Options – A complete and Straightforward Explanation

Options – A complete and Straightforward Explanation


Options still have a kind of nimbus:

Very complicated and only to be understood by a few illustrious financial freaks.

Total nonsense.

There are many misunderstandings about options, even among many financially educated people, simply because the common explanations are unnecessarily complicated.

Therefore, I would like to try today to illustrate the matter a little more vividly.

I am convinced that even if you already have options, you will have a little aha moment after this article.


  • What is an option?
  • How does the rating of options work?
  • Does that also apply to Covered Calls, Spreads and Iron Condors?
  • How people fall for options with options
  • Are the option models perfect?
  • Is it possible to earn money with options trading?
  • Should I hedge my portfolio with put options?
  • Are options an alternative to ETF and stocks?
  • For the sake of completeness: What an option is not
  • Conclusion
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What is an option?

There is so much technical gibberish in this area I want to omit as far as possible. However, we first have to agree on a few terms.

A common definition is as follows:

An option gives the owner the right but not the obligation to buy (call) or sell (Put) a certain commodity within a certain time (American) / at a certain time (European).

American: option may be exercised at any time during the term

European: Option may only be exercised at maturity.

If you represent the above definition strictly graphically, then you can illustrate the two types of options as follows:

Long-call option


Long-put option

If the price of the underlying (ie what the option relates to, eg a stock) is below or above the strike at the time of exercise, it may make sense not to exercise the option.

Simply put, if, for example, a stock is currently traded for € 90 on the market, I will not exercise the right and buy it for $ 100, even if a call would allow me to. Would not be advantageous.

How does the rating of options work?

Here’s the sticking point:

Many know a few models by name, such as Black-Scholes or the binomial model.

You enter a few data in front (such as maturity, risk-free interest, etc.) and at the end you get a number spit out. The fair value of an option.

But what does that mean anyway?

Fair means in mathematics that the expected value is zero.

The classic example is a coin toss. Imagine we both throw a coin and the odds of winning or losing is 50% each. If you win I pay you 10 € and if you lose you pay me 10 €.

Our expected value is 0, because: 0,5 * 10 € -0,5 * 10 € = 0 €

Now let’s take a look at the graphic for the definition of a long call from above:

Long-call option

What is the expected value?

In other words, what’s the worst thing that can happen to you here? Right, that you do not make profit or loss.

What is the best that can happen to you? That the Underlying / Underlying goes off like a rocket and you bring back fat booty.

We may not know the exact probabilities, but we can say that the expectation value is definitely positive, because x * (+ y) – (1-x) * 0 = + xy

So what would you do if someone offered you something with a positive expectation? Right, you would bet as much as possible.

Would that be a fair game? Of course not, because your positive expected value corresponds to the negative expected value of your contract partner.

Trivially speaking, nobody will offer you an option for free. Eh clear.

What now makes an option pricing model, it tries to calculate what the expected value of the above game is. You have to make some assumptions about that, especially how the returns on the underlying are distributed.

Let me illustrate this graphically:

Option Probability distribution

Ok, step by step.

The red curve is the assumed probability distribution for the underlying. Now you go and divide the whole thing into intervals.

In the example above, I picked out an interval at random. It can be seen from the probability distribution that the probability that the underlying is somewhere in between when exercised here is 10% .

On average, for example, you will also have made 5 € profit if you finish in this interval. For our expected value is thus 0.1 * 5 € = 0.50 €

This interval thus contributes 50 cents to the expected value. Of course there are more such intervals.

option probability distribution-2

If you start to make the intervals infinitesimally small and add up the expectation values ​​of all these intervals, you get the expectation value for this option.

option probability distribution-3

All these small intervals with their expected values ​​add up.

Let’s just assume that the expected value for the above option is $ 10.

What would you ask for a bonus so that the game is fair for both sides?

Quite simply, 10 € or better said, exactly the expected value!

We remember, at the beginning of our train of thought, the situation looked like this:

A good deal for the buyer of an option (long), a bad thing for the seller of an option (short).

While the buyer has nothing to lose but can win everything, the seller can lose everything but win nothing.

To try the numbers from our example, the buyer has a positive expected value of 10 € and the seller has a negative expectation of 10 €.

To make the whole thing fair, the buyer of an option now has to prepay the seller for the expected value as a premium.

Finished. Now we have a fair game or a fair valued option.

That’s the basic idea when evaluating options. By the way, this also applies to puts.

Does that also apply to Covered Calls, Spreads and Iron Condors?

Yes. No matter how you combine options and stocks, when Black-Scholes applies, you do not change the expectation.

covered call

The point is, you can use options to create really creative payoffs, but at the end of the day they all have the same expectation from the point of view of Black-Scholes or Cox-Ross-Rubinstein (binomial model) .

iron condor

You can turn yourself upside down, in the end it does not matter what you do or how complex your position is. You do not influence your expected value.

bull spread

If you want a nice overview of a variety of option strategies, then I can recommend you the page “The Options Guide” .

Do not forget: the expected value remains the same!

How people fall for options with options

What appeals to many people are strategies that generate regular revenue from premiums by selling options.

A good example is the Iron Condor. This is usually built up in such a way that the current price is somewhere in the middle and you therefore take the premium even if it does not move.

So you act on the short side and take, for example, the premium regularly every month. Let’s just say, 5% a month is sold as a seller (for the time being).

It sounds great too: Plannable revenue! Well the height is limited but they come regularly.

I love that, every human being does that!

Often people dare to hesitate, realize that it seems to be doing well and after a few months in the firm belief that they have found the Holy Grail for financial freedom.

This goes on for about 20 months (100% / 5% = 20) and then comes the big bang. A big market movement, a crisis or something else consumes all premiums previously received.

Absolute mourning on the part of investors.

All that has happened here is that many small premiums earned regularly have been exchanged for a rare big loss.

Of course, the big bang can happen sooner or later. When exactly, you do not know that. From a mathematical point of view, however, in our example it will appear on average every 20 months.

From the perspective of an option valuation model, nothing changes in your expected value!

Do not forget that.

Short Warning: There are also many self-proclaimed stock market gurus who sell this type of options as a trading system to unsuspecting investors. Absolutely foolproof and extremely profitable.

For only € 49.99 a month.

This is bullshit, of course. As always with such surefire boxes one should ask oneself why these scammers (it must be said so) have to sell their stock market letters and not simply their own system to act for themselves.

Quite simply, after a while, they implode and consume all the previous small gains.

Until then, the milked investor has paid but a few months his contributions to a worthless system.

Are the option models perfect?


It has been proven that certain assumptions of the individual models are not entirely true to reality.

This can be proven by two phenomena in reality:

1. The Volatilitymile

The volatility mlile shows that a closer examination of the impact of volatility on the option price is in disagreement with Black-Scholes.

implied volatility

Without going too deep now, this simply means that volatility in reality does not behave as Black-Scholes assumed.

Higher volatility leads to a higher option price. You can imagine that, the more uncertain the world around you, the more grateful you are for a hedge / insurance.

From the point of view of Black Scholes, the Volatility Mile means that options that are far away from the current price are more expensive than provided in the option valuation model.

Important: From the perspective of the option model, the inconsistency exists! But that does not automatically mean that the market is wrong. Rather, it should be worded that Black-Scholes does not behave as it should in reality!

Therefore, seemingly too expensive options in reality may not be too expensive, but priced just right.

2. Volatility premium

Again, without going too deep, this phenomenon implies that from the model viewpoint (!) Options in the past were systematically too expensive. Because the volatility used in valuing options was slightly overestimated on average.

If something seems to be too expensive, then it is obvious to sell this. So, if options were systematically too expensive, it should have been sold systematically.

There is a so-called PUT-Write Index by the CBOE simulating a constant short sale of puts on the S & P 500.

put index

Source: CBOE

In terms of return this was very similar to the S & P 500 but he was less volatile.

So there is evidence that options in the past (like nobody knows in the future) were actually a bit too expensive as the models suggest.

Is it possible to earn money with options trading?

I have to say that because I can hear a few people in front of the screen and maybe believe in their luck in options trading:

Despite all the criticism, the models are not bad in practice and still prevalent today. The prices are certainly not perfect but especially if we take into account transaction costs and taxes, most of the time is extremely adequate.

If there are occasions when an option is obviously priced dramatically wrong, then the big ones (banks, hedge funds) with their gigantic infrastructure are so fast on the spot, because you have as a small individual investor as good as no chance.

I would not spend too much time building up my own trading system.

Even with the anomalies, these are not normal only from the perspective of the option pricing model . In reality, for example, the smile may be the norm and Black-Scholes the extraordinary.

Also, with regard to the volatility premium, the differences have not been so great that one can say that this would have paid off especially for tax implications.

Should I hedge my portfolio with put options?

In my opinion no and here’s why:

A hedge (“I believe the market collapses soon, I buy a put as an insurance”) is nothing but a kind of market timing associated with costs. Of Markettiming even I hold nothing at all.

Another reason is that as we have seen, the expectation value does not change with an option. This would be a secured position.

put protection

Attentive readers recognize that paying out the hedged portfolio is the exact equivalent of paying out a long call. With the corresponding expected value.

In addition, I still have transaction costs and tax bickering. All in all, my expectation value is no longer zero, but very likely even negative.

I have only a few principles in life but this is definitely one of them:

Stay away from negative expectations!

So I do not secure my depot. It does not do anything, so I do not do it.

As simple as that.

Are options an alternative to ETF and stocks?

Options, as we have just seen, are more of a type of insurance and not an investment.

We want to invest and not open insurance, so despite my love of options, I consider a broader ETF portfolio , which I routinely recommend during my life for more meaningful.

In options itself, I only have some play money to try out a few things in practice and to satisfy my curiosity. Everything of a purely academic nature is understood