A Super Simple Introduction to Options (Calls, puts)

Okay, so in our latest “Super Simple” article, we covered what short selling is. I highly recommend you study that post and understand it well before trying to understand options. I’ll be honest: options are a bit more complicated and a bit harder to understand, but don’t let that stop you, I made this post ridiculously easy to understand. I’ll be honest: everyone can understand the basic part of options if he truly wants to.

As always, we will cover only a very small subset of what options are. Understand that options go extremely far, well past the Ph.D. level. There are, for instance, options on options, but that’s out of the scope of this article.

As I said, don’t let the name or any financial blockage stop you. I am going to make options so simple you’ll understand the basics 100% fifteen minutes from now.

OK so let’s say you buy a phone. The salesman says to you, “At any time during the next 30 days, you can buy another phone for 50% off.”


That’s it?

Yes, that’s it. Next question.

Come on, go a little bit more in depth than that.


An option is the OPTION, but NOT THE OBLIGATION, to do something. I’m going to repeat it because I taught “Introduction to derivatives” in college for two years and half the class didn’t understand it even at the end of the year. I’m serious: I think I repeated over a hundred times and over half the class still didn’t get it. Some people would have graduated and would diplomas by now if they had understood the simple fact:

An option is an OPTION, you do NOT EVER EVER have the obligation to USE IT. You can just drop it in your personal safe and forget all about it forever

Please don’t yell…


So in the example above, in addition to buying a phone, you also got an option. The option states: “You buy a phone at 50% off at any time from now until 30 days have lapsed.” This means that on the 28th day, you could go there and tell the guy, “Hey, I want my 50% off phone.”


Hey, I said no yelling

Sorry but hopefully this time it sticks. You are under no obligation whatsoever to go there and buy that phone at 50% off. Also, note that you cannot go there on the 31th day. If you did, the salesman would say, “sorry, this was only valid for 30 days following your purchase, it’s too late.”

Now, what’s the point of that phone option? Well, let’s say the phone you bought was the iPhone 7 and you plan to give that iPhone to your mother on her birthday. You also want a phone for yourself, but you’re thinking to yourself, “hey, maybe there’ll be another sale in the next 30 days and the iPhone 7 will be 75% off!”. Your reasoning is as follows:

  • If the iPhone 7 is off by more than 50% in the next 30 days, you will buy that phone.
  • Otherwise, you will go to the salesman at the end of the 30th day (just in case there’s a surprise sale at the last minute) and say, “Hey, I got an option to buy an iPhone 7 at 50% off. I want my iPhone 7 and I want it now!”

That’s basically it. You can see right away that an option has a value. Let’s try to simulate the value of our option to buy an iPhone 7 at 50% off.

It would be: [Probability that the iPhone 7 is not more than 50% off in the next 30 days] * [Money you save with that 50% off coupon]

So if an iPhone is $1,000 and there’s a 90% chance the iPhone 7 will not be more than 50% off in the next 30 days, your coupon is worth:

90% * [$1,000 - $500] = $450

That’s it! The salesman just “gave you” $450.

Wait, I thought options were supposed to be complicated!?

Another way to see it is my local cinema: if you go there on Saturday, they give you a coupon for a movie at 50% off at any time, expiring in 30 days. But, you won’t go to the cinema just for the hell of it: you’ll only go back if there’s a new movie that comes out that you want to see (assume that demand doesn’t change with price, for the purpose of this article). If the normal ticket is $10, how much is that coupon worth? Well:

[Probability there’ll be a movie you want to see and that you’ll go back to the cinema in the next 30 days] * [$10-$5]

Get it?

Okay, time to introduce the last element of options (already!): interest.

This is a bit complicated and not really relevant (for now), but you should know that a dollar one month  from now is worth less than a dollar today.

What would you prefer? Having a dollar today or having a dollar a month from now?

Yeah, thought so, but let’s push it a little bit:

What would you prefer? Having a dollar today or having $1,000,000 a month from now?

This is the basic idea of interest: that money can be carried through time. If you invest $1,000 at a bank and the money grows to $1,010 a year from now, the paid has paid you $10 in interest, or 1%. Yes, I know it’s simple, but it’s meant to be. One day, I’ll write an entire article on interest, but for now, let’s stick with that.

Options are affected by interest too. Let’s take the iPhone 7 example in the beginning. I said the coupon was worth $450 because I assumed you would not invest it. But remember: you only have to pay your 50% off iPhone when you buy it. So for the next 30 days, you can place your money in a bank account, earning interest!

Your thought process would be this:

  • You buy an iPhone 7 for your mom. You get a 50% off coupon (option). You can buy an iPhone at 50% at any time during the next 30 days.
  • The cost to buy the iPhone 7 at 50% off would be $500. $500 30 days from now is worth $495 today (i.e. if you place $495 in a bank account right now, you’ll have $500 in it in 30 days).
  • If at any time during the next 30 days you see the iPhone 7 at more than 50% off, you will buy that phone and tear that coupon.
  • Otherwise, at the end of those 30 days, you will withdraw the money from your bank account and buy that phone.

Thus, it only cost you $495 today to get that iPhone at most 30 days from now. It’s a gross simplification, but understand the general idea.

But I want my iPhone now!

We all do.

What about financial options?

OK, the main topic. Let’s go for a non-depreciating, intangible product. Instead of an iPhone, let’s talk about Apple shares. Apple shares are intangible and, unlike material object, no one is going to offer a sale on shares. There is one and only one price for a stock: on the stock market.

Let’s say Apple is at $100 per share. You want to buy an option on Apple. How would it worth?

Well, first, let’s understand that there are two kinds of options: calls and puts.

Calls give you the right to BUY apple shares. Puts give you a right to SELL apple shares. Options typically worth in lots of 100, so one call on Apple would give you the right to buy 100 apple shares. Pretty!

Calls = buy, Puts = sell. Okay!

When you exercise a call or a put, you use the option. It’s gone afterwards. If you exercise a call, you buy 100 shares of Apple. If you exercise a put, you sold 100 shares of AAPL. Note that you do not need to own shares of Apple to exercise a put, i.e. sell them. If you had 0 shares of apple and exercised a put, you’d end up with -100 shares, a negative amount of shares. See: short selling.

So let’s say you buy a call on Apple, expiring in 30 days, at a price of $120. Options have a STRIKE, meaning the price at which they can be exercised. Here, the strike is $120, meaning you’ll have to pay $120 to buy your AAPL shares. The strike can be anything you want; $5`0,000 if you feel like it.

Let’s analyse this call for a minute:

  • You have the right, but not the obligation, to buy 100 shares of Apple at any time in the next 30 days
  • You can buy those shares at $120 per share. Since there are 100 shares per lot, it would take you $120*100=$12,000.

That’s it. That’s a call.

But if AAPL currently trades at $100, I don’t want to buy it for $120!

Not now, that’s for sure, but let’s say that 15 days from now, AAPL jumped to $150 a share. Wouldn’t you like to be able to buy AAPL for $120 then?

An option is said to be in-the-money when it can be exerciced profitably. In our case, with AAPL at $100 and the strike at $120, it would certainly make no sense to exercise our call and buy AAPL at $120 when we can just buy it at $100.

An option is said to be out-the-money when it cannot be exercised profitably, as is the case in the paragraph above.

An option is said to be at-the-money when the price equals the strike, i.e. if AAPL climbed to $120 and we had calls with a strike of $120, the call would be at-the-money.

Too complicated

It does get complex, but let’s go back to the question: how much is our call worth? Well, like our 50% off iPhone coupon earlier:

[Probability we will exercise our call in 30 days] * [Money we save when we exercise our call].

First, understand that it is never optimal to exercise our call before expiration, i.e. the last day. Like in our phone example above, you’ll wait as long as you can to use it. Why? Imagine AAPL goes up to $125. You exercise your option and one second after after you buy it at $120, AAPL crashes to $115. If you had waited just one more second, you wouldn’t have exercised your calls and could have bought it for $115.

It is never optimal to exercise an optimal before the last day when it’s due to expire

An astute reader might note that there are exceptions to the rules above, but they are very rare in practice. In 20 years of trading, I’ve never seen a single situation where it was optimal to exercise an option before expiration (for those curious, with an option, you are not entitled to receive dividends. Say AAPL decides to pay a $50 dividend a week for now. You could choose to exercise your option to buy the shares so you’d get the $50 dividend. It could also be optimal to exercise a put if interest rates are really, really high, but both of those scenarios haven’t happened in decades, if ever. Theory stuff.).

But but but what if I buy a call, the stock goes up and I think the stock will go down next! Couldn’t I exercise my calls? I want to lock my profits!!!

Let me reformulate your question.

Let’s say AAPL is at $120. You buy a call with a $120 strike price for $1. AAPL jumps to $130 and your call is now valued at $15. You have gotten a 1,400% profit.

You think AAPL is going to drop and you want to take your profits on that call. Your question is, “Why not exercice the calls to buy 100 AAPL shares and then resell them?”

Well, you could do that, but you’d lose money: the price of a call depends on two elements: the exercise value, which is how much you’d get if you exercised it, and the time value. In the example above, the exercise value is $130-$120=$10 (since our call is in-the-money by $10). But the call itself is valued at $15, not $10, because there are chances the stock could go even higher. The time value of that call would be the price of the call minus the $10 above, thus $15-$10.

Thus, if you’re really convinced AAPL is going back down, you’d be reselling your calls for $15 and not exercising them to earn $10. Yes, you could exercise your calls then, but you’d be a moron.

Back to pricing…

Now, let’s go back to our formula. The value of a call is:

[Probability we will exercise our call in 30 days] * [Money we save when we exercise our call]

We will exercice our call only if AAPL > $120 in 30 days. If it’s at $119.9, we aren’t going to buy it at $120 when we could buy it at $119.9. Thus, the value of a call is:

[Probability AAPL > $120 in 30 days] * [Money we save when we exercise our call]

For the second bracket, let us consider that: how much money will we save? Well, we will buy it for $120, so we will save whatever difference there is to Apple’s stock price in 30 days. If it’s at $121, we’ll save a dollar. If it’S at $200, we’ll say $80. Thus:

[Probability AAPL > $120 in 30 days] * max[0,Value of AAPL in 30 days - $120]

Note the max element because, again, we will not exercise our option if AAPL is under $120 in 30 days. Say AAPL is at $110 in 30 days, we won’t exercise our calls and we’ll just throw it away. Max(a,b) means the maximum of a and b, so max(1,5)=5.

One last time: remember interest from earlier? Well, again, we are (possibly) buying AAPL 30 days from now. $120 a month from now is worth less today. Let’s say you could place $115 in a bank account and have $120 a month from now. Thus, if you are exercising your call, you are buying AAPL for $115 since you only need $115 today to potentially buy it later.

Price of a call= Value today of: [[Probability AAPL > $120 in 30 days] * max[0,Value of AAPL in 30 days - $120]]

Woah, calls are amazing! But wait a minute… How can I know the value of AAPL in 30 days?

And that’s the true kicker, the punchline to the story: you can’t! Nobody can! And nobody can guess the probability AAPL will be over $120 in 30 days neither!

That’s what makes options fun! If I think the probability of AAPL being above $120 is high and if I think the value of AAPL in 30 days will be super high, I would be ready to pay a lot for that call! But if I thought there were no chances AAPL will be above $120, then I wouldn’t pay much for that option.

Wait, where’s my pretty formula to calculate how much a call is price?

There are none.

But I heard something about Black-Scholes and… and…

Black-Scholes is one model used to price options. It’s simply a model that uses a set of assumptions to project potential stock prices. Truth be told, you could use any model you want to price your options. Black-Scholes is popular due to its theoretical backing and ease of use. It’s an extremely effective model in 95% of cases, but a terrible model in the remaining 5% of cases.

Like all models, Black-Scholes has its strengths and flaws. But we still remain with the fact that nobody really knows how much an option is worth. The price of an option is set by the market, i.e. buyers and sellers.

What other models are used to price options?

A common approach to pricing options is the binomial approach, which is, quite ironically, one of the most effective in statistical terms. Here’s the super simple:

AAPL is at $100. You want to buy a call at $120 expiring in a year. During the next year, AAPL can only do two things: go up to $150 or go down to $50, each with a 50% probability. The interest rate is 0%. What is the value of that call?

Well, the call won’t be exerciced if AAPL goes down to $50 since the price would be under our strike price ($50<$120). It will only be exerced if AAPL goes up to $150. Since there is no interest rate, the price of the call should be:

50% * ($150-$120)=$15

And our call is priced at $15!

This example is borderline an undergrad-level financial problem. I’m not joking. Of course, our models assumes that AAPL can only go to $150 or $50, but all models make assumptions.

It can be shown that the binomial approach eventually becomes the Black-Scholes model under some circumstances. Personally, I like the mesh approach, which is well beyond the scope of this guide.

Lastly, note that there are financial laws and theorems that determine options prices and that sound bound can be establish to limit their value. For instance, for the same expiration T, the same strike K and the same continually compounded, risk-free interest rate r:

Price of the call - Price of the put = Price of the Underlying Stock - K*exp(-rt)

This is the put-call parity, it is based on the risk-neutral approach (also, as some readers might note, on arbitrage constraint). Don’t fret if you didn’t get all that, this is grad school financial stuff, but you can see there is a relationship between the price of a put and the price of a call.

What’s the catch?

Let’s say you buy a call. It means someone, somewhere sold it to you. In other words, someone gave you the right to buy AAPL at $120.

That person won’t do that for free.

I mean, nobody is going to give you something for free, in finance the last place of them all. That person will expect to get compensated. You will have to pay that person. All options carry a premium that the buyer pays and the seller receives (minus a commission).

The more likely the option is to be “in the money”, the higher the premium will be. The higher it can go, the higher the premium will be. Stocks that tend to move a lot tend to have higher option premiums because people expect it to move a lot and thus potentially be worth a lot more if the stock moves in the right direction.

Compare AAPL with Boring Inc. Both companies trade at $100 and you buy options with a strike of $120. If AAPL beats earnings, it can jump to $140 per share. Thus, your option would be worth $140-$120 ($120 is the strike) * 100 shares per lot = $2,000. Compare that to Boring Inc. If Boring Inc jumps, it will only jump to $125. Thus, your option would be worth ($125-120) * 100 = $5,000, a lot less. So the call will be priced at a lower price.

Of course, nobody knows for sure what’s going to happen and Boring Inc. might jump to $200 for all we know, but people use models to predict potential moves. If Boring Inc. has never moved bigly in the past, they assume it’s very unlikely it will move bigly in the future. Again, all models have assumptions. Those models sometimes fail and funds go bankrupt all the time.

One last question: what if I buy options, they’re in-the-money and I forget all about them?

Options that are in the money by $0.01 or more are automatically exercised at the date of expiration. Typically, that’s Friday 4:30PM, after market closes. Yes, magic! So if you have a call at a $120 strike and AAPL is at $120.01 and the market closes, congratulations, you just bought 100 shares of AAPL for $120 per share.  You can also tell your broker, “hey man, I know my calls are in the money, but you know what, I don’t really want AAPL shares in my portfolio and $0.01 is not enough. Plus, it might fall over the week-end. Please don’t exercise those calls, m’kay?” Fun fact: a major source of conflict happens at options expiration when there’s a misunderstanding and major lawsuits and complaints happen against brokers all the time. “I thought you said exercise half! I thought there was a week left on them! I thought I rolled them to next week!” etc. Like casinos, brokers almost always win those complaints.

About the seller of calls…

Yes, you can sell options. You can buy and sell options just like you buy and sell shares (see: Short Selling). I buy and sell options all the time.

Say you sell AAPL calls at $120 strike expiring a year from now. I receive $10 for those calls. If  a year from now AAPL is at $119.99, congratulations, I get to keep the $10 for ABSOLUTELY FREE! FREE MONEY!!!!!

Remember: once a call is expired, it’s GONE GONE GONE.

That’s it?

That’s it. People buy options because they provide more leverage. For instance, let’s say AAPL was worth $100. If you wanted to buy 100 shares, you would need $10,000. If AAPL went up to $150, you would make 100*($150-$120)=$3,000. You have earned $3,000 from an investment of $10,000, a 30% return.

Let’s say instead you paid $2 for some $120 calls on apple. Options are on a lot of 100, so you would only have to pay $200 today. If AAPL jumped to $130, you would earn 100*($130-$120)=$1,000, a 669% return on your money.

Woah! Why don’t everyone buy options?

Because once they expire, they are GONE GONE GONE! You can’t go back and say, “You know what guys, I think I changed my mind. I don’t want this call after all, please give me my money back.” NOPE! I do sell calls all the time and by the time the call expires, usually, I’ll have the money already spent somewhere.

In the example above, if you buy shares instead and hold them and they go to $119.99, you just earned 100 * ($119.99-$100= $1,999, a 19.99% return

If you bought options instead, you just earned 100 * max (0, $119.99-$120)=0, a -100% return.


So options are more risky?


You have no idea how painful it can be when the clock is ticking and your options are barely out-the-money. Similarly, you have NO IDEA how painful it is when you sell calls and the price goes up day after day after day after day… Say you sold a call at a $100 strike for $5 expiring in 30 days. The stock is at $90 on day 1, then $95 on day 2, $98 on day 3, $101 on day 4, $108 on day 5… you have no idea how painful it is emotionally. You can literally bankrupt yourself overnight by selling options and in fact, several people did precisely that. I still remember the day I sold a massive amount of Facebook puts at $80 and every ten minutes, I had lost another thousand of so.

But options can also be used to mitigate risk. Say you bought AAPL for $100 and it goes up to $120. You are afraid it’s going back to $100. You could buy puts with a $120 exercice price. If AAPL went down to $100, you would lose your gain on your AAPL shares (you paid $100 and they are now at $100), but you would earn 100 * ($120-$100)= $2,000 on your puts. Less, of course, the premium you paid for your calls. Say those calls are $5. Since there are 100 shares in a lot, you paid $5*100 and your total gain is now $2,000-$500 = $1,500.

Why not sell the shares directly if you think they are going to fall?

Because you would be forced to pay taxes on your capital gains.


Welcome to the wonderful world of finance.


There are other reasons, of course, but… That’s enough for one day!

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2 Responses to A Super Simple Introduction to Options (Calls, puts)

  1. MB January 31, 2017 at 3:05 pm #

    I think you mean “$500”?
    Thus, your option would be worth ($125-120) * 100 = $5,000, a lot less. So the call will be priced at a lower price.

  2. wt January 31, 2017 at 3:46 pm #


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