CFM13210 - Understanding corporate finance: derivative contracts: options: valuing options

Valuing options

Valuing options - working out how big a premium should be paid, or what the option contract would fetch if sold to a third party - is a complex subject. HMRC staff will not normally need to query the fair value which a company places on an option (or any other sort of derivative contract) in its accounts. Various mathematical models are used to price options. The most widely known of these is the Black-Scholes model, but there are many other approaches.

You may hear the terms intrinsic value and time value used in connection with options.

Intrinsic value

In the example at CFM13200, when the option over the Oakway shares was granted, it was in the money - the strike price was 220p, but Oakway shares were trading at 225p.

If this is an American-style option, which can be exercised at any time up to and including the expiry date, and the company exercises the option then and there, it would make a profit of 5p per share, or £500 on 10,000 shares. £500 is the intrinsic value of the option.

Suppose that the strike price had instead been set at 225p, so that the option was at the money when it was granted. It would have no intrinsic value. And if the strike price had been set at 230p, so the option was out of the money, it would still have zero intrinsic value - there is no such thing as negative intrinsic value.

If the option is a European option, exercisable only after a period of 6 months. The strike price is 220p, and the market value of Oakway shares is 225p. The intrinsic value of the option will be slightly less than £500, because the company can only receive the pay-out in 6 months’ time, and £500 payable in 6 months is worth less than £500 today. It is therefore necessary to discount the £500 to its present value.

Time value

Would the company still have paid a premium to acquire the option if it had been out of the money? It might have done. If the strike price had been 230p, there is nevertheless a chance that, in 6 months’ time, Oakway shares will have risen above that figure, so the company could make a profit on exercising the option.

The time value of an option is, in simple terms, what that chance is worth. This will depend on three things.

  • How long the option has to run before it expires. The nearer an option gets to expiry, the less chance there is of an out of the money option moving into the money. So its time value will decrease as the expiry date draws nearer;

  • The volatility of the underlying asset - the range of values which the price of the underlying asset might take. Suppose, for example, a call option over shares will only move into the money if the share price rises from 300p to 400p. There is much more chance of this happening if the volatility is high than if it is low.

    (Of course, the future volatility cannot be known. On the basis of past experience you might assume it more likely that the price could rise from 300p to 400p if the price had fluctuated between 250p and 500p in the previous year than if the price had never fallen below 290p or risen above 320p. The more volatile the price of the underlying asset, the greater the time value of the option.)

  • Market rates of interest: normally someone who buys an option will pay a premium up-front. They will either have to borrow money to do this, or withdraw money from existing investments. So they will need to factor the time value of money into the price they are prepared to pay for the option.

If an option is out of the money, it will only have time value. If it is in the money, its value will be a combination of intrinsic value and time value.