20. Option Price and Probability Duality
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- čas přidán 5. 01. 2015
- MIT 18.S096 Topics in Mathematics with Applications in Finance, Fall 2013
View the complete course: ocw.mit.edu/18-S096F13
Instructor: Stephen Blyth
This guest lecture focuses on option price and probability duality.
License: Creative Commons BY-NC-SA
More information at ocw.mit.edu/terms
More courses at ocw.mit.edu
We are probably underestimating the great times we are living in. I am basically taking an MIT class for free while sitting on my couch.
Internet is revolutionary
I have had a couple of beers
Yeah, for personal growth, that’s great. But no one cares if you don’t have your diploma from the brick and mortar MIT.
While I hit my bong lol crazy times we live in
Doing the same
All these haters saying this guy doesnt really understand practical finance - he was CEO of Harvard’s endowment and paid nearly $16M in 2015. I think the guy is a legit mathematician and practitioner of finance
He seems legit to me
He's legit. I actually can follow what he says and his math. He just throws terms like zero coupon bonds and martingales which the common person may not know
Richard Chua? Is the same Richard Chua who has been teaching wonderful courses on LinkedIn Learning?
Yeah...What I'm getting is that they're frustrated cause they don't know what he's talking about. There's a reason this is lecture 20 in the video lecture series LMAO
Oh yeah…. my friend met Cesar Romero… so there 😂
Some notable Timestamps:
0:04:47 Introduction
0:11:36 Option--Probability Duality
0:49:38 Fundamental Theorem of Asset Pricing (FTAP)
💯💯💯
BLESS YOU.
Thanks
@@klam77 the to
52:19 he nearly gets it right. he forgets to add the coefficient bRR, which adjusts the expected value of calls by the amount of jPOWs printer activity
Each step of the explanation, each formula has a huge importance in the theory of asset pricing. Excellent content. Best finance course I ever watched in my entire life, and I thought I had good teachers at my university.
The class seemed lost though...
Great lecture, particularly if you are trained in probability
Same a lot of these MIT lectures are brilliant
This is a math class though
You can kiss my asset…..lol sorry I had to be immature
Somehow followed this despite no financial background. An enthusiastic lecturer makes a huge difference
I don’t believe you
@@james3440 Considering the topic and how its presented a foundation in mathmatics let you go further then finance.
Lol k
I have no idea what he’s talking about, not because of the math (though I am rusty, admittedly), as I’m a math minor, but the finance understanding you need is pretty substantial. So yeah I think you’re full of shit.
fat chance
Got baked and now paranoid that there is a pop quiz on this 😱 thanks for the content!
Such a clear exposition, with completely new angles for me on a familiar topic. Brilliant.
Lies again? Platinum Debit
I am the dumbest guy in the entire room. We are halfway I still don’t have a clue what is going on.
God bless the only professor in this course that actually uses the black board and not purely bullshitting without formula or explanation and being annoying as fuck. Will check out his book.
What an exciting professor, bravo.
Best lecture I have seen on Options pricing. I enjoyed this very much
Amazing lecture! And, for the record, he was third wrangler of his Cambridge class back in 1985.
Wat is that
It means he wears cheap Wrangler Dad Jeans.
He was Third Wrangler in 1988.
Wow I can’t believe how humble he is given that he didn’t even tell his class about himself when he was telling them about the top wranglers in different years
so, he was being coy when he gave the vague '198x' year, challenging people to guess who was #3, etc. Then, makes mention of the #3 wrangler becoming more noteworthy the #1s and #2s. Is he hinting that he's worked out something that will fundamentally change how assets are priced/discounted, or something of similar scope and magnitude?
He himself is a third wrangler of his Cambridge class
Really enjoyed Stephen Blythe's lecturing! Amazing lectures thanks for sharing these
I enjoyed the side story about wranglers.
excellent introductory treatment of a topic which is usually mired in infernal stochastic calculus.
Best Pedagogical Skills And Talented Instructor
Very interesting lecture, although I only understood 20% of it.
Try imagining the concepts.
Its normal for that kind of lecture
@@Luiz6968vb It's not. 20% is a fail.
@@Newtube_Channel i see
😂
Excellent course, this is the essence of asset pricing
The Gordon Ramsey of finance
just saw ur comment, I commented the same thing 30 seconds ago. IKR
@@c4lb333 no one can tell me about the hadron collider?! these students are f’ing raw!! GTFO!!
@@Kinnoshachi "idiot sandwiches, all of them"
ramsAy, not ramsey
@@skuzza405 for F**K sake, I'm fired
The project was expected in a very professional manner
As important of a class as you’ll find in academic finance
What ?
This is a fantastic lecture. Also got suckered into buying the book.. wonderful read, too!
Is there anything I can use in my options trading?
You didn't get suckered. You were just enamored by his charm.
Thanks for sharing this information MIT. People don’t have no excuse now a days. If you have a desire to learn imagine where it can take you ….
I feel absolutely enlightened today
bursting with clarity
I found it comforting that my state university classes are as equally equipped.
lol
Shitty university in my third world country is also equally equipped and teaching the same things. Difference is, the students who attend MIT are intellectually elite, meanwhile students in my university are idiots.
@@patrickthepure to be fair, third world countries doesn't have this as a priority.
Stephen Blythe is awesome!
Hey, I found this second video of the same Prof with another new guest instructor. Great to sit in this class again with different topic. And will collect this lecture into my YT library. Hahaha
Hey, where's this second video?
Really interesting how the cancellation of the SSC contributed to the rise of quant finance. The discussion about wranglers was pretty cool, one he didn't mention was the 1973 Senior Wrangler: Lee Hsien Loong, current prime minister of Singapore. Of course the lecture was great too.
Will buy his book to digest all points. They are still available on Ebay and Amazon in 2021.
name of th book ?
What’s the book
Whats the name of the guy
Great work. Ok, so hes not a pure finance lecturer but who is when the application of engineering stats works in the spsce? And what is wrong in applying cross disciplinary mathematics to make money? Especially if it works?
Excellent lecture.
Fantastic, I never thought call butterfly as approximation of pdf of underlying asset
Teacher seems like a bloody legend
Very nice, very well explained.
😊
Excellent video…. Professor
Can't believe 18.S096 is an undergraduate course. There are so many wisdoms in this course.
Why should undergraduate courses not be full of wisdom?
Don't judge a book by its cover.
Is there a reference to the fact mentioned in the "Duality" lecture, namely, that since 2008 there can be options, whose prices diverge from the replicating portfolio?
I think it rather has to do with the way he built the lecture, to go from option pricing to probabilities in the first half and from probabilities to option pricing in the second half.
Maybe it's because US interest rates in the last decade have not been higher than inflation, at times real interest rates turning negative.
Amazing lecture
I disagree with the causal attribution regarding the development of the quant field due to physicists being out of work. The Renaissance (or Medallion) fund had been around for a long while before then. It was inevitable regardless.
Thanks for the masterclass, sir. 💯🔥
what a brilliant teacher
What can be done with this in practice?
Is this useful for option pricers to put a value on the option if they can estimate where the stock will be?
Or would investors want to approximate where the stock could be, and then estimate the option price, and see if there are “discounts” if a firm is charging less than the investor would expect?
If we estimate the stock price density using all the call option prices, somehow find a derivative with respect to k, is the density for stock price actually reasonable?
Thank you MIT!!!!
Nothing says pure math like inventing a notation for something that doesn't exist in real life
Does the application of this theory have any benefit tor economy as a whole ? Or does it only enable some investors to make money from other investors ?
Price and probability are both related to one another. Price of a product is influenced from cost of product, which is influenced from human labor and the machines made by human beings for means, modes and mediums of invention to innovation, designing to development, production to manufacturing, quality controll and research and development quantitatively and qualitatively.
Sooooo buy low, sell high. Got it. LOL
ya he spent 3 years on this book but yet he did not include the solutions to the chapter questions in the book... how can i learn when i don't know where i messed up.
Quite funny being a maths student in the UK, watching a MIT lecturer in the US giving history about Cambridge math in the UK
I've never been to college but all of this makes perfect sense
Awsome analysis please show us using automated tools at the same time. I'd love to to see this in realtime with an automated analysis as well. multi-task
ill take the animated version 😁
Hi,
Thanks a lot for wonderful lecture. I have one question though. While you prove Digital option is derivative of call price with respect to K, do you mean, - lambda call options with strike price K+(1/lambda) equal to sell lambda call options?
Thats correct. Another noteworthy point is that the slope between the two strike prices equals the number of calls purchased. As we let lambda tend towards infinity, the strike price of the calls being sold and bought will converge while the payoff slope tends towards becoming vertical. In essence, that's how we end up with the digital option simply jumping at the strike price.
Simply put, duality leads to conflict while neutrality leads to infinite potentialities.
yes, but will this work on a dice table?
I know I was not gonna understand a thing when I clicked this but still watched it and didnt unerstand anything LOL
So a mortgage back security is a probability distribution?
La que grado pertenecen estas clases están entretenidas, saludos desde Aguascalientes, México.
Un 80% son estudiantes de pegrado en matematica pura (interesados en finanzas) el otro 20% son de ingenierias y afines.
I think if Professor Blythe gets really famous Steve Martin would have an easy job playing him in a movie. Or the other way around.
Ok actually that intro question resonates with what Emanuel Derman mentioned in his book.
This is good for humanity
0 percent of viewers actually learned and applied anythimg from this playlist
@@deedumeday518not quite
this lecture reminds me the movie of alan turing
interesting... *pulls up robinhood and buys 100 call options expiring this week*
This lecturer must be making millions on the trading floor because he understands all the formulae that go into the AI algs running the stock market.
Nope. Probability is everybody's dilemma.
sorry, all the real money is made by frontrunning suckers. the math aint shite
facts @@loupasternak
@ 1:05:05 shouldn’t the limits in the integral be from 0 to x instead of from 0 to infinity?
I see your point, but it is an equivalent formulation as the integral is about [ max(x-k,0) g"(k) ] and not [(x-k) g"(k)].
Where did the 1/Z go in the pdf derivation?
The distribution is evaluated at time t = T where the discount factor evaluates to 1.
No please don’t spread false info, it was just a typo. It was re added later in the lecture
@@joshyman221 thanks!
Strike( k+1/lamda ) how it comes....can anyone explain please ....🙏🏻
It blows my mind that I did this stuff in college. Now it’s like gibberish.
Functions may interfare with one another, is any function which neutrilze it ?
"Gambling" by MIT
So, will the market go up or down?
At czcams.com/video/eG_aRPy1KVE/video.html What does taking lambda to inf means ? why does taking it to inf, is same as dC/dK ? I understand 1/lambda will become 0, but whats happens to lambdas in numerator as multipliers ?
dividing by 1/lambda is the same as multiplying by lambda, hence coming back to the common derivative definition
is 24:19 and 25:29 talking about the same distribution ? namely risk-neutral distribution ?
wtf are you on about? neural? this is as f(x,y)' written as f(x',y). Try again
@@ozicryptoG U ok bro
plz someone can help me to understand how he did to plot the payout function of his portfolio (19min05s) exactly why the graphic comes flat in 1 after k+1/lambda ? thx
after k+1/lambda, your portfolio payout is as follows: You are long lambda options at K, so that payout is lambda*(St-K),you are short lambda options at K+1/lambda, so that payout is lambda*(-St-K+1/lambda). This makes your total payout equivalent to lambda*(St-K-(St-K+1/lambda)), which is equal to lambda*(K-K+1/lambda), which is the same as lambda*(1/lambda), =1.
How & when does this get incorporated into the practice of trading?
i also bought this book and it's great
Which book?
An Introduction to Quantitative Finance
by Stephen Blyth, the lecturer
anyone know the name of the book he brings up at the beginning?
Introduction to Quantitative Finance by Stephen Blyth
Financial engineering market manipulation what’s the difference?
Wow!! So Amazing
So if I understand this correctly..
Buy low, sell high?
Sell your dad
Is there already functions in TOS where this can be seen or be actually applied?
Yes, you can see it in Think or Swim.
I lost track at “lander” whats lander?
I didn't realize 2009 caused that. Wow. That makes a LOT of sense
I could actually feel a wrinkle start forming at about 23 minutes in.
Lol from stress or from you cranium stretching?
Free knowledge 😋
Regardless how intelligent this presser is, tests shouldn't be designed to the point of difficulty, "just incase you want to look in further." Buddy thats why we review the test
Gordon Ramsay of finance.
so good and awesome.
What is lambda
Please EXPLAIN the mathematical formula on your P&L statement for MIT's $27 BILLION endowment of Zero tax liability as a private institution. Also, if your kind enough to explain or the formula for your distribution of funds on your endowment. Thanks.
I hate it when people explain things that quickly then explain it in such a way that you are supposed to know it
Is this just for European options?
If only this helped resurrect my options graveyard. He is so cute
Unless you're working for Renaissance Technologies you shouldn't be fucking around with options. Their entire business model is essentially taking all the money of individual speculators through mathematical superiority.
@@2011blueman how
what is the prerequisite for understanding this video?
Prerequisites
18.01 Single Variable Calculus
18.02 Multivariable Calculus
18.03 Differential Equations
18.05 Introduction to Probability and Statistics or 18.440 Probability and Random Variables
18.06 Linear Algebra
Broad familiarity with linear algebra, statistics, stochastic processes and partial differential equations will be helpful (but not required). Prior knowledge of economics or finance is not required but may be helpful for some lectures.
See ocw.mit.edu/18-S096F13 for more info and course materials. Best wishes on your studies!
The problem with financial theory is it means nothing in a world where the lawmakers feed from the same trough.
The reason I choose not to get a masters degree is that knowledge isnt what seperates me from accumulating more wealth. My last name does. The fact I'm not in career that seeks power does.
Its also why I think we'll collapse just like the soviet union. Its not about what you do anymore, it's about who you do it for and how close to the source of power/wealth you sit.
And NOTHING more.
What about American options? Talk was about European options
Digital clipping on voice is so infuriating to listen to. Harsh noise all over the spectrum.
Analog amps go into compression and everything is relatively well behaved and low pass, but digital is totally unforgiving if your gain is too high. This is the audio equivalent to blowout in photography.
This is all really interesting. What is all the math that I need to understand this? What classes should I take?
Let's see, this is not a comprehensive list but will do:
1) Calculus - 1 year course covering differential and integral calculus
2) Multivariable calculus - double integrals, partial derivatives, maxima, minima etc
3) Ordinary differential equations
4) Probability & statistics
I think that pretty much covers it but the order is very important; You can't do 2, 3 or 4 without 1. I would recommend 1, 4, then 2&3.
You may also need to learn functional analysis to understand a question from the student asking about basis other than call options.
Stonks go up?
Lambda == lamb duh(easy button) == the lamb slain before the foundation of the world.
St == the snake on the cross integrating mankind back in.
Derivative == derive == de river == off river == from riven
Please don't move the camera around when the lecturer writes. We have big enough screens to see the words, and we want to see the entire board.