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So this shows an option on the day of expiration.

Â The value of the option,

Â is called the intrinsic value,

Â this is a call option,

Â and against the stock price.

Â So if it's a call option and now it's the last day,

Â you either exercise now or forget it.

Â If the stock is worth less than $20,

Â the option is worthless.

Â You tear it up and throw it away.

Â You would not pay $20 today,

Â if the stock price were 15 you would not pay $20 to get something worth $15.

Â But if it's in the money on the last day,

Â on the exercise day,

Â the option is worth the difference between the stock price and the option price.

Â So if the stock price is $25,

Â then you would definitely exercise because

Â you pay $20 to exercise it and you can sell the stock immediately.

Â So it's $5, like money in the bank money, lying on the street.

Â Almost everybody does that.

Â The only people who don't exercise in

Â the money options on the exercise date are people who are not paying attention.

Â And I think that's actually rare.

Â Not many people make that mistake.

Â So the value of the option on the last day has to follow this curve.

Â If the stock price is less than the exercise price,

Â here 20, the option is worthless.

Â But if it's above it, it's equal to the stock price minus the exercise price.

Â For put options, it's different.

Â This is the right to sell.

Â So you only exercise it if the option price is below the stock price.

Â Now, there's something called the Put-Call Parity Relation which is a relationship

Â enforced by arbitrage between a put price

Â and a stock price that have the same underlying,

Â the same strike price and the same exercise date.

Â And that says that these two things are equivalent.

Â The first two lines are equivalent.

Â I just put the items in a different order.

Â So the price of the stock has to equal

Â the call price plus the present discounted value of the strike.

Â Now, this is, at any day,

Â and this is technically for European options,

Â but it applies generally to both European and American options.

Â The price of the stock equals the call price

Â plus the present discounted value of the strike price,

Â plus the present guided value of dividends coming in between now and the exercise date,

Â minus the put price.

Â It does hold up pretty well.

Â Intel Corp, I showed you the example from the CBOE.

Â And so, where was it back here.

Â I'm using the first line here,

Â strike price of 27.

Â Now, this was the last price for the option.

Â But, currently the market maker has a bid-ask spread between 6.05 and 6.20.

Â I'll take the midpoint of the bid-ask spread as an indicator of the current market price.

Â And similarly, the same strike price is available for the same date.

Â It's expiring on January 19th of 2018.

Â They're both expiring on the same day.

Â And so, I'll take the midpoint of bid and ask for the put.

Â And then, I'll go back to that slide here.

Â Okay, so this is the midpoint of the call prices.

Â The sum of the two values divided by two, plus the strike price.

Â I'm assuming a zero interest rate to do this quickly in our head.

Â So I'm not taking present values,

Â while interest rates are pretty low now.

Â So I'm being rough when I say that.

Â Now, I have to figure out how many dividends are between now and January 19th 2018.

Â And I didn't carefully figure out.

Â I thought there's about eight of them.

Â So 26 cents times eight is $2.08.

Â And then, this is the mid point of the bid and ask spread for the puts.

Â And I add them all up and I get $32.54.

Â That's pretty close to the stock price of $31.63.

Â Why isn't that exactly the same?

Â Well first of all, most notably I didn't even do the interest rate calculations.

Â So the interest rates are not exactly zero.

Â So that would have bring down the present value of

Â the strike price and the present value of the dividends.

Â But also, there's just some non-synchrony here.

Â I'm looking at the last price comparing that with the dealers, they didn't ask.

Â There's a little timing, looseness here.

Â So it doesn't work out exactly.

Â But generally, it has to work out,

Â that the so-called put-call parity relation has to hold because it's the same thing.

Â You're pricing apples and oranges but it's really apples and apples.

Â Think of it this way, the yellow line is the intrinsic value of a call.

Â The pink line is the intrinsic value of a put.

Â If you add the present value of the strike price to this sum of the puts and calls line,

Â you get the stock price again.

Â And dividends, as well, have to be brought in.

Â So put-call parity is

Â a fundamental relation that actually holds quite

Â well if you do it exactly right in the options market.

Â And what it really means is that,

Â in fact, you don't even need both puts and calls.

Â It's just for convenience.

Â Because they're related to each other through the put-call parity relation.

Â Now, what is the price of an option on a day before the last day.

Â On the last day, it's all simple.

Â The price of the option is the intrinsic value because there is no more risk. It's now.

Â But it's only a negligible risk and over

Â a matter of minutes that it would take you to sell.

Â So this is the intrinsic value which is the value on the last day.

Â On an earlier day,

Â now we're talking about months or years before the exercise date,

Â the stock option is, or whatever option,

Â it's got to be worth more than the intrinsic value because it has option value.

Â So consider here, suppose we're looking at a call option now with a strike price of 20.

Â It says that there is value when the stock price is 15.

Â There is value to the option.

Â Why would it be worth anything if it's out of the money? Well, this is obvious.

Â Because it might go up.

Â So I'm willing to pay something for the option.

Â Suppose the stock price goes up to 25,

Â then my option price is going to be worth a lot on the exercise date.

Â So the option has to be worth something even though it's out of the money.

Â They're never worthless.

Â It might be very minuscule,

Â but there's always a chance that the stock will go up

Â above the exercise price so it has to be worth something.

Â But then, you also, why is it worth more

Â than the underlying value when it's above the exercise price?

Â Well, it's for the same reason that if

Â the stock price will fall below the exercise price,

Â you'd lose the full amount if you own the stock.

Â But when you own the option, you still got something.

Â You got the option value.

Â The option isn't worthless if it has some time to expire,

Â even though its intrinsic value is worthless.

Â You understand what no arbitrage mean.

Â No arbitrage mean no sure profits.

Â Any profit that you make has to entail risk.

Â There's no $10, you see any $10 bills lying on the floor?

Â No, you don't. Why not?

Â Somebody would have picked it up.

Â Somebody at some point must have lost a $10 bill in this room.

Â But it's not there anymore.

Â Those things are rare that you'll ever find

Â one because the first person to see it picks it up.

Â So similarly, we don't expect to see the put-call parity relation violated.

Â If that were violated, I can tell you.

Â Here's a good job for you,

Â drop out of college and invest in

Â disparities between put-call parity and you make money for sure.

Â So you might as well just push it to the limit

Â and borrow millions of dollars and just do it on a big scale.

Â So it's so simple and obvious, once you look at it.

Â You can be sure that there are guys out there right now,

Â arbitrageur making profits from the tiny discrepancies and put-call parity.

Â But they eliminate the discrepancy. And when they do

Â