The Easiest Way to Derive the Black-Scholes Model

Binomial Option Pricing Model || Theory & Implementation in Python

В СТАРОЙ ОБЩАГЕ НА КОВРИКЕ МЫ НАШЛИ ПОХИЩЕННОГО ПАРНЯ БЕЗ ЕДЫ И ВОДЫ.

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Binomial Options Pricing Model Explained

Perfiliev Financial Training

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In this video, we'll explore the Binomial Options Pricing Model. This is a very simple model that demonstrates the basics behind derivatives pricing.
It requires only some basic arithmetic - there is absolutely no stochastic calculus or anything complicated like that.
But at the same time, it clearly demonstrates many of the fundamental concepts within quantitative finance, and it can even be used to derive the Black-Scholes formula.
In this video, I’ll present the basics behind the model and we’ll use it to price an actual call option.
00:00 Introduction to Binomial Model
01:33 Constructing a Binomial Tree
06:39 Creating a Hedged Portfolio
10:59 Comparison with Real-life Probabilities
15:06 Conclusion
If you have any questions or suggestions, feel free to let me know. Thank you for watching!

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22 июл 2024

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Комментарии : 134

@PerfilievFinancialTraining 2 года назад

Hello friends! Thank you so much for watching! I’ve only recently started on RU-vid, 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!

@chamanthawickramarathne2029 2 года назад

Actually, you explain everything in an easy-to-understand way. Keep it up.👍

@kevw5473 2 месяца назад

This was such a great clear explanation and your passion for teaching is so apparent. You make an amazing teacher!

@Leshic2 2 года назад

Excellent.. Wow.. Outstanding to have somebody of your experience, sharing options and trading from this perspective. Thank you. (here after seeing your interview a week ago) By the way, I love how you presented it with the phone call. Excellent. I had to watch it a 2nd time and frequently skipped back to better grasp points. (our minds often wander when listening...)

@harshvardhanranvirsingh9473 2 года назад

Perfect Timing! I was actually reading the Risk Neutral Valuation in a 2-period binomial model! Once again great video! Looking more like these!

@PerfilievFinancialTraining 2 года назад

Hi Harshvardhan, oh nice :) Hope this was useful and helped with understanding the risk-neutral valuation (although I haven't touched upon risk-neutral probabilities in the video). Thanks so much for watching! :)

@jongxina3595 Год назад

Really good video! Especially for a beginner like me. Thanks!

@annieyang4420 4 месяца назад

The most understandable content of this topic in just 15min after viewing so many similar. I saw most of your video was published 2 yrs ago and saw you started to publish new video lately, keep up working on it you are great! Have subscribed to your channel and looking forward more great stuff!

@PerfilievFinancialTraining 3 месяца назад

Thank you so much for your kind words! :) It's really appreciated!

@tanchienhao 7 месяцев назад

Best explanation on options pricing! Especially the part where you emphasise that the probability doesn’t matter, we are trading volatility not the stock!

@nicolumps8362 Месяц назад

This is the clearest explanation I have ever seen, thank you!

@riccardoformenti4332 2 года назад

Keep up this math inclined videos, the best content you’ve published by far

@PerfilievFinancialTraining 2 года назад

Hey Riccardo! Wow, thanks for your feedback! :) Noted :) Thanks for watching!

@TheKgpatriot Год назад

Thank you! That was a great explanation! Good luck with your channel Sergei!

@alaataktokani8884 11 месяцев назад

i really really liked your expalnation. it is funny, enjoyable, simple and informative. the skitch in between is a great addition lol

@christopherrose5554 2 года назад

Great video! thank you for a practical example Such amazing content from a brand new channel.

@PerfilievFinancialTraining 2 года назад

Hi Christopher, thank you so much for your feedback! It's great to hear :) Will try to do more videos like this one.

@kenmayer9334 2 года назад

Great video. Straight to the point. Thank you.

@PerfilievFinancialTraining 2 года назад

Hi Ken, thank you so much for watching! Glad you enjoyed it :)

@dianaluna2263 5 месяцев назад

That was sooo good. Super clear and lovely to watch. Thank youuuu

@PerfilievFinancialTraining 5 месяцев назад

Thank you! Appreciate it.

@Revelcember 4 месяца назад

Back then I was taught some arbitrary method to derive P and 1-p and determine the option price in Binomial Model. Although the mentioned method was easy, it lacked logic and therefore was forgettable. You explained this method very Logically and succinctly. Now I can’t forget the derivation, even if I want to. Thanks for the video😁

@Joey-pn8qp 7 месяцев назад

Best explanation I've seen on this topic!

@faithonchoke4430 3 месяца назад

amazing video.thankyou

@alilawati87 Год назад

You are gifted! I was struggling to understand Shreve’s book. Your explanation is awesome. Now what about including interest rate in the model.

@alexanderlapanowski3866 2 года назад

I really appreciate this video. I worked through all of Shreeve Volume 1, and a part of Volume 2, and I was a bit worried that the Binomial Asset Pricing model was too easy or simple to be used in practice. I'm glad that some experienced quants/strats think that it's worthwhile.

@PerfilievFinancialTraining 2 года назад

Hi Alexander, yeah, not only it's good for academic/teaching purposes, but it's also sometimes used for American option pricing, alongside finite-difference methods.

@alexanderlapanowski3866 2 года назад

In Volume 1 and in this video, the up and down factors are explicitly given. However, in volume 2, he connects the model to geometric browninan motion by plugging in the volatility of the stock, giving specific upward and downward factors, and showing that the BAPM converges to the geometric brownian motion. Which do you think is the more useful formulation? Shouldn't it be easier to just take historical stock price data and compute the volatility that way? How would one go about computing the upward and downward factors in practice?

@sbrown103 2 года назад

Really enjoyed this. Thanks!

@PerfilievFinancialTraining 2 года назад

Hi Scott, thank you for watching! Hope it was useful :)

@joaoviniciusalvesprado7423 Год назад

Thanks from Brazil, bro!

@Inbirman Год назад

thank you, you explained it very clearly!

@beelineunitel 4 месяца назад

I really enjoyed the way you explained it! Something I wasn’t able to fully understand before watching your video! :) I wanted to mentioned one thing that I find perplexing: The calculation of the stock EV is not correct, which in turn - makes it appear as if the option is miss priced at the 0.40 level. 0.40 level for the option is actually a correct level because the stock spot should be trading at $99.6 and not $100 (40%*102+60%*98) *assuming zero rates etc etc.

@armandomadero2930 2 года назад

Sooo goood ! Thank you.

@Gurugaming440 2 месяца назад

Thank you so much u explained it very well love from India

@wenwendong4163 2 года назад

Thank you great work

@ratonxiify 2 года назад

Amazing video!!!

@PerfilievFinancialTraining 2 года назад

Hey Andres, thank you for watching! Glad you liked it :)

@angeldiazgarcia7145 2 года назад

Wow, great content!! Just introducing myself in the options markets world and amaze of seeing how beautiful it is!

@PerfilievFinancialTraining 2 года назад

Thank you! Yeah, there's a lot of interesting stuff in the options space - you can never stop learning :)

@anrm6 2 года назад

Best video on yt re Binomial. Do you have a video for going beyond one step? Like maybe for American options or embedded options in Bonds?

@anshjain3169 Год назад

too helpful. also, love the enthusiasm.

@21sNeeo 7 месяцев назад

thanks you so much sir. really clear.

@melisaesgici2254 10 месяцев назад

Great video!!!! Thank you

@jcbprod Год назад

The best teacher ever seen.

@chickensoup4479 Год назад

great videos bro keep going bros

@ctoxyz 2 месяца назад

love it! #mustsee

@nikolaykogut7546 2 года назад

Thanks Sergei... I really liked the video

@PerfilievFinancialTraining 2 года назад

Hi Nikolay, thank you so much! Really glad you liked it :)

@enfantrouge666 2 года назад

Thanks for sharing, now I can understand the model

@PerfilievFinancialTraining 2 года назад

Hey Frank, thanks for watching! Glad it helped! :)

@tiago_holanda Год назад

hahahahha the phone call wasnt on my expectations. Amazing video !! owned a new subscribe !

@ramanujraychoudhury4398 2 года назад

One of the best videos on Option pricing and I must salute to your presentation skills and more precisely the way you spiced up the video with real life like scenario. Best wishes for your channel. Please make video series on Option pricing and if possible include real life scenarios of OTC derivative markets.. But nevertheless very nice video

@PerfilievFinancialTraining 2 года назад

Hey Ramanuj, thank you so much for your kind words. Very happy you liked the video so much! All the best to you too!

@Natasha-ky3uj 2 года назад

Awesome! Thank you

@PerfilievFinancialTraining 2 года назад

Thank you for watching!

@vaibhavchauhan7915 Год назад

Explained very well and had a great presentation. The vibe wasn't theoretical/academic, rather practical.

@pinaki_ghosh 10 месяцев назад

that call was amazing

@wilsonhenriquezmora9017 Год назад

Thank you mate

@hellodre 2 года назад

Just listened to you on the "Confessions of a market maker" Podcast! I had your video thumb nail pop up several times of the big trade and the iceberg, so now I know who you are! I just hit your sub button, So I'll be watching more of your vids! Btw, I have been steadily investing little by little since 2018, and started to trade forex a year ago. Keep up the great work!

@PerfilievFinancialTraining 2 года назад

Hey, thanks for your support! Good luck and all the best!

@luismarialacomaaller2646 2 года назад

Very good explanation and very instructive

@PerfilievFinancialTraining 2 года назад

Thank you! :) That's really great to hear!

@Seed-qj6jk 2 года назад

🤣🤣 this video is just brilliant, informative and hilarious. Keep them coming

@PerfilievFinancialTraining 2 года назад

Thank you! Will do my best :)

@evdoxiapikouni545 Год назад

YOU ARE AMAZING. THANKS 🎁🎁🎁

@user-wt8dt8zv1c Год назад

Gosh thank you!!

@dam-ib9fs Год назад

xD loved the skit entertaining & informational vid, ty

@sameerbhattarai2328 Год назад

You make everything easy to understand. As we know, pricing of options doesn't depend on drift of stock or probability of stock going up/down. But, why are we using a risk-neutral valuation method which uses the probability of bull/bear to determine the value of an option? Can you please clarify regarding this?

@super9_55 2 года назад

Great content, thank you. I wonder if you can have more content that bridges the gap between retail investors and professionals like yourself.

@PerfilievFinancialTraining 2 года назад

Thank you for your comment and for watching the video! I will try to do my best, as time allows :)

@dinkysniff Год назад

This is a really cool video and a nice explainer on the binomial model. If anyone watching this is confused how Δ was calculated as 0.25 it might be helpful to have a further explanation because it assumes the viewer understands how to simplify the equation - in that case then it might be helpful to understand the steps; It's explained that it's needed to find the value of Δ that makes the portfolio riskless. The portfolio consists of a long position in Δ shares and a short position in one call option. We can see in the first step it's demonstrated that 102Δ -1 = 98Δ (you can also express as; 102Δ - 98Δ = 1) You can simplify this equation to 4Δ = 1 (because difference between 102 & 98 is 4) Finally, you can solve for Δ by dividing both sides of the simplified equation by 4, which gives; Δ = 1/4 = 0.25

@Thts_nique Год назад

you are heaven sent because I was confused, but if I write it as -1+102*(delta)=98*(delta) would the answer be the same?

@hamzamohammed3992 8 месяцев назад

Thank You soo much !

@dinkysniff 8 месяцев назад

@@hamzamohammed3992 glad it helped!

@arusrhythm440 2 месяца назад

It's really really very helpful. Thank you so much. The way of your explanation is too good. Currently I'm pursuing MBA in Finance and after that I'm thinking about preparing for CFA. Can you suggest me is this a right decision?

@marcogelsomini7655 2 года назад

12:48 nice point!

@vishnukallingal7611 3 месяца назад

can you explain why the premium on the short option is not being collected in the down move, just that i didn't grasp that particular concept

@tradingforveteransandservi8797 2 года назад

Wow just wow man

@Aripb88 Год назад

Hi, thank you for the detailed and easy to understand walkthrough! Is there an easy way to explain why the probability of each future state isn’t taken into account with the neutral portfolio equality. For example why isn’t it (0.4)(-1 + 102Delta) = (0.6)(98Delta) to find delta?

@AhmadAli-uu3tr 9 месяцев назад

Hey thank you so much. This was very helpful. If you dont mind, i kind of got lost around 12:40z you mentioned the “growth rate” and “probability” interchangeability. Could you elaborate more. What should i search to further understand what you mean by how the probability of either direction has no affects on price? Thanks

@NishantMehtamehtanishant6197 2 года назад

Really good quality content...

@PerfilievFinancialTraining 2 года назад

Hi Nishant, thank you so much! Glad you think so :)

@NishantMehtamehtanishant6197 2 года назад

I need not mention but for me this video brought much more clarity then CFA curriculum could. :P

@PerfilievFinancialTraining 2 года назад

@@NishantMehtamehtanishant6197 Thanks Nishant, really glad that I could help with this! :) Good luck with CFA! :)

@raulzevallos3399 11 месяцев назад

What happened with this magnificus channel, best ever

@AbdulRaheemAziz7087 2 месяца назад

good😀😀

@bigal5413 2 года назад

great video sergei! i will point out that in the anglo system, the ¢ (cent sign) goes *after* the number, eg, 40¢, even though the $ sign goes before, $40. i know, i know...why? i don't know.

@PerfilievFinancialTraining 2 года назад

Perfect, thanks for pointing that out! Hahaha, I purposefully wrote the cent sign in front... I figured if the $ sign goes in front, so must the cent sign go in front too! :P

@FredBuys2005 2 года назад

Good job, might want to consider darker/thicker white board markers. 🙏🏻

@PerfilievFinancialTraining 2 года назад

Hi Fred, yes, definitely! I've noticed that too after recording. The green was barely visible - had to manually make it darker in the editing software. Will either use thicker markers or something else in the future. Thanks for watching!

@JoseThomas-bq3bn Месяц назад

In the video it said that the stock price can either move to 102 or 98. Does this assumption of 102 and 98 impact the option price, if I am expecting a move of 105 and 90 does the fair value of option changes?

@hellotrading3245 10 месяцев назад

What actions we can take based on greeks values ? Are there any channels that share that ?

@marysmith3710 2 года назад

Great video. I just was hoping for clarification. So the price of the stock is completely irrelevant to the price of the options??

@rudrapratapmahida1957 2 года назад

Great video, can we make videos on IV . Need more clear content on volatility ( impact on options pricing , how it increases and decrease)

@PerfilievFinancialTraining 2 года назад

Thank you for watching - will try my best to make a few vids on IV in the future.

@ramkhurana9590 Год назад

Hey, I enjoyed ur explaination, but how would your answer differ if the interest was 5 percent?

@mihirbpi Год назад

For this hedging to work perfectly in real life then the stock must actually follow a binomial tree model correct? So does what model we assume a stock follows affect the option price? Like what if we assume a Black-Scholes model is what's real for example. I guess my question is does what model we use matter and is developing better models for stock prices useful or is binomial tree enough?

@sakshisoni396 11 месяцев назад

Hello, i understand that the portfolio is hedged when the probabilities 0.4 and 0.6 dont affect our profit or loss....but i had a doubt here that if 0.4 changes to 0.1 then the value we got...24.5 would also change and then will it not impact our option price?

@fernandadelaflor2594 Год назад

Te amo demasiado

@giovanniberardi4134 2 года назад

Hi. I have 2 considerations (with the assumption of risk free rate=0). I don't know if I'm right. 1) DELTA is the ratio between ITM value and total range i.d. expected volatility (in this case 1/4=0.25). STRIKE 100 -> With expected values 98 and 110 then DELTA = 10/12 or 0.83. With expected values 90 and 102 then DELTA= 2/12=0.17. With simmetrical values then DELTA= 0,5. That's the delta in ATM that we all know. In reality ATM Delta is slighty different from 0,5 due to lognormality assumption in B&S. So if we consider an extremely skewed distribution instead of lognormal then our ATM delta would be far away from 0,5, as per the examples above? 2) Risk neutral probabilities (different from probability p in the video, I use notation "np") could be calculated as the ratio between expected down move and expected volatility. So we could calculate V as a weighted mean of 2 expected values. V= np* Va - (1-np)*Vb. Va and Vb are call value at t+1. So considering numbers in the video -> np= (100-98)/(102-98)= 0,5 -> V= 1*0,5 - (1-0.5)*0= 0,5. Considering instead the other examples above: 1) V=2/12*10 - 0 = 1,7. 2) V= 10/12*2-0= 1,7 In the last 2 example it's clear that call value doesn't depends by the direction of the expected moves but by the overall volatility.

@PerfilievFinancialTraining 2 года назад

Thank you for sharing this!

@Potencyfunction Месяц назад

It is a shame for those mass -media traders that pretend to be "in da* trend" with stocks and investing when they in fact do not have a slight idea about the foundation of those things. This is mattery/subject on the level B in Math, Probability and Differential Calculus, but some people prehaps did not had car to go to high school at the right time. Is call brand retardation. If you lost your education due to others, do not forget them and study by your self, instead to appear in public with a high degree of stupidity. They do not understand, those stupid fuckers are all Bitcoin business mans.

@JoseThomas-bq3bn Месяц назад

We are getting extra 10 cents for heging. So should we buy stock from that 10 cents to hedge the option we sold? Or we need to buy 50 cents worth stocks. And can you do a video that says how to rebance the portfolio so that we stayed hedged.

@mohdharis4471 Год назад

how do you determine the number of steps?

@Juoa794 7 месяцев назад

Hello, I did not understand why just charging the expected value is not enough since it already factors in the probabilities. Can you please elaborate?

@Potencyfunction Месяц назад

@Juoa794 How about you go to your country education website on high-school level B Math and start studying there by your own bcz you seems stupid to understand anyway.

@alejandrogaliana 2 года назад

Hello, How do you estimate the up and down movement? What happens if the stock moves much higher or lower than that? How can you hege that? Thanks!

@PerfilievFinancialTraining 2 года назад

Hi Alejandro, in this simple model, the up and down movements are chosen at the start - that's just something you decide. When pricing real options, you can choose the up/down sizes depending on the stock's volatility. Thank you for watching the video!

@Potencyfunction Месяц назад

@alejandrogaliana It happened that a stupid is talking. Go study low and high conjuncture on the Trend first. After you have understood the TREND come back here and have a normal question not a question for mental delayed persons.

@MontyCantsin Год назад

In an efficient market, shouldn't the stock price be equal to its expected value, in which case the option can also be priced according to its expected value?

@miquelmalaga 2 года назад

I knew you were trying to sell something through RU-vid!

@PerfilievFinancialTraining 2 года назад

Hahaha, options? :)

@miquelmalaga 2 года назад

@@PerfilievFinancialTraining just remember give me the same price you gave to your other client

@Potencyfunction Месяц назад

@@PerfilievFinancialTraining Go find your probability for future .

@rishabhaggarwal466 2 года назад

Hey made videos on analysing investment also

@PerfilievFinancialTraining 2 года назад

Hi, thank you for your suggestion! :) Will try to do my best!

@seiv16 2 года назад

Please make a video explaining the basics of options

@PerfilievFinancialTraining 2 года назад

Hi Hector, thank you for watching this video! I do plan to make an options intro video, however, not really sure when yet...

@seiv16 2 года назад

@@PerfilievFinancialTraining broo thanks for answer. I just downloaded options trading for dummies

@Terminator_420 Год назад

Can you show the calculation where risk-free interest rate is non-zero?

@Potencyfunction Месяц назад

Try to mix now all the formulas . go find beta market that is another formula CAPM.

@whaliensabr 8 месяцев назад

Bro what in the omegaverse🤣🤣 I never thought about it

@luisvalle8293 Год назад

crack. thanks.

@MorganBrown 2 года назад

Time for some new markers 😂

@PerfilievFinancialTraining 2 года назад

Hahaha, definitely! :D And that's even after I corrected some colours in the editor to make them more visible!

@MorganBrown 2 года назад

@@PerfilievFinancialTraining I was watching on an iPad, so maybe it looks better on a desktop

@gabrielparreno10 2 года назад

Delta =0.25. Why you put In the ecuation P= -1+102 delta = 24.5?

@cesartonelli6943 2 года назад

El valor del portfolio en el nodo up: -1 el precio de la opción shorteada en t=0, la devolvemos, mas el valor de las delta stock que compramos en t=0, 102 x delta debe ser igual a 98x delta que es el valor del portafolio en el caso down. Avisa si lo necesitas en inglés.

@PerfilievFinancialTraining 2 года назад

Hi Gabriel, yes, as @César Tonelli explained, if we have a value for a delta, we can plug it into our portfolio equation and solve for P. This will give us our portfolio value at T+1, which should be the same at T.

@PerfilievFinancialTraining 2 года назад

@@cesartonelli6943 Thank you for your explanations!

@gibsonmweene8898 Месяц назад

The writings are not clear use a more darker tip

@Potencyfunction Месяц назад

0,25 ! What is that? Stochastic variable x eller y. If you throw one coin , one function have 2 : discrete and continuos. If you throw to dices can make 2 stochastic varaible and that measure the eyes " the sum in dices" If we throw "5" and "2" the sum will be 7. So x=(5,2) and y=(1,6) . the fucking sum can not be lower than 2 and greater than 12 according to the dice model. If y shall be 3 , there are 2 probabilities (1,2) (2,1) P( y=3)= 2/36 ; Why do you talk stochastic variable at the basic level on such a complicate mode and what is it they do not get there ?

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