Pricing of an Index Option
The price or premium of an option is comprised of intrinsic value and time value.
Intrinsic value is the difference between the strike price of an option and the spot underlying index (i.e. the amount an option buyer can get if he/she exercises the option immediately). Intrinsic value is always positive or zero. It can never be negative.
Time value is the amount of time remaining until the expiration of the option. It is the difference between the option premium and intrinsic value. Time value can be regarded as the value investors are willing to pay for the possibility that they could make a profit from their option position during the life of the option.
Apart from supply and demand in the market, other factors influencing the premium of an index option include the value of underlying index, strike price, volatility, time to expiration and interest rate.
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Underlying index |
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Strike price |
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Volatility |
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Time to expiration |
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Interest rate |
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Underlying index
The underlying index here is referred to the HSI. The higher the value of the HSI, the higher the value of a call option, and the lower the value of a put option.
Strike price
Strike price is the specified price at which the option buyer and seller trade the HSI. An HSI Option is referred to as "in-the-money", "at-the-money" or "out-of-the-money", depending on the current HSI level and the strike price of the option. The following table shows the status of an HSI Option contract in relation to the HSI level and strike price.
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HSI Level > Strike Price |
In-the-money (ITM) |
Out-of-the-money (OTM) |
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HSI Level = Strike Price |
At-the-money (ATM) |
At-the-money (ATM) |
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HSI Level < Strike Price |
Out-of-the-money (OTM) |
In-the-money (ITM) |
Only an ITM option has intrinsic value. ATM and OTM options have no intrinsic value.
Volatility
Volatility is a measure of the fluctuation of the value of the underlying index. It may be seen as representing the degree of risk to the option seller. Higher volatility indicates greater probability that the option may, within the life of the option, move in-the-money and hence the higher the chance the option seller incurs a loss. The greater the volatility, the greater the risk to the option seller. The greater the risk, the higher the premium the option seller demands for the risk taken.
Volatility can usually be classified into historical volatility and implied volatility.
Historical volatility refers to the range of price movements of the underlying index over a specified period of time. When using historical volatility as an input in the option pricing model, it should be noted that future volatility may not necessarily be the same as historical volatility.
Implied volatility refers to the volatility implied by the option's current market price. It reflects market participants' different views about future market movement.
Time to expiration
The longer the time to expiration, the greater the value of an option as there is a greater probability that the movement of the underlying index will make the option become in-the-money. When an option draws nearer to expiry, the decline of time value (what is called time decay) increases rapidly.
Interest rate
A higher interest rate is likely to lead to higher call option premiums and lower put option premiums, reflecting the cost of funding. A call option buyer can defer paying for the underlying index until expiry of the option and invest the funds in other interest-earning instruments during this period. If the interest rate rises, more interest can be earned on the funds. Hence, a call option is worth more to the option holder when the interest rate increases. Nevertheless, the interest rate is normally the least influential factor affecting the option premium.