Читать книгу Binary Options - Hamish Raw - Страница 34

The $99.90 profile is always just 10 cents out-of-the-money and is always perceived to have good chance of being a winning bet. Only over the last day does time erosion really take effect with a near precipitous price fall from 35 to zero. The $99.50 profile paints a different picture as this upbet is always 50¢ out-of-the-money and the market gives up on the bet at an earlier stage. On comparing the gradients of the $99.90 and $99.50 profiles, the former has a shallower gradient than the $99.50 profile for most of the period but then as expiry approaches, this relationship reverses as the gradient of the $99.90 profile increases and becomes more steeply sloping than the $99.50 profile.

This gradient that we are referring to in Fig 2.2.1 is known as the theta. The theta of an option is defined by:

The theta is therefore the ratio of the change in the price of the option brought on by a change in the time to expiry of the option.

To provide a more graphic illustration Fig 2.2.2 illustrates how the slopes of the time decay approach the value of the theta as the incremental amount of time either side of the 2 days to expiry is reduced to zero. The gradient can be calculated from the following formula: