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5. Closing out

Thus far, we have only considered situations where options run to expiry. In practice, buyers and sellers tend to close out their positions before expiry by adopting equal and opposite new positions that exactly cancel out the original positions.

• If I have a long/short call position in GBP/USD, I can close it out by selling/buying the identical call option at the respective bid/offer rate.
• Likewise, if I have a long/short put position in GBP/USD, I can close it down before exercising by selling/buying the identical put option at the bid/offer rate

5.1 Closing out before expiry – worked example

GBP/USD spot is 1.5770/75. I am bullish about GBP/USD and decide to buy two 3-month call option contracts at a strike price of 1.6000. The GBP/USD long call premium is quoted at 0.0233/0.0235.

• I buy in at 0.0235 USD, putting up margin of 5,875 USD
• Sterling duly appreciates to 1.6400/05 after 1 month and I decide to close out without waiting for expiry. Meanwhile, the option premium has risen to 0.0503/0.0507. My profit is:-
  (0.0503 – 0.0235) X 125,000 X 2 – 5,875 = 825 USD

  Had GBP/USD fallen instead to 1.5600/50 and the option price to 0.0206/0.0208, my loss would have been :-

  (0.0235 – 0.0206) X 125,000 X 2 = 725 USD

6. Option pricing

Thus far, we have not answered the question of how options are priced. The option premium is made up of two components, intrinsic value and time value.

option premium = intrinsic value + time value

6.1 Intrinsic value

Intrinsic or “objective” value measures the degree to which the option is in the money. Out-of-the-money and at-the-money currency options have zero intrinsic value. In–the-money currency options have intrinsic value equal to the difference between the spot and exercise rate.

6.2 Time Value

Time or “subjective” value reflects the probability that a currency option will expire in the money, which is measured by the delta statistic. The delta also estimates the movement in the option price as a result of a change in the underlying currency.

Factors that determine time value of currency options are: -

• Term to expiry: The longer an option has to expiry the greater the probability that it will expire in the money.
• The volatility of the underlying currency pair: Rising historical volatility is reflected in rising option premiums. The sensitivity of time value to changes in volatility is measured by the vega statistic.
• Interest rate differentials: Call option premiums rise when the base currency interest rate falls relatively to that of the secondary currency, and vice versa for puts. The sensitivity of time value to changes in interest rates is measured by the rho statistic.

The most important property of time value is that it decays to zero by expiry. The rate of decay is gradual at first but accelerates as the option draws to expiry. The rate of time decay is measured by the theta statistic.

Time value is maximised at the money. Deep out-of-the-money options have low time value because the probability of expiry in the money is small. Deep in-the-money options also have low time value because the market is reluctant to pay much of a premium for an event (i.e. expiry in the money) that looks highly likely.

For currency option buyers, the option price at any time reflects the state of a continuous tussle between intrinsic and time value. Even if a currency option moves into the money, the option price will fall if the gain in intrinsic value is overwhelmed by falling time value.

Finally, although at-the-money options have the most time value, they have the greatest amount of time value to lose over the remaining term to expiry.