20. Option Price and Probability Duality

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  • Опубліковано 11 січ 2025

КОМЕНТАРІ • 528

  • @WhiteNoiseChannel111
    @WhiteNoiseChannel111 3 роки тому +1360

    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.

    • @tanmayasahu5171
      @tanmayasahu5171 3 роки тому +31

      Internet is revolutionary

    • @28gbb
      @28gbb 3 роки тому +46

      I have had a couple of beers

    • @nickn4812
      @nickn4812 3 роки тому +30

      Yeah, for personal growth, that’s great. But no one cares if you don’t have your diploma from the brick and mortar MIT.

    • @onzah3515
      @onzah3515 3 роки тому +20

      While I hit my bong lol crazy times we live in

    • @KonnanPL
      @KonnanPL 3 роки тому +4

      Doing the same

  • @SeikoVanPaath
    @SeikoVanPaath 4 роки тому +260

    Some notable Timestamps:
    0:04:47 Introduction
    0:11:36 Option--Probability Duality
    0:49:38 Fundamental Theorem of Asset Pricing (FTAP)

    • @apierre6
      @apierre6 3 роки тому +1

      💯💯💯

    • @klam77
      @klam77 3 роки тому +2

      BLESS YOU.

    • @saxoman1995
      @saxoman1995 3 роки тому

      Thanks

    • @bobannisic1586
      @bobannisic1586 2 роки тому

      @@klam77 the to

    • @bilyonarelifestile2226
      @bilyonarelifestile2226 2 роки тому +2

      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

  • @richardchua8006
    @richardchua8006 4 роки тому +705

    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

    • @DennisRay99
      @DennisRay99 3 роки тому +8

      He seems legit to me

    • @vetiarvind
      @vetiarvind 3 роки тому +55

      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

    • @r.a.28
      @r.a.28 3 роки тому +5

      Richard Chua? Is the same Richard Chua who has been teaching wonderful courses on LinkedIn Learning?

    • @ethansolly96
      @ethansolly96 3 роки тому +36

      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

    • @FeelGoodInspiration
      @FeelGoodInspiration 3 роки тому +4

      Oh yeah…. my friend met Cesar Romero… so there 😂

  • @gerardomoscatelli9035
    @gerardomoscatelli9035 5 років тому +163

    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.

    • @Usman-ml4ig
      @Usman-ml4ig 4 роки тому +3

      The class seemed lost though...

    • @bleacherz7503
      @bleacherz7503 4 роки тому +8

      Great lecture, particularly if you are trained in probability

    • @vittoriooconnor7071
      @vittoriooconnor7071 3 роки тому +5

      Same a lot of these MIT lectures are brilliant

    • @IcyDeath91
      @IcyDeath91 3 роки тому +1

      This is a math class though

    • @driventoaccount3276
      @driventoaccount3276 2 роки тому

      You can kiss my asset…..lol sorry I had to be immature

  • @yd_
    @yd_ 3 роки тому +85

    Somehow followed this despite no financial background. An enthusiastic lecturer makes a huge difference

    • @sadface7457
      @sadface7457 3 роки тому +1

      @Tetrachloro Mysticide Considering the topic and how its presented a foundation in mathmatics let you go further then finance.

    • @Youtubeuser1aa
      @Youtubeuser1aa 3 роки тому +1

      Lol k

    • @Great_PatBingsoo
      @Great_PatBingsoo 3 роки тому +5

      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.

    • @onefortysix6955
      @onefortysix6955 3 роки тому

      fat chance

  • @pharaohgarmar5611
    @pharaohgarmar5611 3 роки тому +36

    Such a clear exposition, with completely new angles for me on a familiar topic. Brilliant.

    • @NazriB
      @NazriB 3 роки тому +1

      Lies again? Platinum Debit

    • @driventoaccount3276
      @driventoaccount3276 2 роки тому +1

      I am the dumbest guy in the entire room. We are halfway I still don’t have a clue what is going on.

  • @rafanovak
    @rafanovak 3 роки тому +53

    Amazing lecture! And, for the record, he was third wrangler of his Cambridge class back in 1985.

    • @galiltm5168
      @galiltm5168 3 роки тому +3

      Wat is that

    • @bilyonarelifestile2226
      @bilyonarelifestile2226 2 роки тому +6

      It means he wears cheap Wrangler Dad Jeans.

    • @jwonz2054
      @jwonz2054 2 роки тому +1

      He was Third Wrangler in 1988.

    • @justinchang9977
      @justinchang9977 2 роки тому +1

      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

    • @justinidiot7161
      @justinidiot7161 2 роки тому

      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?

  • @jiancongwang1268
    @jiancongwang1268 8 років тому +43

    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.

  • @sihouma87
    @sihouma87 3 роки тому +16

    Best lecture I have seen on Options pricing. I enjoyed this very much

  • @aaamos16
    @aaamos16 3 роки тому +28

    What an exciting professor, bravo.

  • @joshuapowell7485
    @joshuapowell7485 3 роки тому +10

    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 ….

  • @zkkrhfhska
    @zkkrhfhska 3 роки тому +7

    excellent introductory treatment of a topic which is usually mired in infernal stochastic calculus.

  • @amitdey8884
    @amitdey8884 4 роки тому +59

    He himself is a third wrangler of his Cambridge class

  • @retrofutur1st
    @retrofutur1st 3 роки тому +22

    Got baked and now paranoid that there is a pop quiz on this 😱 thanks for the content!

  • @droneaerial9140
    @droneaerial9140 3 роки тому +51

    I found it comforting that my state university classes are as equally equipped.

    • @swiss9495
      @swiss9495 3 роки тому +1

      lol

    • @patrickthepure
      @patrickthepure 3 роки тому +18

      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.

    • @RidDik417
      @RidDik417 3 роки тому +1

      @@patrickthepure to be fair, third world countries doesn't have this as a priority.

  • @bmwman5
    @bmwman5 6 років тому +394

    Very interesting lecture, although I only understood 20% of it.

  • @shumetnecho1471
    @shumetnecho1471 3 роки тому +1

    Best Pedagogical Skills And Talented Instructor

  • @Kinnoshachi
    @Kinnoshachi 3 роки тому +135

    The Gordon Ramsey of finance

    • @c4lb333
      @c4lb333 3 роки тому +1

      just saw ur comment, I commented the same thing 30 seconds ago. IKR

    • @Kinnoshachi
      @Kinnoshachi 3 роки тому +1

      @@c4lb333 no one can tell me about the hadron collider?! these students are f’ing raw!! GTFO!!

    • @c4lb333
      @c4lb333 3 роки тому +1

      @@Kinnoshachi "idiot sandwiches, all of them"

    • @skuzza405
      @skuzza405 3 роки тому

      ramsAy, not ramsey

    • @Kinnoshachi
      @Kinnoshachi 3 роки тому +1

      @@skuzza405 for F**K sake, I'm fired

  • @bleacherz7503
    @bleacherz7503 4 роки тому +16

    As important of a class as you’ll find in academic finance

  • @RollenJokers
    @RollenJokers 6 років тому +28

    I enjoyed the side story about wranglers.

  • @dansokolsky3963
    @dansokolsky3963 4 роки тому +23

    This is a fantastic lecture. Also got suckered into buying the book.. wonderful read, too!

    • @dennykeaton9701
      @dennykeaton9701 2 роки тому

      Is there anything I can use in my options trading?

    • @exploringwithdave5926
      @exploringwithdave5926 2 роки тому

      You didn't get suckered. You were just enamored by his charm.

  • @JimXiaZhang
    @JimXiaZhang 6 років тому +14

    Can't believe 18.S096 is an undergraduate course. There are so many wisdoms in this course.

    • @wedeldylan
      @wedeldylan 5 років тому +3

      Why should undergraduate courses not be full of wisdom?

    • @niceday2015
      @niceday2015 3 роки тому

      Don't judge a book by its cover.

  • @antikoerper256
    @antikoerper256 3 роки тому +7

    Really enjoyed Stephen Blythe's lecturing! Amazing lectures thanks for sharing these

  • @nxkyt
    @nxkyt 2 роки тому +1

    Teacher seems like a bloody legend

  • @johnchessant3012
    @johnchessant3012 Рік тому +3

    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.

  • @gerardomoscatelli9035
    @gerardomoscatelli9035 5 років тому +9

    Excellent course, this is the essence of asset pricing

  • @miguelinigoseno6058
    @miguelinigoseno6058 2 роки тому +1

    I know I was not gonna understand a thing when I clicked this but still watched it and didnt unerstand anything LOL

  • @sare-st8ni
    @sare-st8ni 2 роки тому +1

    The project was expected in a very professional manner

  • @mountainman9145
    @mountainman9145 2 роки тому +4

    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.

    • @gorporpio
      @gorporpio 2 роки тому

      Nope. Probability is everybody's dilemma.

    • @loupasternak
      @loupasternak 2 роки тому +1

      sorry, all the real money is made by frontrunning suckers. the math aint shite

    • @patzer9137
      @patzer9137 Рік тому

      facts @@loupasternak

  • @anabilkanungoe1728
    @anabilkanungoe1728 23 дні тому +1

    What's the meaning of -lambda calls at strike k+1/lambda. negative amount of contracts ? 17:20

    • @elvipora4167
      @elvipora4167 22 дні тому +1

      Yes. Long lambda calls at strike K and short lambda calls at strike K+1/lambda.

  • @Josh-ge1cr
    @Josh-ge1cr 3 роки тому +5

    interesting... *pulls up robinhood and buys 100 call options expiring this week*

  • @anwaypradhan6591
    @anwaypradhan6591 11 місяців тому

    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.

  • @whatsup4807
    @whatsup4807 3 роки тому +4

    Will buy his book to digest all points. They are still available on Ebay and Amazon in 2021.

  • @whatsup4807
    @whatsup4807 3 роки тому +8

    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

  • @Ab-ii4oc
    @Ab-ii4oc 2 роки тому +1

    Fantastic, I never thought call butterfly as approximation of pdf of underlying asset

  • @waynevanilla
    @waynevanilla 2 роки тому +2

    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.

  • @kyleucf
    @kyleucf 2 роки тому +1

    It blows my mind that I did this stuff in college. Now it’s like gibberish.

  • @robertocaesar
    @robertocaesar 2 роки тому +2

    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.

  • @j121212100
    @j121212100 3 роки тому +2

    Stephen Blythe is awesome!

  • @dumbgiant2765
    @dumbgiant2765 3 роки тому +2

    I've never been to college but all of this makes perfect sense

  • @Angela-lm3dm
    @Angela-lm3dm 2 роки тому

    Quite funny being a maths student in the UK, watching a MIT lecturer in the US giving history about Cambridge math in the UK

  • @xqt39a
    @xqt39a 2 роки тому +2

    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 ?

  • @MRGEEE3K
    @MRGEEE3K 3 роки тому +6

    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

  • @aryamanful
    @aryamanful 5 років тому +2

    I feel absolutely enlightened today

  • @tenax8964
    @tenax8964 2 роки тому +1

    I hate it when people explain things that quickly then explain it in such a way that you are supposed to know it

  • @maximegrossman2146
    @maximegrossman2146 4 роки тому +3

    bursting with clarity

  • @michaelward2293
    @michaelward2293 3 роки тому +10

    If only this helped resurrect my options graveyard. He is so cute

    • @2011blueman
      @2011blueman 3 роки тому +3

      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.

  •  9 місяців тому

    Thanks for the masterclass, sir. 💯🔥

  • @erickjian7025
    @erickjian7025 3 роки тому +2

    is 24:19 and 25:29 talking about the same distribution ? namely risk-neutral distribution ?

  • @Dsc1965Capricornsnake
    @Dsc1965Capricornsnake 2 роки тому +1

    Excellent video…. Professor

  • @SphereofTime
    @SphereofTime 5 місяців тому +1

    11:57 option probability duality

  • @yatapote
    @yatapote 3 роки тому +4

    This is good for humanity

  • @jewmenomorev2611
    @jewmenomorev2611 2 роки тому +2

    Wow!! So Amazing
    So if I understand this correctly..
    Buy low, sell high?

  • @bookzdotmedia
    @bookzdotmedia 2 роки тому +1

    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

  • @miriconklin4720
    @miriconklin4720 3 роки тому +2

    Very nice, very well explained.
    😊

  • @evenTyler
    @evenTyler 3 роки тому +4

    I could actually feel a wrinkle start forming at about 23 minutes in.

    • @igorpisarev9132
      @igorpisarev9132 3 роки тому +1

      Lol from stress or from you cranium stretching?

  • @TylerHNothing
    @TylerHNothing 8 років тому +36

    i also bought this book and it's great

    • @janhoffken7850
      @janhoffken7850 8 років тому +4

      Which book?

    • @TylerHNothing
      @TylerHNothing 8 років тому +16

      An Introduction to Quantitative Finance
      by Stephen Blyth, the lecturer

  • @whiteeagle5969
    @whiteeagle5969 2 роки тому +3

    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

    • @DaniiMarie333
      @DaniiMarie333 2 роки тому

      ill take the animated version 😁

  • @brexit9279
    @brexit9279 2 роки тому

    MIT SUPPORTS THE GLOBAL AGENDA!

  • @naveedali1406
    @naveedali1406 Рік тому +1

    what a brilliant teacher

  • @DanOneOne
    @DanOneOne 4 роки тому +33

    So glad I didn't pay for this course...

  • @whippet71
    @whippet71 3 роки тому +7

    yes, but will this work on a dice table?

  • @TylerHNothing
    @TylerHNothing 2 роки тому +1

    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?

  • @micropenny6056
    @micropenny6056 3 роки тому +1

    watch this at 1.5x speed for time saving. 2x if you are brave

  • @Alex-jk7xu
    @Alex-jk7xu 3 роки тому +9

    "Gambling" by MIT

  • @bicepjai
    @bicepjai 3 роки тому +4

    At ua-cam.com/video/eG_aRPy1KVE/v-deo.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 ?

    • @zenusb
      @zenusb Рік тому

      dividing by 1/lambda is the same as multiplying by lambda, hence coming back to the common derivative definition

  • @davidlowe8597
    @davidlowe8597 3 роки тому +10

    Would have been helpful if you plugged in numbers from a real stock/ Call option to see if any of this actually works

    • @AE-cc1yl
      @AE-cc1yl 3 роки тому

      thanks for your contribution...

    • @DaniiMarie333
      @DaniiMarie333 2 роки тому

      There's a kid called "MitchRayTA" on youtube who uses this on crypto calls and is always right

    • @Juanmaturriago
      @Juanmaturriago 2 роки тому +2

      What do you mean if any of this works, most brokers determine the bid or ask prices on this math. It’s a given thing

  • @AzriRich88
    @AzriRich88 2 роки тому +1

    I just heard one thing from the whole thing, whiskey😂😂😂

  • @TheIllerX
    @TheIllerX 3 роки тому +3

    Excellent lecture.

  • @DmitryKarpeyev
    @DmitryKarpeyev 8 років тому +5

    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?

    • @rhonkvs3929
      @rhonkvs3929 7 років тому +5

      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.

    • @mozartmaia6333
      @mozartmaia6333 3 роки тому

      Maybe it's because US interest rates in the last decade have not been higher than inflation, at times real interest rates turning negative.

  • @rewtnode
    @rewtnode 7 років тому +4

    @ 1:05:05 shouldn’t the limits in the integral be from 0 to x instead of from 0 to infinity?

    • @amadouyorothiam5804
      @amadouyorothiam5804 6 років тому +9

      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)].

  • @leooz8071
    @leooz8071 2 роки тому +1

    So, will the market go up or down?

  • @chavorocket
    @chavorocket 2 роки тому +3

    Nothing says pure math like inventing a notation for something that doesn't exist in real life

  • @BrianM216
    @BrianM216 2 роки тому

    I just watched an hour of a smart guy telling me the market is priced in

  • @leer.watson4673
    @leer.watson4673 2 роки тому

    13:50 time when I no longer could comprehend.

  • @navargas
    @navargas 2 роки тому +3

    Simply put, duality leads to conflict while neutrality leads to infinite potentialities.

  • @splugereport
    @splugereport 3 роки тому +11

    Where did the 1/Z go in the pdf derivation?

    • @joshyman221
      @joshyman221 3 роки тому +1

      No please don’t spread false info, it was just a typo. It was re added later in the lecture

    • @splugereport
      @splugereport 3 роки тому

      @@joshyman221 thanks!

    • @rahularora2716
      @rahularora2716 4 місяці тому

      @@joshyman221 Can you please tell me how he figured the Butterfly Probability

  • @shantsol1
    @shantsol1 3 роки тому +2

    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.

  • @naveenkumarc7081
    @naveenkumarc7081 2 роки тому +2

    What is lambda

  • @matthewmc4363
    @matthewmc4363 2 роки тому

    We are basically striking his ball sake.
    Nice book I’ll read after knowing that math can make you rich. And if you know you are right. Place a call. And if you know they are wrong. Place a put.
    Horse racing.
    You cannot replicate this at the rate of the real world trade.
    That being said. Knowing how it works make you understand imbalances.

  • @prashantrai1240
    @prashantrai1240 Рік тому

    Functions may interfare with one another, is any function which neutrilze it ?

  • @toddbearden7251
    @toddbearden7251 13 днів тому

    What he doesn’t tell you is the probability of the event changes based on what options and how much have been purchased. So, if everyone buys calls the market will go down with 100% probability. If 50/50 calls puts,the market will stay flat and theta will just rot you options away. Always remember people the stock market is a rigged against you as an investor. They can see your trades, they know what you’re holding and they know the probability of what you’ll do next. Basically, you are playing cards with your cards showing and their cards hidden, and they can draw from the deck as they wish. It’s a lose/lose. I always say, the best time to sell an option is 5 minutes after you buy it. That is, until they identify you as a scalper. Once they’ve seen you trade the computer has already built models on you - use multiple accounts and don’t make the same trades or you’ve already lost

  • @investingthelike111
    @investingthelike111 2 роки тому +3

    if this works why is this guy not sitting on his mega yacht

  • @c4lb333
    @c4lb333 3 роки тому +4

    Gordon Ramsay of finance.

  • @kh19208
    @kh19208 5 років тому +4

    this lecture reminds me the movie of alan turing

  • @yli5531
    @yli5531 3 роки тому

    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.

  • @juanecheverria8386
    @juanecheverria8386 2 роки тому +1

    I lost track at “lander” whats lander?

  • @dinusiva3019
    @dinusiva3019 2 роки тому

    Strike( k+1/lamda ) how it comes....can anyone explain please ....🙏🏻

  • @zaccy
    @zaccy 2 роки тому +1

    I watched all of this so I can understand how dumb I am

    • @ajcook7777
      @ajcook7777 7 місяців тому

      Something tells me you still don't know how dumb you are.

  • @djayjp
    @djayjp 3 роки тому +2

    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.

    • @viraatdas
      @viraatdas 6 місяців тому

      Medallion fund was founded in 1988. Defunding of the super hadron collider happened in 1983.
      It was inevitable, yes, but it definitely expedited the quant field.

  • @felicityc
    @felicityc 2 роки тому

    I didn't realize 2009 caused that. Wow. That makes a LOT of sense

  • @justducky8508
    @justducky8508 Рік тому

    How & when does this get incorporated into the practice of trading?

  • @fs2641
    @fs2641 3 роки тому

    Ok actually that intro question resonates with what Emanuel Derman mentioned in his book.

  • @ultimo4955
    @ultimo4955 2 роки тому +2

    Imagine watching this and expecting to gain anything from this

    • @loupasternak
      @loupasternak 2 роки тому +1

      you need an imagination just to realize its useless

  • @emanuellandeholm5657
    @emanuellandeholm5657 3 роки тому +3

    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.

  • @bhavinmoriya9216
    @bhavinmoriya9216 2 роки тому

    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?

    • @pandakiller3089
      @pandakiller3089 Рік тому +1

      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.

  • @jacobhy9645
    @jacobhy9645 2 роки тому

    When the S&P algo pops wide cuz of this little spider it's gonna eat ALL the flies

  • @DavidGatto
    @DavidGatto 3 роки тому +2

    Yes, we love problems that are unsolvable - barring Divine Intervention

  • @robloxinaalisa8440
    @robloxinaalisa8440 3 роки тому

    all that talent goes to finances to make the already very rich richer

  • @StevenSmith68828
    @StevenSmith68828 3 роки тому

    Financial engineering market manipulation what’s the difference?