the level of interest rates, while put option value varies directly with the level of interest rates.

Shape of the Yield Curve

The value of an embedded call option increases as interest rates decline. When the yield curve is upward sloping (i.e., normal), the more distant one period forward rates are higher than the one period forward rates in the near future. Because a higher interest rate scenario limits the probability of the call option being in the money, the value of a call option will be lower for an upward sloping yield curve.

As an upward sloping yield curve becomes flatter, the call option value increases.

The value of a put option increases with interest rates. When the yield curve is upward sloping, the probability of the put option going in the money is higher. Put option value therefore declines as an upward sloping yield curve flattens.