When participating in a forum about option trading, I have noticed that some of the participants did not know about a few basics relations in pricing options. The question I saw was a long the line of “The difference between Call 100 and Call 90 looks very big to me”.
It had occured to me that some people are not aware of some of the basic pricing rules that YOU SHOULD know.
The Bull Spread
Consider two Call Options. One with a 100 strike and the other with a 110 strike. We know that the 100 Call would be worth more than the 110 strike. You should notice C(100)-C(110) < 110-100 = 10. That is, the price difference would always be less than the difference of the strikes.
As always with options, relations like these are based upon the no arbitrage rule. Let's take a scenario in which we buy the C(100) and sell the C(110). You should notice that the maximum amount of money we can do with this spread is when the underlying passes the 110 mark. That is when we earn 10$. Now that we know the maximum of money we can earn, how much would you pay for such a contract? Would you pay more than 10$ for a portfolio that will earn you no more than 10$? That is the reason that such a spread will always be less than the difference of strikes(as an aside note, it would be less than 10$ divided by the interest rate for that period)
Hedge Relation
Is it possible that an option on a stock would be worth more than the stock? The answer is no. And yet again, this is true because of arbitrage relations. If such an event were to happen, you could make riskless money. How so? You would sell the option and buy the stock with that money(since the option is worth more than the stock, you’d also be left with some money in your pocket).
When the option expires, it either expires worthless(in which case you end up with the stock you bought) or you have to sell the stock by the amount of the strike price.
In the next part, I’ll discuss what is known as the butterfly spread and how does it impact the pricing of options.
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