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Premiums and Values of Traded Options

The asymmetric nature of returns with regard to the price of the underlying instrument, and mirror image of returns to the holder and the writer, mean that options have a value to the holder even if the current stock price is below the call option’s strike price or above the put option’s strike price. The holder of such an option should be able to sell the option for a cer tain amount to a third par ty. This is referred to as the option’s premium. The price of a traded option can be broken into two par ts, its intrinsic value and its life or time value:
Intrinsic value. The intrinsic value is simply the profit that would be realized if the option was in-the-money and exercised. The intrinsic value is zero when the option is either at-the- money or out-of-the-money.
Life or time value. In addition to the price of the underlying instrument there are three factors that determine the value of an option’s premium, the volatility of the price of the underlying instrument, time to expiration and the level of interest rates.
Time. The longer the exercise period the greater the value of the option’s value. This is pretty obvious. If the option is out-of-the-money and expires next week there is less oppor tunity for the bond’s price to rise above that of the strike price than if it expires in six months.
Volatility. The value of the bond will var y with changes in the yield cur ve. The more volatile that interest rates are the more volatile will be the bond’s price. Higher volatility is good for option holders due to the asymmetric nature of returns relative to the bond’s price. If the bond price falls below the strike price it doesn’t matter if it falls a little or a lot as we won’t exercise the option in any event. If the bond’s price rises a lot our profit on exercise will be much greater than if it only rises a little.
The writer (or seller) of an option is paid a premium by the holder (buyer) of the option. This price may be lower or higher than the value implied from option valuation models.
The option’s premium also varies with the level of interest rates but this is far less significant as a factor than either time or volatility. Its effect is also far more subtle and difficult to explain simply. For our pur poses it is sufficient to note that the level of interest rates does affect an option’s value and leave it at that for now.
The first of the following two char ts shows the traded and intrinsic values of the above call option plotted against bond price. The following characteristics are wor th noting:
The value of the premium falls as the option moves deep into or out-of-the-money.
When the option is either deep in-the-money or deep out-of-the-money its value varies with that of the bond’s price.
The second char t shows the rate of change in percentage terms of the option’s traded value against the bond’s price. In the context of this chapter this has little significance but we will be picking up on this in Par t III when we look at trading strategies and risk management. This has the following impor tant characteristics:
The rate of change of the option’s value does not var y in a linear way with bond price.
The rate of change is greatest when the option is close to being at-the-money and
The rate of change reverses direction at a par ticular bond price. Char ts of the first form, which plot the price of one instrument against a single factor (in this case bond price), are sometimes referred to as delta char ts. Risks resulting from changes in the price against this factor are referred to as delta risk.