Why Option sellers make money - The Mathematics behind it

Actually, sellers don't make always money but they do so consistently. On the other hand, buyers lose money as they miss to find a good strike to buy, so they make a loss even after having the potential of making unlimited profit with limited risk. Most of the time, the option buyers tend to buy OTM strike, because that costs them a little less. But they forget that those strikes are OTM, because they have less likelihood to expire in the money.

If a strike does not expire in the money, goes worthless, at the very same point, option sellers cut the cake. Option buying needs a precise methodology to select an option strike for buying whereas sellers go for mathematics that makes them consistent money even after taking a huge risk and unbalanced risk and rewards.

Let's understand the mathematics:

When someone is bullish on an underlying, he buys call options of the underlying and pays an initial amount known as premium. This call option buyer gains when underlying expires above the strike that he has bought. If the market goes in his way, he makes money. On the other hand, A call seller who has a bearish view on underlying. The call option sellers gains if the underlying expires below the strike that he has sold. A Call seller receives the premium.

Similarly, a put buyer who has a bearish view on the underlying he buys put option and pays a premium for it. If underlying expires below his strike that he has bought he makes money. And who has sold the put, has a bullish view on the underlying and he receives the premium from put buyer. The put sellers gain only if the underlying expires above the strike he has sold.

We can conclude from above: a call buyer is bullish, a call seller is bearish; a put buyer is bearish, a put seller is bullish.

Profit Potentials:

Call and Put option buyers have unlimited profit potential and limited risk. But, Call and put sellers have unlimited risk but limited profit potential.

	Buyers	Sellers
Risk	Limited	Unlimted
Profit	Unlimted	Limited
Opinion	Up	Down
Opinion	Down	Up
Zero Sum	+X	-X

80 per cent of the time, option sellers make money. The other know fact is 80 per cent of the options contracts expire worthless where the option sellers gripped on. Because of this fact, they play on the volatility and the time decay, we no them as Vega and Theta in Option Greeks.

Mathematically, the market favours the option sellers as 66% of the time it helps them. 

Market Trends,

Bullish + Bearish + Consolidation = 100%

Bullish = 33% = Call Buyers Win.

Bearish = 33% = Put Buyers Win.

Consolidation = Call and Put Buyers lose = Call and Put Sellers win.

Bullish + Consolodation = 33% + 33% = Put writers win

Bearish + Consolidation = 33% +33% = Call Writers win.

Vega, Theta and Option Sellers

Generally, Option sellers apply for short vega and short Theta strategies. Short vega means, professional option sellers, sell those options that have high volatility and as Volatility is mean reverting, they get benefits out of it. 

The other things that help them the most is the time decay that is measured in theta. Though, Option sellers take high risk for limited profit but they are compensated with time decay. As we move towards expiry the premium falls and sellers bag the profit.

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