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Alan Cring Productions in association with the Emergent Light Studio presents

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the Illinois State Collegiate Compendium, academic lectures in business and economics.

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This is business finance, FIL 341 for autumn semester 2024.

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Today, the Black-Scholes Options Pricing Model.

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Before we do that, let's have a look at the numbers for the day.

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And this is one of the weirdest things.

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We're all asking the same question.

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Why did the Fed cut rates yesterday and nothing happened,

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and then today the markets just went cuckoo bananas?

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Were they all stoned last night or something?

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We can't figure out what the heck, how this happened.

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But there's no reasonable way because the markets were expecting

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a quarter percent cut in the discount rate.

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Okay, so if the Fed says, well, we cut the discount rate by a quarter percent,

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we wouldn't see much of a reaction because it was already impounded in the expectations.

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But when the Fed cuts the discount rate by a full 50 basis point,

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that should have sent the markets.

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Traders should have started making monkey sounds and swinging from trees, and they didn't.

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And then this morning, all of a sudden, look, and the Dow is climbing like gangbusters.

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You've got the Dow is up, oh, holy cow, more than a percent and a half.

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The S&P is up 2 percent, and the NASDAQ is closing in on a 3 percent increase.

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That almost qualifies as a white swan.

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So, I mean, okay, we'll take it for what it's worth.

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That the markets waited to see if it was real or if they were dreaming or something like that.

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So we got a great day, a really hard day up.

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And it's almost more than we would have expected out of this.

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And notice that it spiked. At the bell, boom, it was up.

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And then, interestingly enough, as the day has gone along, it has continued a slow grind upward,

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mostly as traders are beginning to see positive impact on more and more industries.

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And that this is really strong good news.

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So the initial jump was just the cut in the discount rate.

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The slow growth of price, rise of prices after that, is assessing impact industry by industry, company by company.

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And it's all favorable. There's not much of a downside.

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And you'll see there are sub-sectors that are just going crazy.

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The darker part of it is crude oil is showing some signs of life upward.

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And that is primarily because of just a little bit more concern about the Middle East,

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because Israel is blowing up people with pagers and now with walkie-talkies.

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And there's a concern that this is going to piss off Hezbollah more.

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And they may start some more serious attacks out of Lebanon.

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And then Israel will respond with more attacks on Lebanon.

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And then Iran will get involved in it and it'll be all kinds of fun.

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Not much chance of that. As you can see, oil isn't spiking.

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But there is a little bit more of a war premium beginning to slip in to the prices.

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Nothing really to worry too much about.

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And you notice that gold did a bouncy bounce there, and it's up a little bit too.

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War kind of gets gold bugs excited sometimes.

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But moving over here.

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Now here's the interesting one.

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Ten-year bond yield is going up.

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One of the perverse effects is you see now bond yields going up, that means bond prices are going down.

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Bond prices are going down would mean that investors are selling bonds.

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Well, actually, that makes all the sense in the world.

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The world is making sense right now because investors are grabbing equities.

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So they're selling bonds and jumping toward equities.

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And of course what that does is buying the equities drives equity prices up.

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And at the same time, though, selling the bonds drives bond prices down and bond yields up.

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So you're seeing the other side of that.

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Even though the discount rate was cut, that should cause yields to go down.

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In fact, the opposite is happening because there's so much excitement about equities.

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Investors are pulling out of bonds to buy equities.

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And of course pulling out of the bonds drives bond prices down and the bond yields up.

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So the counteractive effect on the Fed's discount rate cut is that it can have that backlash,

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the backwash of causing bond yields to actually increase.

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Fortunately, that should be a temporary phenomenon.

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We see it happen.

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And eventually the sell-off in bonds will abate and we'll be back to the bond yields going down.

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But for now, that's not good news.

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Bonds yields are going up, so we've got higher interest rates.

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Although right now in the consumer market, if I'm not mistaken, mortgage interest rates on mortgages just hit a...

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they have gone below what they were in 2022.

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So bond mortgage rates are going down.

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That should stimulate the construction industry, big sector of the economy, and all that good stuff.

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And loans on auto loans, I have tracked those over the last couple of days and they are sliding too.

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I ran into...I did something kind of evil yesterday.

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I talked to this car dealer I know, former student from years and years ago,

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and I said, what's your best rate right now?

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And he said, for you, 4.39%.

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That is lower than it has been in a long time.

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I mean, you had car loans at 7.29%, 6.99%, and he's trying to wheel and deal with me at 4.39%.

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I feel bad about making him think I was going to buy a car, but he'll get over it.

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Okay, so you see, interestingly enough, that Tokyo and London also responded favorably to what's happening here.

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Interestingly, though, over in London, the exchequer of the currency said,

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we're not going to lower interest rates right now.

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So he was putting the kibosh on...the Americans did it, so we're going to do it too.

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He said, no, we're not. They're still fighting inflation.

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They got...they jumped into the fight later than we did.

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So did the Europeans.

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And so they're going to have to hold their interest rates higher for a little longer than we will,

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just because they've got...they started dealing with the inflation problem later than we did.

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And so that is credit to the Fed, and I've criticized the Fed to the point where I've described them in fairly harsh terms.

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I think at one point I described them as the Antichrist.

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That's a little harsh, but right now they've done a pretty hella good job of managing rates.

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Now, look at it.

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You saw this effect yesterday and the day before, but look at, for example, Citi.

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Well, let's try that again.

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Citi.

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Oh, I kicked the plug out again.

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I've got to stop doing that, because they're going to start fussing, I'm ruining their USB port here.

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Okay, Citi.

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Look at that.

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Look at that.

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5% up on the bank.

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Of course, interest...and so that was one that you could almost bet would have happened.

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But if we had known...if I'd known that the Fed was going to cut as hard as it did,

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I would have gone long some call options on Citi.

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But look at Bank of America.

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3% up.

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I wonder if a dog like Wells Fargo...I didn't look at Wells before, WFC.

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Even Wells Fargo is up 3%.

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I mean, the banking sector is just rolling...they're in hog heaven while we're in interest rate slop right now.

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So they're happy with this.

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This is good news for them.

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Other sectors of the economy.

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Telecom had had a good run for a little bit, and then they sort of petered out.

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I wonder what they're doing.

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They're down.

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Interesting. Verizon.

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Down. So the telecoms are not happy about this, what's happening here.

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But that's them going over consumer goods.

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Let's try...let me try Kroger.

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Just...yep.

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Walmart.

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Ooh, look at Walmart.

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Walmart got spanked.

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Let's have a look at Target.

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Oh yeah.

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Walmart.

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I'm not sure what's ticking off the investors about Walmart, but I mean the rest...a lot of it's looking really good right now.

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Looking at consumer basics.

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Colgate-Palmolive.

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Down.

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Why is it that interesting?

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I wonder where that is.

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Medical and...medical.

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Down.

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So this is not all the way across the board.

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It looks like...what am I thinking?

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Come on, come on, come on.

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Let's look at Palantir.

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Whoa, Palantir.

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That is one of those toy stocks.

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You can put money into that one time and make a lot of money out of it, and throw it in a couple of months later, and you will lose your shirt.

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It's a nasty, unfriendly kind of stock.

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Moderna.

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Well, pay attention.

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MRNA.

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Shouldn't...yeah, it shouldn't react too much.

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Moderna.

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Not showing much signs of life.

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Johnson & Johnson.

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J&J.

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Huh, isn't that interesting?

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So this is not all ships rise in the rising tide.

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There are some that are not taking this well at all.

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Which, you know, that's their thing.

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It kind of surprises me, though, that Johnson & Johnson and those are not doing so well right now.

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Coming across here, going back to a couple of old friends.

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The Bull Play.

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It's not on a stock.

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It's on the general sentiment.

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TQQ is Bull.

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Should be...holy cow.

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I mean, that is just stupid good.

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Just happy good.

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And of course, it's Dark Cousin SQQ, the Bear.

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Pretty much about the opposite.

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So the bears are being spanked and the bulls are being fed an extra bale of hay.

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So this is one of those things, that 9%.

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That is...now, again, we are talking about financial options here.

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So the whole thing about this is that if I were to look here, TQQQ...

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Let me go back to it.

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And I'm going to look at the options.

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So let's take it out.

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Expiration on the 26th...27th, sorry.

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On the 27th.

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Now, keep in mind, the 7169.

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We're going to look at one that's just out of the money at 72.

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Just for sharts and giggles, 72 on it.

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See how it's done today.

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Oh, quit.

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72. Look at this options change.

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Right there. See, just out of the money at 72.

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And we run over here.

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Hello.

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Percent change from yesterday on the 72 option.

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Why does it keep doing that?

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Percent change on the 72 option.

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317%.

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Now, these are highly leveraged, highly risky instruments.

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I am guessing that if you had thrown in...that was probably...

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God, I don't know what that would have been to cause that.

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If you had bought yesterday at a dollar...

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It probably was less than a dollar yesterday.

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Today, it is a dollar 96.

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So you would have, on the swing, for one option, have made 96 times 100.

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So you would have made $96 on a single option on this.

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Just in one day.

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If you had thrown 10...if you had gotten 10 contracts, you would have made a really lot of money in a single day on this.

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And if you...look...

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Okay. I might as well say, bid and ask.

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191, 196. You would have bought it at...

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Yesterday, it would have been a lot less than this.

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It's too late to buy this now because the information is already impounded.

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You're not going to make anything off it at this point. It's not worth it.

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But today, you'd buy at a dollar 96.

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If you wanted to write one of these options, you would write it at 191.

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I would not recommend that because there still could be some push upward in it.

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Now, over here, I'm not familiar with options chains on Yahoo.

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Open interest volume. There.

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This number...see this implied volatility?

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This is one of our most important numbers.

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And I have a spreadsheet where you can calculate implied volatilities.

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I have an Excel sheet. I'll upload it. You won't have to need it for this course.

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But you can calculate them yourself.

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And a service like Yahoo, it's...I mean, they're usually pretty close.

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But you can do it yourself in Excel, finding implied volatilities.

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It's just a matter of putting in the data.

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What you'll do is you'll put in historical data.

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And then Excel will make the adjustment to turn it into a forward-looking volatility.

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Now, oftentimes, a service like Yahoo, it would take the market data

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and then back into the implied volatility that would match that data.

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That's where the term implied comes in.

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So they're not really giving you an implied volatility.

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They're not calculating one like we figured out that it exists.

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They're just taking the market numbers and solving for the sigma

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so that that's what they're giving you, is what is already known.

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Now, let me take you on a little bit of a journey here for just a few minutes.

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And we're going to walk that sheet.

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And here it is.

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Now, let me explain...well, let me do something here.

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Something...let me see if there's a way that I can put up this slide for you to see here.

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That is a...how shall I put it?

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A pleasant version of the Black-Scholes options pricing model.

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These two functions, these are functions, N.

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N evaluated at D1 and N evaluated at D2.

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And there are the formulas for what you plug in to the N formula.

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For D1, you would actually calculate this incredible mess right here.

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Plug it in to the N function.

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00:19:35,000 --> 00:19:40,000
And then you would get the D2, which is D1 minus the implied volatility

240
00:19:40,000 --> 00:19:43,000
times the square root of the time remaining on the option.

241
00:19:43,000 --> 00:19:47,000
And you would plug that into this N formula.

242
00:19:47,000 --> 00:19:51,000
The N formula, those are integrals.

243
00:19:51,000 --> 00:19:53,000
They are integrals.

244
00:19:53,000 --> 00:19:58,000
They are actually that long S with a mess inside of it.

245
00:19:58,000 --> 00:20:03,000
Those integrals are the normal distribution function.

246
00:20:03,000 --> 00:20:10,000
And another part about that is that in mathematics,

247
00:20:10,000 --> 00:20:13,000
you are often, almost always in undergrad math,

248
00:20:13,000 --> 00:20:18,000
you are taught what are called closed form solutions.

249
00:20:18,000 --> 00:20:21,000
In other words, you are shown an integral and the integral...

250
00:20:21,000 --> 00:20:23,000
Well, let me do it this way.

251
00:20:23,000 --> 00:20:26,000
I'm giving you a little bit of background here.

252
00:20:26,000 --> 00:20:36,000
For example, the integral of x squared dx is one third of x to the third

253
00:20:36,000 --> 00:20:39,000
plus the constant of integration C.

254
00:20:39,000 --> 00:20:42,000
You saw that somewhere in your dark past.

255
00:20:42,000 --> 00:20:44,000
That's a closed form solution.

256
00:20:44,000 --> 00:20:49,000
In other words, we know what the result is as an equation.

257
00:20:49,000 --> 00:21:07,000
The problem is that when you get into functions like the integral of e to the rt sigma dt,

258
00:21:07,000 --> 00:21:10,000
that doesn't have a solution.

259
00:21:10,000 --> 00:21:13,000
It does not have a closed form solution.

260
00:21:13,000 --> 00:21:21,000
The way you find those numbers mathematically on paper in Excel

261
00:21:21,000 --> 00:21:24,000
is you have to take a guess.

262
00:21:24,000 --> 00:21:29,000
And then you keep taking guesses that get closer and closer to...

263
00:21:29,000 --> 00:21:35,000
The difference between this one guess and the next one gets smaller and smaller and smaller.

264
00:21:35,000 --> 00:21:38,000
That's called iterative solutions.

265
00:21:38,000 --> 00:21:41,000
And that's what Black-Scholes does.

266
00:21:41,000 --> 00:21:43,000
It has these functions.

267
00:21:43,000 --> 00:21:49,000
That's related to a normal distribution function.

268
00:21:49,000 --> 00:21:52,000
There are no closed form solutions.

269
00:21:52,000 --> 00:21:57,000
If you want to calculate the normal distribution at some value,

270
00:21:57,000 --> 00:22:00,000
you have to do an iterative calculation.

271
00:22:00,000 --> 00:22:04,000
Little calculators as well as big calculators, Excel,

272
00:22:04,000 --> 00:22:07,000
they do that for you.

273
00:22:07,000 --> 00:22:13,000
So let me take you back over here.

274
00:22:13,000 --> 00:22:16,000
As you can see, it is actually...

275
00:22:16,000 --> 00:22:23,000
You plug in all of these numbers here, and it does all of that there.

276
00:22:23,000 --> 00:22:28,000
In other words, those equations that I just showed you, it does those for you.

277
00:22:28,000 --> 00:22:33,000
Instead of you having to do it, it does it for you.

278
00:22:33,000 --> 00:22:44,000
And these actually, if you look, this is actually the formula for the normal distribution

279
00:22:44,000 --> 00:22:50,000
evaluated at.3616.

280
00:22:50,000 --> 00:22:56,000
This is the normal distribution evaluated at.2505.

281
00:22:56,000 --> 00:23:03,000
I'm telling you the background to convince you do not ever touch those numbers on that side.

282
00:23:03,000 --> 00:23:04,000
They're done for you.

283
00:23:04,000 --> 00:23:13,000
And this, my good people, these are your Greeks that I talked about on Tuesday.

284
00:23:13,000 --> 00:23:14,000
The Greeks.

285
00:23:14,000 --> 00:23:20,000
And each of them tells you something, and I'm not going to go into it in deep detail in this class.

286
00:23:20,000 --> 00:23:26,000
Take.347, and we will use these like a boss.

287
00:23:26,000 --> 00:23:34,000
But for now, all we're going to do is just walk through so you can see some of the processes that go on.

288
00:23:34,000 --> 00:23:39,000
Now, what comes out of here, this is your goal line.

289
00:23:39,000 --> 00:23:45,000
Finding the arbitrage-free prices of calls and puts.

290
00:23:45,000 --> 00:23:52,000
And then if you're a trader, you look at what the actual market says it is.

291
00:23:52,000 --> 00:23:56,000
They should be very, very close.

292
00:23:56,000 --> 00:24:13,000
If they deviate somewhat more, like for example, I might look at this option and I see that a call with these parameters is right now trading at 10.40.

293
00:24:13,000 --> 00:24:21,000
Well, the black shoals, the arbitrage-free equilibrium is 10.4577.

294
00:24:21,000 --> 00:24:27,000
So I know that briefly this option is underpriced.

295
00:24:27,000 --> 00:24:36,000
So I would buy these and I would buy and others would, doing the calculations, would buy them.

296
00:24:36,000 --> 00:24:46,000
And the price would rapidly move back toward, through the buying pressure, move back toward $10.45, $0.46 per option.

297
00:24:46,000 --> 00:24:49,000
That's what's called arbitrage.

298
00:24:49,000 --> 00:24:52,000
It is the discipline of the market.

299
00:24:52,000 --> 00:24:58,000
If prices deviate more than a little bit, traders are going to come in and move.

300
00:24:58,000 --> 00:25:05,000
Now, suppose on the other hand that you see that right now this option is priced at $10.50.

301
00:25:05,000 --> 00:25:07,000
The market is pricing at 10.50.

302
00:25:07,000 --> 00:25:12,000
That means that right now it is above equilibrium.

303
00:25:12,000 --> 00:25:20,000
So in this case, I would write options, write call options, because I would sell them at a price higher than what they should be.

304
00:25:20,000 --> 00:25:31,000
And as I flooded the market, as traders wrote options, they'd flood the market, supply of options would go up, and that would push the price back down toward equilibrium.

305
00:25:31,000 --> 00:25:33,000
That's what the black shoals does.

306
00:25:33,000 --> 00:25:36,000
It gives us where it should be.

307
00:25:36,000 --> 00:25:47,000
Now, suppose that the price right now, aha, I see that the price is $10.44 and I know it should be $10.46.

308
00:25:47,000 --> 00:25:50,000
You're not going to do anything with that.

309
00:25:50,000 --> 00:25:52,000
In other words, there's going to be some rattle.

310
00:25:52,000 --> 00:26:00,000
Now, if you're a ginormous trader doing high volume, high frequency, you can take advantage of it.

311
00:26:00,000 --> 00:26:04,000
But as a small time trader, it's not worth even trying.

312
00:26:04,000 --> 00:26:11,000
So for us, we need to see enough of a deviation to be able to move.

313
00:26:11,000 --> 00:26:15,000
I have a famous story that's of my own.

314
00:26:15,000 --> 00:26:24,000
Once I saw a deviation of about $0.07 on a call option from black shoals.

315
00:26:24,000 --> 00:26:26,000
And what did I do?

316
00:26:26,000 --> 00:26:34,000
I saw my numbers, I saw this, and so what I did was I just stopped and I checked my numbers all again.

317
00:26:34,000 --> 00:26:38,000
By the time I got back to trade it, it was right back on that number right there.

318
00:26:38,000 --> 00:26:40,000
It just pissed me off.

319
00:26:40,000 --> 00:26:47,000
So it's going to happen very quickly because these computers that are doing this, they can do this really fast.

320
00:26:47,000 --> 00:26:53,000
So it's almost like it's partly, yeah, just academic.

321
00:26:53,000 --> 00:26:55,000
Okay, that's great.

322
00:26:55,000 --> 00:27:02,000
But also, where you can still do some arbitrage is on small cap stocks,

323
00:27:02,000 --> 00:27:08,000
where there might be a delay in big dogs seeing them, they do not watch those.

324
00:27:08,000 --> 00:27:12,000
So yeah, it still can be used.

325
00:27:12,000 --> 00:27:23,000
But if you're talking about ginormous stocks, Target, Ford, Pfizer, Tesla, you're not going to get anything.

326
00:27:23,000 --> 00:27:27,000
You see a deviation, you see an arbitrage opportunity.

327
00:27:27,000 --> 00:27:33,000
By the time your neurons fire here and get to your paws, it'll be gone.

328
00:27:33,000 --> 00:27:38,000
But do appreciate that this still is useful to us.

329
00:27:38,000 --> 00:27:47,000
And one of the nicest things is that we can play and see how options behave, see what they do.

330
00:27:47,000 --> 00:27:55,000
So suppose that I have an option that I buy today.

331
00:27:55,000 --> 00:28:10,000
So I'm going to put in 76, I'm sorry, 76, so that we have, let's say, nine, I hope no one's played with this.

332
00:28:10,000 --> 00:28:22,000
What's today, the 20th? No, the 19th.

333
00:28:22,000 --> 00:28:30,000
And we want one that is two weeks later.

334
00:28:30,000 --> 00:28:46,000
October the 4th, 10, 4, 2024.

335
00:28:46,000 --> 00:28:59,000
It's not going to work for me. It's not going to work for me.

336
00:28:59,000 --> 00:29:02,000
There we go.

337
00:29:02,000 --> 00:29:06,000
Option explorations. I see I was bitching about that.

338
00:29:06,000 --> 00:29:10,000
So anyway, now let's do one here.

339
00:29:10,000 --> 00:29:12,000
Let's say we have an asset price.

340
00:29:12,000 --> 00:29:20,000
In other words, the underlying is a stock that's right now selling at 74.20.

341
00:29:20,000 --> 00:29:29,000
And we'll grab one that's at 75, has a strike price of 75.

342
00:29:29,000 --> 00:29:42,000
Now the time to expiration, in this case, that's.04195 years.

343
00:29:42,000 --> 00:29:47,000
Actually, it's using this one. Isn't that interesting?

344
00:29:47,000 --> 00:29:53,000
I don't know why it's doing that, but I could fix that or you could probably even fix that.

345
00:29:53,000 --> 00:30:05,000
Let me just put in 10, 4, 2024.

346
00:30:05,000 --> 00:30:11,000
So this is giving you, I think something's weird about this.

347
00:30:11,000 --> 00:30:14,000
You'll want to do it down here, I guess.

348
00:30:14,000 --> 00:30:23,000
But anyway, okay, so that's.0411 of a year.

349
00:30:23,000 --> 00:30:32,000
And if you wanted to, you could just put in that cell C13 equals however many days divided by 365.

350
00:30:32,000 --> 00:30:37,000
You could do it that way if this is getting wonky.

351
00:30:37,000 --> 00:30:43,000
Now, this is the sigma, the volatility, the implied volatility.

352
00:30:43,000 --> 00:30:47,000
You can look it up, you can calculate it yourself.

353
00:30:47,000 --> 00:30:56,000
But whatever it is, let's say that we have an implied volatility of 8.96%.

354
00:30:56,000 --> 00:30:59,000
Now we'll put in the risk-free rate.

355
00:30:59,000 --> 00:31:05,000
Usually we put in the current price of a short-term T-bill.

356
00:31:05,000 --> 00:31:17,000
In this case, well, I'm going to guess that it's, let's say a short-term T-bill right now is yielding 3.89%.

357
00:31:17,000 --> 00:31:33,000
Now, the Black Scholes Options Pricing Model works as long as you can express the dividend as a percent of the underlying asset price.

358
00:31:33,000 --> 00:31:46,000
If it can't be done that way, then you have to go to the binomial model over here to do it.

359
00:31:46,000 --> 00:31:52,000
But in this case, we're going to say this stock pays no dividend.

360
00:31:52,000 --> 00:32:00,000
So once we put in all these numbers, you can see the call price and the put price.

361
00:32:00,000 --> 00:32:08,000
Now notice in this one that this exercise price, the stock is out of the money,

362
00:32:08,000 --> 00:32:15,000
and there's not a lot of time left for it to get into the money.

363
00:32:15,000 --> 00:32:23,000
So you're going to see the put, there's more likely that it's going to finish, expire out of the money.

364
00:32:23,000 --> 00:32:28,000
That's why the put is going to be higher value than the call.

365
00:32:28,000 --> 00:32:38,000
Because right now the put is in the money, and so it's going to have a nice in the money little piece to it.

366
00:32:38,000 --> 00:32:49,000
Now, all of these, these, not much I can say, but you can see more about it if I change some of the parameters.

367
00:32:49,000 --> 00:32:56,000
But before I change too many parameters, let us watch what happens as you look at a higher strike price.

368
00:32:56,000 --> 00:32:58,000
Let's just change the strike price.

369
00:32:58,000 --> 00:33:01,000
Remember that the underlying is 74.20.

370
00:33:01,000 --> 00:33:05,000
So the first strike we looked at was 75.

371
00:33:05,000 --> 00:33:09,000
Now let's take it to 76.

372
00:33:09,000 --> 00:33:15,000
Now notice that makes the call further out of the money and the put deeper into the money.

373
00:33:15,000 --> 00:33:20,000
So we should see the call go down and the put go up.

374
00:33:20,000 --> 00:33:22,000
Spank me Jesus, look.

375
00:33:22,000 --> 00:33:24,000
You see it?

376
00:33:24,000 --> 00:33:26,000
Let's take it even further.

377
00:33:26,000 --> 00:33:35,000
Let's say that we're, the underlying is 74.20 and the exercise price is 77.

378
00:33:35,000 --> 00:33:37,000
Well, the call sucks.

379
00:33:37,000 --> 00:33:44,000
The put is deep enough in the money, it's going to be worth a lot, it's going to be worth a lot at this point.

380
00:33:44,000 --> 00:33:52,000
Because there is a very good chance that the stock is not going to make it to 77.

381
00:33:52,000 --> 00:33:55,000
So the call is going to be pennies.

382
00:33:55,000 --> 00:34:01,000
But there is a very good chance that the stock will finish below 77.

383
00:34:01,000 --> 00:34:05,000
So the put is going to be almost a sure bet.

384
00:34:05,000 --> 00:34:09,000
That's why it will cost you more to buy one of those.

385
00:34:09,000 --> 00:34:11,000
Do you follow it?

386
00:34:11,000 --> 00:34:13,000
Okay, cool beans.

387
00:34:13,000 --> 00:34:18,000
Let's take it back here to 75.

388
00:34:18,000 --> 00:34:28,000
Now let's take the time to expiration and let's increase that we are going to do this one on the 11th.

389
00:34:28,000 --> 00:34:39,000
10, 11, 2024.

390
00:34:39,000 --> 00:34:43,000
Did you see what happened?

391
00:34:43,000 --> 00:34:44,000
Let me take it again.

392
00:34:44,000 --> 00:34:45,000
Let me go back.

393
00:34:45,000 --> 00:34:46,000
Look at the call and the put.

394
00:34:46,000 --> 00:34:49,000
When there were two weeks to expiration.

395
00:34:49,000 --> 00:34:52,000
This was two weeks to expiration.

396
00:34:52,000 --> 00:34:53,000
Okay.

397
00:34:53,000 --> 00:35:01,000
Now let's take it forward back to the...

398
00:35:01,000 --> 00:35:02,000
Do you see them?

399
00:35:02,000 --> 00:35:10,000
Both the call and the put become more valuable because there is more theta premium.

400
00:35:10,000 --> 00:35:12,000
Do you follow it?

401
00:35:12,000 --> 00:35:14,000
Let's take it even further out.

402
00:35:14,000 --> 00:35:18,000
Let's say that we got this one finishes on the 18th.

403
00:35:18,000 --> 00:35:24,000
10, 18, 2024.

404
00:35:24,000 --> 00:35:26,000
Watch the call and the put.

405
00:35:26,000 --> 00:35:35,000
They should both increase in value because there is more time for that gas diffusion to hit either high or low.

406
00:35:35,000 --> 00:35:39,000
And so in this one...

407
00:35:39,000 --> 00:35:43,000
Look at that.

408
00:35:43,000 --> 00:35:49,000
This is why I like to do it with these especially in a course like this.

409
00:35:49,000 --> 00:35:59,000
Not so much so you know how you've memorized the equations and you can do them rapidly on your little calculator so you can see what the dynamics are.

410
00:35:59,000 --> 00:36:01,000
Now let's take this out.

411
00:36:01,000 --> 00:36:03,000
Let's just leave it where it is for the time being.

412
00:36:03,000 --> 00:36:08,000
And let us change the standard deviation.

413
00:36:08,000 --> 00:36:14,000
In other words, how widely the gas is diffusing.

414
00:36:14,000 --> 00:36:20,000
Is it going like this, like this, or is it diffusing like this from a physics point of view?

415
00:36:20,000 --> 00:36:22,000
And if we do that, let's change this.

416
00:36:22,000 --> 00:36:31,000
Watch what happens to the call and the put prices if I change this to let's say 15%.

417
00:36:31,000 --> 00:36:33,000
See how they both become more valuable?

418
00:36:33,000 --> 00:36:37,000
Because there is more chance that both of them will finish in the money.

419
00:36:37,000 --> 00:36:45,000
Because there is a wider spread of possibilities on it.

420
00:36:45,000 --> 00:36:47,000
Take it another...

421
00:36:47,000 --> 00:36:49,000
Ow, that hurt like hell.

422
00:36:49,000 --> 00:36:53,000
Now let's look at the risk free rate.

423
00:36:53,000 --> 00:36:56,000
Now this is a subtler one.

424
00:36:56,000 --> 00:36:58,000
Let me take this one...

425
00:36:58,000 --> 00:37:01,000
No, I'll leave it where it is. That's okay.

426
00:37:01,000 --> 00:37:09,000
Let me take the risk free rate and let me raise the discount rate to 5%.

427
00:37:09,000 --> 00:37:14,000
And let's see what happens to the call and the put price.

428
00:37:14,000 --> 00:37:22,000
Call 99, put 156.

429
00:37:22,000 --> 00:37:26,000
Do you see something weird that happened there?

430
00:37:26,000 --> 00:37:30,000
Let me go back to the first ones.

431
00:37:30,000 --> 00:37:35,000
The call was 99 and the put was 156.

432
00:37:35,000 --> 00:37:40,000
Now let's bring the discount rate up.

433
00:37:40,000 --> 00:37:50,000
The call and the put didn't do the same thing.

434
00:37:50,000 --> 00:37:53,000
Let me back it up.

435
00:37:53,000 --> 00:38:02,000
The call goes up, the put goes down.

436
00:38:02,000 --> 00:38:04,000
Isn't that an interesting effect?

437
00:38:04,000 --> 00:38:07,000
The interest rate dynamic for a call.

438
00:38:07,000 --> 00:38:11,000
Now you can see it in the book or the PowerPoint presentations,

439
00:38:11,000 --> 00:38:13,000
the put call parity theorem.

440
00:38:13,000 --> 00:38:16,000
Puts and calls are related by an equation.

441
00:38:16,000 --> 00:38:21,000
But the practical implication, which is what I'm trying to teach you here,

442
00:38:21,000 --> 00:38:30,000
is that calls actually respond positively to increases in interest rates.

443
00:38:30,000 --> 00:38:35,000
Puts respond negatively to increases in interest rates.

444
00:38:35,000 --> 00:38:38,000
And vice versa.

445
00:38:38,000 --> 00:38:45,000
So if you reduce interest rates, that tends to bring down call prices,

446
00:38:45,000 --> 00:38:50,000
but it tends to improve put prices.

447
00:38:50,000 --> 00:38:55,000
So what happened with the Fed cutting that discount rate more than we expected?

448
00:38:55,000 --> 00:38:57,000
I can't show it to you.

449
00:38:57,000 --> 00:39:01,000
I should have captured some data from a few days ago.

450
00:39:01,000 --> 00:39:09,000
But what it did was it bumped the calls and the puts in opposite directions.

451
00:39:09,000 --> 00:39:19,000
So when the interest discount rate went down, call prices eased up a bit.

452
00:39:19,000 --> 00:39:22,000
But put prices went up a bit.

453
00:39:22,000 --> 00:39:27,000
And if you think of the logic of it, just the financial logic of it,

454
00:39:27,000 --> 00:39:33,000
higher interest rates tend to suppress business activity

455
00:39:33,000 --> 00:39:37,000
because the present value of future expected cash flows goes down.

456
00:39:37,000 --> 00:39:42,000
Well, wouldn't that be adverse to a stock price?

457
00:39:42,000 --> 00:39:47,000
So that's what's going on here.

458
00:39:47,000 --> 00:39:55,000
It's simply the mathematics, universe's mathematical way of taking that into account.

459
00:39:55,000 --> 00:39:58,000
So whatever we think we're doing in business,

460
00:39:58,000 --> 00:40:07,000
we're really just the complete slaves of processes that happen way beyond finance.

461
00:40:07,000 --> 00:40:09,000
I just thought I'd bring that one up.

462
00:40:09,000 --> 00:40:14,000
It's kind of an interesting little thing.

463
00:40:14,000 --> 00:40:24,000
But with respect to the Black-Scholes options pricing model, the equation itself,

464
00:40:24,000 --> 00:40:30,000
I mean, you can do the equation and all these formulas I've shown you,

465
00:40:30,000 --> 00:40:32,000
they're just doing it for you.

466
00:40:32,000 --> 00:40:37,000
So in the book's homework, they give you all the,

467
00:40:37,000 --> 00:40:42,000
find all of these formulas, the risk-free rate, the standard deviation,

468
00:40:42,000 --> 00:40:50,000
the natural log of P of the underlying price over the strike price, and all of that.

469
00:40:50,000 --> 00:40:54,000
This, all you have to do is put in the numbers and it will come out for you.

470
00:40:54,000 --> 00:41:00,000
You'll be just fine using the Black-Scholes, this model right here.

471
00:41:00,000 --> 00:41:04,000
The only caution I have is, it looks like there's some kind of a,

472
00:41:04,000 --> 00:41:07,000
it's getting pissy about this little piece over here.

473
00:41:07,000 --> 00:41:09,000
So when you put in your expiration date,

474
00:41:09,000 --> 00:41:13,000
put it in this slot right here instead of up there at the top.

475
00:41:13,000 --> 00:41:15,000
I'm not sure what's going on with that.

476
00:41:15,000 --> 00:41:19,000
But once you put it there, it will calculate the number of years,

477
00:41:19,000 --> 00:41:24,000
the number of days divided by 365, and then it will reflect it over here.

478
00:41:24,000 --> 00:41:29,000
This is where the action happens on it, is right in here.

479
00:41:29,000 --> 00:41:35,000
And again, this is the Black-Scholes options pricing model.

480
00:41:35,000 --> 00:41:37,000
Oh, I did want to show you one more thing.

481
00:41:37,000 --> 00:41:38,000
Sorry about that.

482
00:41:38,000 --> 00:41:41,000
This is geek stuff, the numbers.

483
00:41:41,000 --> 00:41:46,000
Okay, we've got all these parameters put in here.

484
00:41:46,000 --> 00:41:48,000
What happens if there's a dividend?

485
00:41:48,000 --> 00:41:58,000
Now remember, a dividend wouldn't matter unless it occurs during the life of the option.

486
00:41:58,000 --> 00:42:03,000
It wouldn't matter because it's not going to affect, well, tiny bit maybe,

487
00:42:03,000 --> 00:42:07,000
because of the expectation of the dividend, but realistically.

488
00:42:07,000 --> 00:42:14,000
But watch what happens if there is a dividend that is paid during the life of the option.

489
00:42:14,000 --> 00:42:20,000
Watch the call in the put, 0.99 and 1.56.

490
00:42:20,000 --> 00:42:33,000
Let's say we have a 1% dividend.

491
00:42:33,000 --> 00:42:37,000
Again, you have an odd effect.

492
00:42:37,000 --> 00:42:40,000
Why did the call price reduce?

493
00:42:40,000 --> 00:42:50,000
Because that dividend is actually going to decrease the price of the stock.

494
00:42:50,000 --> 00:42:54,000
Because the dividend, as the dividend is approaching,

495
00:42:54,000 --> 00:42:59,000
that dividend begins to impound in the price you would pay.

496
00:42:59,000 --> 00:43:05,000
So if you buy the stock and the dividend is going to be there, you get gravy.

497
00:43:05,000 --> 00:43:15,000
So in this case, the dividend as it's building, if the dividend, after it is paid, the stock price will drop.

498
00:43:15,000 --> 00:43:17,000
That's the way dividends work.

499
00:43:17,000 --> 00:43:24,000
It's an underlying, there's so much noise that you won't really see much of it.

500
00:43:24,000 --> 00:43:37,000
But if these are dividend dates, ex-dividend dates, stock prices will do that.

501
00:43:37,000 --> 00:43:42,000
See, because the dividend, if you're holding the stock, you get the dividend.

502
00:43:42,000 --> 00:43:48,000
So as the dividend is approaching, the present value of it out here is small.

503
00:43:48,000 --> 00:43:52,000
But as you get closer to the time the dividend is paid,

504
00:43:52,000 --> 00:43:55,000
it begins to get closer and closer to the dividend itself.

505
00:43:55,000 --> 00:44:00,000
And then when the dividend is paid, flub, and then flub, and all that.

506
00:44:00,000 --> 00:44:09,000
So what's happening with the call option is that it is literally, it is, if you have a call option,

507
00:44:09,000 --> 00:44:18,000
buy it here, expiration here, the price of the stock is going to drop during the life,

508
00:44:18,000 --> 00:44:21,000
during the time you have the call option.

509
00:44:21,000 --> 00:44:25,000
So you get kind of this little surprise effect in here.

510
00:44:25,000 --> 00:44:30,000
And so call options tend to shave, be a little bit cheaper,

511
00:44:30,000 --> 00:44:38,000
simply because they are going to, by definition, lose some value during the life of the option.

512
00:44:38,000 --> 00:44:44,000
You're running toward a goal, and then you suddenly get on a hill and you fall backward.

513
00:44:44,000 --> 00:44:47,000
Puts are the other way, though.

514
00:44:47,000 --> 00:44:54,000
Let me go back, watch the put.

515
00:44:54,000 --> 00:45:02,000
Puts would be the opposite way, simply because you're on the other side of the transaction.

516
00:45:02,000 --> 00:45:05,000
You don't have to pay the dividend.

517
00:45:05,000 --> 00:45:09,000
It's kind of a way you get the dividend.

518
00:45:09,000 --> 00:45:14,000
But anyway, now one last thing just to show you something.

519
00:45:14,000 --> 00:45:20,000
Let me take this option out.

520
00:45:20,000 --> 00:45:24,000
Look at the theta.

521
00:45:24,000 --> 00:45:29,000
That's the one that is the premium for length of time.

522
00:45:29,000 --> 00:45:31,000
Let's get this option in closer.

523
00:45:31,000 --> 00:45:44,000
Let's do 10, 11, 24, and watch the theta.

524
00:45:44,000 --> 00:45:48,000
What happened to it?

525
00:45:48,000 --> 00:45:50,000
Let's take it in.

526
00:45:50,000 --> 00:46:05,000
10, 4.

527
00:46:05,000 --> 00:46:16,000
The theta decay is getting stronger, because you're getting closer and there's not as much time for something great to happen.

528
00:46:16,000 --> 00:46:27,000
That is saying that for every dollar the option moves, the underlying moves,

529
00:46:27,000 --> 00:46:38,000
the call option will lose about 11.25 cents of its value.

530
00:46:38,000 --> 00:46:39,000
That's one way of interpreting it.

531
00:46:39,000 --> 00:46:42,000
There are other ways of interpreting it, too.

532
00:46:42,000 --> 00:46:44,000
Now, where are we starting?

533
00:46:44,000 --> 00:46:46,000
Let's take it in one more, 19.

534
00:46:46,000 --> 00:46:52,000
Let's say 10, 4, 2020.

535
00:46:52,000 --> 00:46:59,000
No, no, 10, no, 9, 26.

536
00:46:59,000 --> 00:47:06,000
9, 26, 2024.

537
00:47:06,000 --> 00:47:09,000
Watch the theta.

538
00:47:09,000 --> 00:47:14,000
It's decaying at a very strong rate now.

539
00:47:14,000 --> 00:47:24,000
14, almost 15% value lost for every change, $1 change in the underlying.

540
00:47:24,000 --> 00:47:34,000
So that just shows you theta decay is real, and that's why as you get closer and closer to the expiration date,

541
00:47:34,000 --> 00:47:44,000
the options will get closer and closer to either zero or just the stock price minus the strike price,

542
00:47:44,000 --> 00:47:48,000
because the theta premium is just vanishing.

543
00:47:48,000 --> 00:47:54,000
And every stock and options chain is going to be different.

544
00:47:54,000 --> 00:47:57,000
There's no all of them do the same thing.

545
00:47:57,000 --> 00:48:04,000
It has to do with the theta uses every last one of these parameters.

546
00:48:04,000 --> 00:48:07,000
Some of them use only a couple of them.

547
00:48:07,000 --> 00:48:13,000
But I do want to point out, what was I going to say?

548
00:48:13,000 --> 00:48:19,000
Oh, your book will have you calculate some D1s and D2s in that formula.

549
00:48:19,000 --> 00:48:24,000
For God's sake, try to do it this way instead of trying to, because if you're like me,

550
00:48:24,000 --> 00:48:30,000
once I get about three numbers in and then I have to hit a divided by, I know I'm going to get the wrong answer.

551
00:48:30,000 --> 00:48:32,000
But you might be better than I am at it.

552
00:48:32,000 --> 00:48:35,000
But anyway, this is all for you.

553
00:48:35,000 --> 00:48:39,000
And it's again, I strongly encourage you not to share this.

554
00:48:39,000 --> 00:48:41,000
This is this is pro stuff.

555
00:48:41,000 --> 00:48:47,000
This isn't the toys that you can share on to get likes on TikTok.

556
00:48:47,000 --> 00:48:49,000
This is the real stuff.

557
00:48:49,000 --> 00:48:51,000
But anyway, that's all I have for you today.

558
00:48:51,000 --> 00:48:54,000
I thank you.