Options trading is often likened to gambling and casinos, with option buyers being labeled the gamblers and option sellers likened to being the casino or “house”. This is a false and arrogant analogy, and I’ll explain why.
Just like in the world of casinos, options trading is a game of probabilities. To illustrate this let’s take a balanced six sided dice, where the probability of any of the numbers 1 thru to 6 coming up is the exactly the same i.e. a uniform distribution. Let’s assume that whatever number comes up is your monetary payout, so if you landed a 5 for example, you’d receive a payout of £5. What would be a fair price to pay for a throw of the dice ? The “fair value” is defined as being the price at which, over many throws, you would neither win or lose but break-even, in other words the expectancy is zero. This “fair value” is easily calculated by adding all the payoffs and dividing by the number of possibilities which in the case of the six sided dice is 1+2+3+4+5+6 / 6 = 3.5. So if you bought (or sold) the bet for £ 3.50 you would neither win or lose but break-even - no edge – no advantage, in the long run. However If you could buy the bet for less than £ 3.50 you’d have an edge, or if you could sell the bet for more than £ 3.50 you’d have an edge. But buy OR sell this bet at fair value (£ 3.50) - no edge – no advantage.
What about a Call option on (say) the number 5, which pays out £ 5 if the number 5 lands. What’s it fair value ? Again, add the payoffs and divide by the number possibilities. In this case the fair value of a Call option on the number 5 is…. 5 / 6 = £ 0.83 3 recurring. So if the number 5 Call option is bought (or sold) for £ 0.83 you’ll neither win or lose in the long run but break-even – no edge – no advantage. If however, you could buy this option for less than £ 0.83 you’d have an edge, or if you could sell this option for more than £ 0.83 you’d have and edge. But buy OR sell this option at fair value (£ 0.83) - no edge – no advantage.
This simple probability concept above applies to pricing options too. However, whereas a 6-sided dice has a “uniform” distribution, stock and commodity asset prices have a “normal” distribution. Simple put, a normal distribution means that the probability of asset price change reduces as we move away from the mean (average) price. In other words a 1% price change is more likely than a 2% price change, and a 2% price change is more likely than a 3% price change and so on.
Calculating probabilities for the “normal distribution” is a rather more complex, but we can use the well known “Black Scholes" model to work them out. I can’t be bothered to explain in any detail the mechanics of the BS equation, but I can simply say that, just like in the dice example above, the equation adds up all the possible payouts and divides by the number of possibilities and calculates the fair value or theoretical value (ThVal) of any option. However, and this is critical, we must input an implied volatility figure into the model. This should be the future volatility of the underlying asset. If we can get that future volatility forecast right and use that figure as the implied volatility in our model, then we can calculate the ThVal of any option. And by selling options trading for more than ThVal and buying those trading at less than ThVal we have an edge, and over the long run will make certain profits.
However, and this is even more critical, future volatility cannot be known in advance. Nobody knows how to calculate future volatility, and they never will. So whenever you look at a particular option trading in the market, you cannot know whether the edge lies in buying or selling it. Only when the option expires can you then look back at volatility in the underlying and comparing that figure with the implied volatility of the option. Then, and only then, can you say with certainty who had the edge.
So in conclusion, where option implied volatility is different from historic volatility (as is almost always the case) one party (writer / buyer) will have had an edge BUT this cannot be known until the option expires.
Sometimes the writer has the edge, sometimes the buyer has the edge, but over the long run neither writer nor buyer has any inherent edge.
A word on “edge”. We all know who has the edge when walking into a casino, but we also know that you can still win a fortune from the casino despite their edge. Similarly if you own a Casino you can lose a fortune, despite your having an edge. Having an edge is no guarantee of profits in the short term, only the long term.
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