P4-Time Value of an Option

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ACCA P4考试：Time Value of an Option
The intrinsic value of the option was based on the assumption that the option would be exercised or lapse today. However, if there is still time until the expiry of the option then it will have a higher total value than its intrinsic value because:
value is placed upon the possibility that the option will become worth exercising, or more worthwhile, between now and the expiry date; and
the purchase of a call option is effectively a form of borrowing for which there is an interest cost which is part of the cost of the option.
1 Components of Time Value
There are three components of the time value:
(1) time to expiry;
(2) expected volatility of the underlying asset; and
(3) the level of interest rates.
2 Time to Expiry
The longer the period to expiry of the option the higher the time value of the option.
The longer the period to expiry, the greater the chance of the option moving into the money and therefore profitable to exercise.
3 Volatility of Underlying Asset
If the price of the underlying asset (e.g. share price) is expected to be highly volatile then the value of the option rises.
This is because there is a greater chance of a "price spike" in the underlying asset, which could move the option deep into the money and lead to a large profit upon exercise.
4 Level of Interest Rates
If a call option is purchased, then only a small proportion of the total price of the underlying asset needs be paid immediately in the form of the premium. The remainder (i.e. the exercise price) will be paid if and when the option is exercised. This is similar to buying the underlying asset on credit.
Therefore the higher the level of interest rates the higher will be the value of the call option.
The opposite applies to put options—the owner of a put has to wait until the expiry date (if European style) before receiving the exercise price. If interest rates rise then the present value of the exercise price falls and with it the value of the put option.
N(d2) represents the probability that the shareholders' call option will be "in the money" on its expiry date, in which case the value of assets would exceed the redemption price of debt. Therefore 1 ? N(d2) measures the probability that the value of assets will not cover the repayment of debt in which case there would be default. Hence 1 ? N(d2) estimates the probability of default.