The Easiest Way to Derive the Black-Scholes Model

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  • Опубликовано: 23 ноя 2024

Комментарии • 101

  • @PerfilievFinancialTraining
    @PerfilievFinancialTraining  3 года назад +25

    Hello friends! Thank you so much for watching! I’ve only recently started on RUclips, and this is one of my first videos. I really hope you’ll find it interesting and somewhat entertaining. Please, please do subscribe to the channel - at this early stage, your support has a HUGE impact, and absolutely every person counts. I am doing this full-time now, and if you want to see how it goes, it would be great to have you on board! As always, feel free to reach out for any feedback, questions and suggestions. You can ping me on Twitter or via email in the channel description. Thank you for your help and support!

    • @zkkrhfhska
      @zkkrhfhska 3 года назад

      Have you seen the derivation via Wang's transform? I come from an insurance maths background and I found that the "easiest" for me. I've also see a good explanation based on option price : probability duality which was very intuitive

  • @anandkulkarni2111
    @anandkulkarni2111 2 года назад +6

    The proof is very intuitive. I recommend that you discuss why those terms like dt*dt and dt*dw tend to zero since they are infinitesimally small. It just helps people from non financial math background a bit more.

  • @burnoutparidise1
    @burnoutparidise1 3 года назад +32

    "This is left as an exercise for the reader". Oh lord. It's my math classes all over again.

    • @PerfilievFinancialTraining
      @PerfilievFinancialTraining  3 года назад +6

      Hahaha, sorry for the flashback :) I also couldn't stand it when math textbooks did that!

  • @steez54321
    @steez54321 2 года назад +11

    This is actually the best explained derivation I've found on RUclips so far. Thank you so much!

  • @Zzzexie
    @Zzzexie Год назад +3

    This is absolutely this best video for BSM! And the explanation is much easier to understand than the green book Thx

  • @sdsa007
    @sdsa007 8 месяцев назад

    I like that this video was a concise overview! It made everything connect! It complements the other videos that I saw where I got stuck in the weeds... which means I have a good understanding of the high-speed sections, but I still needed this overview to confirm all the math substitutions! Thanks!

  • @richardxue1506
    @richardxue1506 11 месяцев назад +4

    insanely high efficiency. Thank you for the great work

  • @scentilatingone2148
    @scentilatingone2148 3 года назад +3

    Brings back memories of Dif EQ class! I would have learned alot more with you as a professor.

  • @Tweeteketje
    @Tweeteketje Год назад +1

    Great content, super clear! I hope you will make more videos! Why I think this is fantastic, is that it is intuitive, clear, step-for-step and yet concise.

  • @alovyachowdhury9143
    @alovyachowdhury9143 2 года назад +4

    This is fantastic! Thanks for the clear indications about the assumptions on delta hedging and portfolio growth at risk-free rate, it made for a really easy to follow derivation

  • @jon5532
    @jon5532 3 года назад +14

    This is awesome. I'm probably going to watch it a few times to get comfortable with all the material. Thanks for the knowledge!

    • @PerfilievFinancialTraining
      @PerfilievFinancialTraining  3 года назад +1

      Thank you for watching! If anything's unclear or confusing, feel free to let me know - would be happy to help out!

  • @Jenna-iu2lx
    @Jenna-iu2lx 8 месяцев назад

    The explanations are so clear, thank you so much for this video!

  • @Lexis.options
    @Lexis.options 3 года назад +7

    This was the best math lesson! You have a love for teaching and made it easy to understand. Looking forward to more of the same!

    • @PerfilievFinancialTraining
      @PerfilievFinancialTraining  3 года назад +1

      Hi Lexi, thank you so much for your kind words! I'm really glad to hear it was easy to understand :) Thank you!

  • @salimrhmaritlemcani1936
    @salimrhmaritlemcani1936 Год назад

    Amazing strating point thanks a lot. clarifies a lot !
    The only thing that I think would be relevant to point out is that this is the Black Scholes Merton differential equation, not the Black Scholes formula: they are similar but serve different purposes.
    The black sholes formula is a closed-form solution derived from the BSM differential equation.
    Black Scholes Merton differential equation is used to calculate the fair value of European-style options and to determine the option's sensitivity to changes in various factors, such as the underlying asset price and time, while the Black Scholes formula provides a mathematical formula for calculating the theoretical price of a European-style call or put option.
    Thanks for the content!!

  • @harryj1081
    @harryj1081 3 года назад +10

    Great video as always. I’d be thrilled if you could elaborate more on option trading strategies that the cornwall capital turned 110k to 80MM from the big short. Apparently they relied heavily on the models and maximize the Convexity of option.

    • @PerfilievFinancialTraining
      @PerfilievFinancialTraining  3 года назад +1

      Hi Harry, that's an interesting story! Haven't heard of it, thank you. If time permits, I'll try to check it out! Thanks for watching! :)

  • @kurian0_0
    @kurian0_0 8 месяцев назад

    So easy and clear to understand

  • @nikolaykogut7546
    @nikolaykogut7546 3 года назад +2

    Thanks Sergei... I really liked the video

  • @RishabhKhare
    @RishabhKhare 10 месяцев назад +2

    Really good explanation. Thanks for doing this!

  • @dylan-kt7kd
    @dylan-kt7kd 2 месяца назад

    Amazing video, thank you

  • @TrungPham1310xx
    @TrungPham1310xx Год назад

    You're much better than my lecturer and I have to pay for it.

  • @bomfim04
    @bomfim04 2 года назад +2

    Amazing Chanel! Hello from Brazil!

  • @joaoricardosimas2036
    @joaoricardosimas2036 2 года назад

    This is awesone! Thank you Perfiliev!

  • @raulzevallos3399
    @raulzevallos3399 Год назад

    AMAIZING EXPLANATION FINALLY I UNDERSTAND IT. THANKS

  • @patrickaungier3197
    @patrickaungier3197 5 месяцев назад

    Awesome work, thank you !

  • @774471jr
    @774471jr 3 года назад +2

    9:20 "annnd, that's pretty much all you have to do" lol
    Loving your channel!! I know the basics of options, but you definitely make it easier to understand all these complicated things.

  • @harshvardhanranvirsingh9473
    @harshvardhanranvirsingh9473 3 года назад +5

    Perfect!! looking for more content like this!

  • @choicedeals5041
    @choicedeals5041 3 года назад +6

    Hi there!
    This is great content and you have made it really easy to understand complex concepts.
    Could you make an episode to explain and demystify what exactly is a Partial Differential Equation (PDE) and how this is different from other types of models e.g. trees, monte carlo
    Thank you!

    • @PerfilievFinancialTraining
      @PerfilievFinancialTraining  3 года назад

      Hello, yes, of course, it's certainly something I could do. I am a bit short on time at the moment to film/present everything I want, but I've noted your request and will do my best. Thank you for watching this video!

    • @CAfinalspeedruns
      @CAfinalspeedruns Год назад +1

      I know it's been 2 years so you probably figured it out by now, but Khan Academy has an excellent playlist on multivariate calculus where you can find the relevant video for what a partial derivative is

  • @riccardoformenti4332
    @riccardoformenti4332 3 года назад +4

    Keep it going, loving the content

  • @UniversalDegen
    @UniversalDegen 3 года назад +4

    Damn this is like Sheldon Cooper level shit. Awesome explanation 😃

    • @PerfilievFinancialTraining
      @PerfilievFinancialTraining  3 года назад +1

      Hahaha, thank you so much for watching and for your feedback! :) Really glad it was useful :) All the best!

  • @federicocremonini4741
    @federicocremonini4741 10 месяцев назад +2

    Thank you so much!

  • @aj_actuarial_ca
    @aj_actuarial_ca 5 месяцев назад

    Very well explained. Are you an actuary?

  • @mindingthedata4218
    @mindingthedata4218 3 года назад +4

    Another incredible video! Cannot wait for the next one :)

  • @jonathanseo6728
    @jonathanseo6728 Год назад

    My major is civil engineering, and I also learned about stokes theorem. It’s look similar as Brownian motion is that I first impressive part. And second is that I listened your lecture from 0 to end. But I don’t have any idea about how to treat my stock portfolio 😅😅

  • @sergeyyatskevitch3617
    @sergeyyatskevitch3617 3 года назад +3

    Hmmm..... d2S technically is not a "square" of the dS, but rather a second differential, thus the issue here is how to treat a differential of the stochastic process W. I understand that you tried to simplify the process, but omitting several important math steps in understanding this equation, led LTCM to its demise. But I enjoyed your way of presenting this very important, but complex equation. BTW, this equation is very well known in Theoretical Physics as the Fokker-Plank equation. Cheers!

    • @PerfilievFinancialTraining
      @PerfilievFinancialTraining  3 года назад +1

      Hi Sergey, thank you for your feedback and insights! Indeed, I haven't noticed I called the second derivative a "square" :) That would be a video-level typo :) Thank you!

  • @hassamkhan7861
    @hassamkhan7861 3 года назад +3

    Video is short and To the point and i really like it though, looking for more practical content .
    But there certain topic which people should be comfortable with, stochastic calculus and stats , . Im sure these prerequisite would be handy . For further topics .

    • @leoafrifanus
      @leoafrifanus 3 года назад +1

      Most intuitive trading view is the one you presented ! Some people like to say the discounted option price is a martingale, then apply Ito to it and say the drift is 0, but that’s too abstract vs this one ! Great content man !

    • @PerfilievFinancialTraining
      @PerfilievFinancialTraining  3 года назад +1

      Hi Mohd, thank you. Yeah, I see what you mean - it is indeed just theory. I'll probably do a few of these at the start, as I experiment with different topics/subjects. Hopefully will have more practical stuff later on too! Thanks for watching! :)

    • @PerfilievFinancialTraining
      @PerfilievFinancialTraining  3 года назад

      @@leoafrifanus Thank you, glad you like it! :) Yeah, hahaha, I know that derivation and it is too abstract indeed (especially if one doesn't know much about martingales or risk-neutral expectations etc)...

  • @ttwtrader
    @ttwtrader 3 года назад +3

    Hi Sergey, great video. Thank you. Is there any way to visualize the formula in terms of graphs? So, to "play" around with different "parameters" and see the graphical output? Could you add or do that as sequel of this video using mathematica for example?

    • @PerfilievFinancialTraining
      @PerfilievFinancialTraining  3 года назад

      In this video, I'm discussing the Black-Scholes equation, which still needs to be solved to get an options' pricing formula. The Black-Scholes equation can be written in terms of Greeks: Theta + 1/2 * vol^2 * spot^2 * Gamma + rS * Delta - rV = 0. And you can visualise the Greeks via a simple Black Scholes calculator. Unfortunately, I can't give you a link, since RUclips hides comments with links, but google "perfiliev financial black scholes" and check out the first link!

    • @ttwtrader
      @ttwtrader 3 года назад

      @@PerfilievFinancialTraining Thanks a lot.

    • @ttwtrader
      @ttwtrader 3 года назад +1

      Btw, it can be done in Mathematica as well.

    • @PerfilievFinancialTraining
      @PerfilievFinancialTraining  3 года назад

      @@ttwtrader Definitely! To be honest, even a simple Excel sheet can do :)

  • @vvardhan14
    @vvardhan14 3 года назад +3

    Thanks a lot buddy !!

  • @lukedoyle7802
    @lukedoyle7802 Год назад

    This is the Magnum Opus of Black Scholes explanation videos

  • @paulmalliga9996
    @paulmalliga9996 2 года назад

    Thank you for your work!! :D

  • @bongiwelanga1706
    @bongiwelanga1706 7 месяцев назад

    Thank you!!

  • @ddyms
    @ddyms 3 года назад +1

    Awesome video. Thanks :)

  • @Vijaykumar1614SK
    @Vijaykumar1614SK 3 года назад +3

    fantastic

  • @lebleb8603
    @lebleb8603 3 года назад +1

    Awsome! Can you explain how Cem get his levels?

    • @PerfilievFinancialTraining
      @PerfilievFinancialTraining  3 года назад

      Thank you for watching the videos! I'd have to dig into that a bit more, to come up with a good explanation. If time allows, I'll try to get into it. Thank you!

    • @lebleb8603
      @lebleb8603 3 года назад +1

      @@PerfilievFinancialTraining thank you for your reply!

  • @christopherrose5554
    @christopherrose5554 3 года назад +3

    Hey found you on Twitter and love the videos
    Will you provide any practical examples in the future? EG Using these equations to construct a hypothetical neutral portfolio of apple

    • @PerfilievFinancialTraining
      @PerfilievFinancialTraining  3 года назад

      Hey Christopher, thank you for watching the videos! Glad you liked them :) Yeah, this one was a purely theoretical video - I'll try to do more practical stuff in the future if time allows. Thanks again!

  • @miquelmalaga
    @miquelmalaga 3 года назад +3

    Sir, what are you selling and how can I buy it?

    • @PerfilievFinancialTraining
      @PerfilievFinancialTraining  3 года назад +1

      Hi Miquel! Thank you so much for your support! At the moment, I don't have much to offer, but I will let you know as soon as I do :)

  • @amirulfadlan1718
    @amirulfadlan1718 2 года назад

    OMG HAHAHAHAHAHAHAA thank you so so much for this simpler equation. Its so hard to understand the one from the textbook. thank you sir!
    😁

  • @giovanniberardi4134
    @giovanniberardi4134 2 года назад

    Hi Sergei! I have a question. Is there an intuitive reason explaining why dt*dw=0 dt*dt=0 and dW*dW=dt? Why the uncertain factor in the price model is dropped when it is plugged in the BS model? Is it the direct consequence of the hedging? Thank you very much

  • @xntumrfo9ivrnwf
    @xntumrfo9ivrnwf 3 года назад +3

    Hey, ya silverback s twitter: great video! Some 'comments' (lol), or rather tiny points that *maybe* might help:
    - title of the video will turn some people off. Why not something like "... intuition behind the BS formula" etc. 'Derive' is scary for some people... actually thinking about this now, unless you are splitting your content between more technical and more intuitive, etc. --> in that case cool, you can just put relevant videos in a playlist
    - have you / will you do a binomial option pricing? if you have, apologies, been swamped so am catching up on good channels
    - ^^ same for no-arbitrage bounds --> that's a really easy intro to all of this; P-C parity?
    - Idea: create a quick XLS template to calculate this and let people follow along?

    • @PerfilievFinancialTraining
      @PerfilievFinancialTraining  3 года назад

      Hey Nick! Great to see you here! :) These are some great suggestions, thank you so much!
      - Title + thumbnails - I am trying to improve on those and make them less "scary".
      - Playlist - yes, as soon as I add a few more videos in a similar genre, I'll start grouping them into playlists.
      - Binomial model - funny you should mention it, as I did it alongside this video.
      Thanks for the other suggestions! Much appreciated!

  • @Timbel26
    @Timbel26 10 месяцев назад

    Hello,I need help on linear fractional black-scholes model.

  • @user-cz8lv7lw5u
    @user-cz8lv7lw5u Год назад

    Thanks bro.

  • @HaigInstruments
    @HaigInstruments 7 месяцев назад +1

    If it is risk free, then how did people use this knowledge to beat the markets?

    • @freqh
      @freqh 3 месяца назад

      "Don't try to measure the water depth with both legs" is a old saying... It's base on fair price, but reality is different in the market... Market might be overvalued or undervalued most of the times because of greed, fear, emotions, natural calamities, war etc.

  • @leedunkelberger9768
    @leedunkelberger9768 Год назад

    great stuff " )

  • @nemachtianimx343
    @nemachtianimx343 2 года назад

    Gracias!

  • @sanjithramanmohan8971
    @sanjithramanmohan8971 2 года назад +1

    That was some reallyy dope explanation ! Can you derive it into the formulae which they give for N(d1) and N(d2) .It'd really help if you put more videos on stochastic calculus and stuff too !
    Thank you so much !

  • @AaronLloyd-Jones
    @AaronLloyd-Jones 6 месяцев назад

    The best way to derive a premium formula for an option is how I do it (and recommend others do also), and this is not the Black-Scholes formula:
    The Black and Scholes equation is wrong: The Black and Scholes (risk-neutral) premium is the first moment of the option expiry for an asset that has all risk and no market return (the risk-neutral measure), that which has been debased of market return (by holding portfolio returns fixed flat at r). This idiotic asset (the risk-neutral measure) is stochastically dominated by bonds in that bonds have the same return (r) but without the risk whilst it is stochastically dominated by stocks since stocks earn market return for the equivalent amount of risk:
    bonds have LOWER RISK for the SAME RETURN as the debased market asset (the risk-neutral measure)
    whilst
    stocks have HIGHER RETURN for the SAME RISK as the debased market asset (the risk-neutral measure)
    Either way, the 'risk-neutral measure' is totally idiotic and stochastically dominated by all non-redundant asset classes. It is not deep and it is not abstract. All it is is the market asset without return (which is then used to price the derivative and so is wrong and inaccurate).
    If a trader wants an option, then he must not take an offsetting position that nullifies the option position. There is nothing risk-neutral about that. An option premium must have a mean mu in the drift term, otherwise it is wrong... wrong for derivatives and wrong for efficient and non-communist finance.
    nb: I had to say 'no risk' when I sat several of the courses in undergraduate (almost two decades ago). It was clear as day to me then that it was inaccurate (and proved by me definitively now more than one decade ago).
    I debunk Black and Scholes fully here: drive.google.com/file/d/1drOy89roxTawddpbFv03MEgrNSRwPRab/view?usp=drive_link
    here is new theory for markets (crystal ball formula): drive.google.com/file/d/1POgaFZxaXpGPbxDh8p9IHP_Kr2-VXok5/view?usp=drive_link
    PhD examiner report 3: drive.google.com/file/d/1z2Cflnp1uQ059GIonv2lzfqOj0EcMXrv/view?usp=drive_link
    PhD examiner report 2: drive.google.com/file/d/1K07G377R0ZSUs9ax6EXAzYealrjbo2vS/view?usp=drive_link
    PhD examiner report 1: drive.google.com/file/d/1BXwbk-uFrQDH_es_T5FiIJOnJ_42oA0q/view?usp=drive_link

  • @ffust3740
    @ffust3740 3 года назад +3

    Please!! We want the martingale approach!!

    • @PerfilievFinancialTraining
      @PerfilievFinancialTraining  3 года назад

      Hi Ferran, hahaha :) I think that would take us all the way to the solution and not just the BS PDE, right?

  • @Jupiter1423
    @Jupiter1423 2 года назад +1

    Ill just use a bs calc thx

  • @apundude
    @apundude 2 года назад

    Great video.. Can u just give an example with market datas on how it actually works as a risk free model by choosing and stock and it's underlying option?

  • @kennethamoahnyame4678
    @kennethamoahnyame4678 3 года назад +2

    "easiest"

    • @PerfilievFinancialTraining
      @PerfilievFinancialTraining  3 года назад

      Hahaha, as easy as it can be :) But yes, I agree, even this method is based on some relatively complex mathematical concepts.

  • @quant-prep2843
    @quant-prep2843 3 года назад +4

    Guys are we in heaven?

  • @tsunningwah3471
    @tsunningwah3471 11 месяцев назад

    zhins

  • @chihuahuafink3644
    @chihuahuafink3644 Год назад

    I knew I’m a 100% nerd when I thoroughly enjoyed going through all the math 🧮