20. Option Price and Probability Duality

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  • Опубликовано: 11 янв 2025

Комментарии • 528

  • @WhiteNoiseChannel111
    @WhiteNoiseChannel111 3 года назад +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 года назад +31

      Internet is revolutionary

    • @28gbb
      @28gbb 3 года назад +46

      I have had a couple of beers

    • @nickn4812
      @nickn4812 3 года назад +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 года назад +20

      While I hit my bong lol crazy times we live in

    • @KonnanPL
      @KonnanPL 3 года назад +4

      Doing the same

  • @SeikoVanPaath
    @SeikoVanPaath 4 года назад +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 года назад +1

      💯💯💯

    • @klam77
      @klam77 3 года назад +2

      BLESS YOU.

    • @saxoman1995
      @saxoman1995 3 года назад

      Thanks

    • @bobannisic1586
      @bobannisic1586 2 года назад

      @@klam77 the to

    • @bilyonarelifestile2226
      @bilyonarelifestile2226 2 года назад +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 года назад +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 года назад +8

      He seems legit to me

    • @vetiarvind
      @vetiarvind 3 года назад +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 года назад +5

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

    • @ethansolly96
      @ethansolly96 3 года назад +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 года назад +4

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

  • @gerardomoscatelli9035
    @gerardomoscatelli9035 5 лет назад +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 года назад +3

      The class seemed lost though...

    • @bleacherz7503
      @bleacherz7503 4 года назад +8

      Great lecture, particularly if you are trained in probability

    • @vittoriooconnor7071
      @vittoriooconnor7071 3 года назад +5

      Same a lot of these MIT lectures are brilliant

    • @IcyDeath91
      @IcyDeath91 3 года назад +1

      This is a math class though

    • @driventoaccount3276
      @driventoaccount3276 2 года назад

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

  • @yd_
    @yd_ 3 года назад +85

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

    • @sadface7457
      @sadface7457 3 года назад +1

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

    • @Youtubeuser1aa
      @Youtubeuser1aa 3 года назад +1

      Lol k

    • @Great_PatBingsoo
      @Great_PatBingsoo 3 года назад +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 года назад

      fat chance

  • @pharaohgarmar5611
    @pharaohgarmar5611 3 года назад +36

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

    • @NazriB
      @NazriB 3 года назад +1

      Lies again? Platinum Debit

    • @driventoaccount3276
      @driventoaccount3276 2 года назад +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 года назад +53

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

    • @galiltm5168
      @galiltm5168 3 года назад +3

      Wat is that

    • @bilyonarelifestile2226
      @bilyonarelifestile2226 2 года назад +6

      It means he wears cheap Wrangler Dad Jeans.

    • @jwonz2054
      @jwonz2054 2 года назад +1

      He was Third Wrangler in 1988.

    • @justinchang9977
      @justinchang9977 2 года назад +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 года назад

      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 лет назад +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 года назад +16

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

  • @aaamos16
    @aaamos16 3 года назад +28

    What an exciting professor, bravo.

  • @joshuapowell7485
    @joshuapowell7485 3 года назад +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 года назад +7

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

  • @amitdey8884
    @amitdey8884 4 года назад +59

    He himself is a third wrangler of his Cambridge class

  • @retrofutur1st
    @retrofutur1st 3 года назад +22

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

  • @droneaerial9140
    @droneaerial9140 3 года назад +51

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

    • @swiss9495
      @swiss9495 3 года назад +1

      lol

    • @patrickthepure
      @patrickthepure 3 года назад +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 года назад +1

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

  • @bmwman5
    @bmwman5 6 лет назад +394

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

  • @shumetnecho1471
    @shumetnecho1471 3 года назад +1

    Best Pedagogical Skills And Talented Instructor

  • @Kinnoshachi
    @Kinnoshachi 3 года назад +135

    The Gordon Ramsey of finance

    • @c4lb333
      @c4lb333 3 года назад +1

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

    • @Kinnoshachi
      @Kinnoshachi 3 года назад +1

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

    • @c4lb333
      @c4lb333 3 года назад +1

      @@Kinnoshachi "idiot sandwiches, all of them"

    • @skuzza405
      @skuzza405 3 года назад

      ramsAy, not ramsey

    • @Kinnoshachi
      @Kinnoshachi 3 года назад +1

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

  • @bleacherz7503
    @bleacherz7503 4 года назад +16

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

  • @RollenJokers
    @RollenJokers 6 лет назад +28

    I enjoyed the side story about wranglers.

  • @dansokolsky3963
    @dansokolsky3963 4 года назад +23

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

    • @dennykeaton9701
      @dennykeaton9701 2 года назад

      Is there anything I can use in my options trading?

    • @exploringwithdave5926
      @exploringwithdave5926 2 года назад

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

  • @JimXiaZhang
    @JimXiaZhang 6 лет назад +14

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

    • @wedeldylan
      @wedeldylan 5 лет назад +3

      Why should undergraduate courses not be full of wisdom?

    • @niceday2015
      @niceday2015 3 года назад

      Don't judge a book by its cover.

  • @antikoerper256
    @antikoerper256 3 года назад +7

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

  • @nxkyt
    @nxkyt 2 года назад +1

    Teacher seems like a bloody legend

  • @johnchessant3012
    @johnchessant3012 Год назад +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 лет назад +9

    Excellent course, this is the essence of asset pricing

  • @miguelinigoseno6058
    @miguelinigoseno6058 2 года назад +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 года назад +1

    The project was expected in a very professional manner

  • @mountainman9145
    @mountainman9145 2 года назад +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 года назад

      Nope. Probability is everybody's dilemma.

    • @loupasternak
      @loupasternak 2 года назад +1

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

    • @patzer9137
      @patzer9137 Год назад

      facts @@loupasternak

  • @anabilkanungoe1728
    @anabilkanungoe1728 23 дня назад +1

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

    • @elvipora4167
      @elvipora4167 22 дня назад +1

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

  • @Josh-ge1cr
    @Josh-ge1cr 3 года назад +5

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

  • @anwaypradhan6591
    @anwaypradhan6591 11 месяцев назад

    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 года назад +4

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

  • @whatsup4807
    @whatsup4807 3 года назад +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 года назад +1

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

  • @waynevanilla
    @waynevanilla 2 года назад +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 года назад +1

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

  • @robertocaesar
    @robertocaesar 2 года назад +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 года назад +2

    Stephen Blythe is awesome!

  • @dumbgiant2765
    @dumbgiant2765 3 года назад +2

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

  • @Angela-lm3dm
    @Angela-lm3dm 2 года назад

    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 года назад +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 года назад +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 лет назад +2

    I feel absolutely enlightened today

  • @tenax8964
    @tenax8964 2 года назад +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 года назад +3

    bursting with clarity

  • @michaelward2293
    @michaelward2293 3 года назад +10

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

    • @2011blueman
      @2011blueman 3 года назад +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 месяцев назад

    Thanks for the masterclass, sir. 💯🔥

  • @erickjian7025
    @erickjian7025 3 года назад +2

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

  • @Dsc1965Capricornsnake
    @Dsc1965Capricornsnake 2 года назад +1

    Excellent video…. Professor

  • @SphereofTime
    @SphereofTime 5 месяцев назад +1

    11:57 option probability duality

  • @yatapote
    @yatapote 3 года назад +4

    This is good for humanity

    • @deedumeday518
      @deedumeday518 Год назад +1

      0 percent of viewers actually learned and applied anythimg from this playlist

    • @sebastiansantolalla9184
      @sebastiansantolalla9184 8 месяцев назад

      @@deedumeday518not quite

  • @jewmenomorev2611
    @jewmenomorev2611 2 года назад +2

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

  • @bookzdotmedia
    @bookzdotmedia 2 года назад +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 года назад +2

    Very nice, very well explained.
    😊

  • @evenTyler
    @evenTyler 3 года назад +4

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

    • @igorpisarev9132
      @igorpisarev9132 3 года назад +1

      Lol from stress or from you cranium stretching?

  • @TylerHNothing
    @TylerHNothing 8 лет назад +36

    i also bought this book and it's great

    • @janhoffken7850
      @janhoffken7850 8 лет назад +4

      Which book?

    • @TylerHNothing
      @TylerHNothing 8 лет назад +16

      An Introduction to Quantitative Finance
      by Stephen Blyth, the lecturer

  • @whiteeagle5969
    @whiteeagle5969 2 года назад +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 года назад

      ill take the animated version 😁

  • @brexit9279
    @brexit9279 2 года назад

    MIT SUPPORTS THE GLOBAL AGENDA!

  • @naveedali1406
    @naveedali1406 Год назад +1

    what a brilliant teacher

  • @DanOneOne
    @DanOneOne 4 года назад +33

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

  • @whippet71
    @whippet71 3 года назад +7

    yes, but will this work on a dice table?

  • @TylerHNothing
    @TylerHNothing 2 года назад +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 года назад +1

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

  • @Alex-jk7xu
    @Alex-jk7xu 3 года назад +9

    "Gambling" by MIT

  • @bicepjai
    @bicepjai 3 года назад +4

    At ruclips.net/video/eG_aRPy1KVE/видео.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 Год назад

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

  • @davidlowe8597
    @davidlowe8597 3 года назад +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 года назад

      thanks for your contribution...

    • @DaniiMarie333
      @DaniiMarie333 2 года назад

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

    • @Juanmaturriago
      @Juanmaturriago 2 года назад +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 года назад +1

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

  • @TheIllerX
    @TheIllerX 3 года назад +3

    Excellent lecture.

  • @DmitryKarpeyev
    @DmitryKarpeyev 8 лет назад +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 лет назад +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 года назад

      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 лет назад +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 лет назад +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 года назад +1

    So, will the market go up or down?

  • @chavorocket
    @chavorocket 2 года назад +3

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

  • @BrianM216
    @BrianM216 2 года назад

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

  • @leer.watson4673
    @leer.watson4673 2 года назад

    13:50 time when I no longer could comprehend.

  • @navargas
    @navargas 2 года назад +3

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

  • @splugereport
    @splugereport 3 года назад +11

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

    • @joshyman221
      @joshyman221 3 года назад +1

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

    • @splugereport
      @splugereport 3 года назад

      @@joshyman221 thanks!

    • @rahularora2716
      @rahularora2716 4 месяца назад

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

  • @shantsol1
    @shantsol1 3 года назад +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 года назад +2

    What is lambda

  • @matthewmc4363
    @matthewmc4363 2 года назад

    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 Год назад

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

  • @toddbearden7251
    @toddbearden7251 13 дней назад

    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 года назад +3

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

  • @c4lb333
    @c4lb333 3 года назад +4

    Gordon Ramsay of finance.

  • @kh19208
    @kh19208 5 лет назад +4

    this lecture reminds me the movie of alan turing

  • @yli5531
    @yli5531 3 года назад

    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 года назад +1

    I lost track at “lander” whats lander?

  • @dinusiva3019
    @dinusiva3019 2 года назад

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

  • @zaccy
    @zaccy 2 года назад +1

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

    • @ajcook7777
      @ajcook7777 7 месяцев назад

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

  • @djayjp
    @djayjp 3 года назад +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 месяцев назад

      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 года назад

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

  • @justducky8508
    @justducky8508 Год назад

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

  • @fs2641
    @fs2641 3 года назад

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

  • @ultimo4955
    @ultimo4955 2 года назад +2

    Imagine watching this and expecting to gain anything from this

    • @loupasternak
      @loupasternak 2 года назад +1

      you need an imagination just to realize its useless

  • @emanuellandeholm5657
    @emanuellandeholm5657 3 года назад +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 года назад

    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 Год назад +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 года назад

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

  • @DavidGatto
    @DavidGatto 3 года назад +2

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

  • @robloxinaalisa8440
    @robloxinaalisa8440 3 года назад

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

  • @StevenSmith68828
    @StevenSmith68828 3 года назад

    Financial engineering market manipulation what’s the difference?