To assess the potential risks and possible rewards of options, the following are used sensitivity indicatorswhich is commonly referred to as greeks. When using vanilla options, one does not only refer to the five well-known Greeks, but also delves into more complex matters related to determining the risk measure of option contracts. With binary (numerical) options The case for sensitivity assessment is both more complicated and simpler.
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Binary options: the math is still the same
The difficulties are due to the fact that the math of binary options is understandable and easy to calculate using well-known models only for European options. However, European binary options are less interesting in terms of investment attractiveness compared to American binary options. The reason is obvious, - American binary will be executed the instant the underlying asset reaches the barrier (strike prices). Whereas holders of European binary options under the same circumstances must remain in the position until the option expires if they intend to maximize the value of the contract payout.
At the same time, the models for estimating the value of American binary options, although they exist, are rather difficult to understand and to use them in calculation tasks. In addition, research in the field of solving the problem of calculating the price (and Greeks) of binary options has not yet resulted in a clearly acceptable model. The fact that in practice banks often use their own developments, which are usually closed, also adds to the complexity.
The most important Greek of binaries is delta
At the same time, however, there is some good news. In fact. For binary options, almost all the main sensitivity indicators (gamma, theta, vega, ro) are of little importance. At any rate, their effect on the option price is so small compared to the deltathat the use of Greeks becomes meaningless. At least to the extent that it is practiced with vanilla options. The exception is when managing large option portfolios, which individual investors usually do not deal with.
The delta profile of binary options is identical to that of vanilla options with the same strike as the barrier of the binary option (see Figure 1), simply because the return profile of the binary option is the delta of the corresponding vanilla option (with the same strike as the barrier). And since the gamma of the vanilla option is a private derivative of the delta on the underlying asset, we get this identity (delta of binary = gamma of vanilla option).
Profile of an American Binary (say, tangent, or one-touch) has the same shape with a slightly higher expression when approaching the option strike price (1.31 from the example above). And, of course, at any time to expiration, the profile of the "American" will tend to the delta of the European binary at the option expiration date (red line in Fig. 1). It is also natural that the right side of the delta of the American binary (above the strike price) will simply not exist, because when the barrier is reached, this option will be immediately exercised (see Fig. 2).
Moreover, the final segment of the path to the barrier for the American binary is extremely difficult to accurately calculate. And it is unnecessary. Since in close proximity to the barrier, market makers prefer to close options trading (in any case, this is what Saxo Bank does). Therefore, if your binary is a few points away from the barrier, you will not be able to close the position if you want to. Either you have to hope for an option execution or wait for a pullback from the barrier level.
Of course, sometimes it makes sense to consider also theta (sensitivity to time to expiration), and vega (sensitivity by volatility). However, it should be noted: the volatility of an option directly affects the probability of reaching the barrier that we are actually trading the option. Therefore, as they say, everything is already in the prices.
As for the theta, it can also be said that its importance for a binary trader is of very little significance if it is a simple speculation. A much more important role is played by another circumstance. Namely, whether or not we have managed to guess for the time period in which the option will be alive, whether or not the underlying asset will reach the binary barrier.
Mikhail Chekulaev, author of the book "Financial Options." with the support of Saxo Bank