By Hamish Raw
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Extra resources for Binary Options
7 10 0 0. 10 8 0 0. 9 10 0 1. 10 00 1. 1 illustrates how thetas change with the underlying. The assumed strike price is $100 and four separate times to expiry are displayed. 1. It is apparent how little effect time has on the price of an upbet with 50 days to expiry as the 50-day profile is almost flat around the zero theta level. 33 Binary Options 2. Another point of note is that theta is always zero when the binary is atthe-money. In hindsight this should be reasonably obvious since it has already been pointed out that an at-the-money binary is always worth 50.
10 8 0 3. 10 2 0 3. 10 6 0 4. 10 00 4. 1 At the underlying of $96 there is very little difference in price between the 12% and 25% downbet prices indicating a very low absolute vega, compared to the gap between the 4% and 1% prices indicating a high vega. 1. 6 10 0 0. 10 0 0 0. 10 4 0 0. 10 8 0 1. 10 2 0 1. 10 6 0 2. 0 10 0 2. 10 4 0 2. 10 8 0 3. 10 2 0 3. 10 6 0 4. 10 0 0 4. 1 The 25% price profile translates to an almost flat zero vega while the 12% vega barely deviates more. The 4% vega tops out at around the absolute level of 6% whereas the 1% vega disappears from the graph.
The underlying below $99, is also 40%. 2 Lognormal Distribution There is a flaw with using the normal distribution for modelling the price movements of financial and commodity instruments and that is that absolute price movements are assumed. For example, if a healthy company has a share price trading at £1, should the probability of the share going down £1 be the same as the share going up £1? In effect, are the odds of the healthy company going bust with absolutely no assets producing a zero share price the same as the odds of the healthy company doubling the share price to £2?