Binomial Options Pricing Model Explained

[@PerfilievFinancialTraining]

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

[@harshvardhanranvirsingh9473]

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]

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! :)

[@riccardoformenti4332]

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

[@PerfilievFinancialTraining]

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

[@jonnyx850]

And here is a second question: The result shows that the option price at t=0 is independent of the probability p. That is, whether p=0.0001 or 0.9999, you assert that the option price is still 50 cents at t=0, right? But now let's assume that p=1. That is, our model asserts with certainty that the stock price will move to $102. In that case, and with an interest rate of 0%, the option would clearly be worth $1 since I'm assured a payout of $1 at expiry if p=1. So your model asserts that the option price is 50 cents from p=0.000001 to p=0.9999999, but then the option price discontinuously jumps to $1 as p converges to 1? The discontinuity implied here seems to be fatal flaw for the model. Can you defend against that argument?

[@jonnyx850]

I have a question: You mentioned that companies calculate the probability p using statistics and data analysis, etc, but you also mentioned that they play no role in the calculation of the option price. If the transition probabilities don't affect the derivative price at all, then why would companies bother calculating p? Also, assuming a company does bother with calculating p, and assuming they have SOME amount of faith in that calculation (otherwise, again, why would they calculate it?), why wouldn't the company use that extra information when deciding how much they really need to hedge? As an extreme example, if a company calculated p=90% that the stock would go down and they had faith in it, then it seems like they would find it less necessary to hedge the full amount. Instead of buying 0.25 shares as a hedge, it seems like they might only buy 0.2 or 0.15 shares or even less if they were fairly certain the stock price would drop.

[@ratonxiify]

Amazing video!!!

[@PerfilievFinancialTraining]

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

[@JoseThomas-bq3bn]

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?

[@chamanthawickramarathne2029]

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

[@alilawati87]

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

[@christopherrose5554]

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

[@PerfilievFinancialTraining]

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

[@sbrown103]

Really enjoyed this. Thanks!

[@PerfilievFinancialTraining]

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

[@jongxina3595]

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

[@rishabhaggarwal466]

Hey made videos on analysing investment also

[@PerfilievFinancialTraining]

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

[@ramanujraychoudhury4398]

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]

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

[@NishantMehtamehtanishant6197]

Really good quality content...

[@PerfilievFinancialTraining]

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

[@NishantMehtamehtanishant6197]

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

[@PerfilievFinancialTraining]

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

[@annieyang4420]

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]

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

[@FredBuys2005]

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

[@PerfilievFinancialTraining]

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!

[@luismarialacomaaller2646]

Very good explanation and very instructive

[@PerfilievFinancialTraining]

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

[@Seed-qj6jk]

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

[@PerfilievFinancialTraining]

Thank you! Will do my best :)

[@Leshic2]

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...)

[@arusrhythm440]

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?

[@MrIamprasadbabu]

In this Video, we've considered the stock price will reach to 102 on the upside and 98 on the downside. But, how far is that realistic in real life? And who would give us these limits 102 / 98? Another thing I would like to mention is that, I'm writing this from India, so if you can add anything (if u know) relevant to Indian context, please do share.

[@kenmayer9334]

Great video. Straight to the point. Thank you.

[@PerfilievFinancialTraining]

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

[@miquelmalaga]

I knew you were trying to sell something through KZbin!

[@PerfilievFinancialTraining]

Hahaha, options? :)

[@miquelmalaga]

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

[@Potencyfunction]

@@PerfilievFinancialTraining Go find your probability for future .

[@mariamanos5461]

If you sell a call option to someone to buy a $100 stock at strike price of $101 in a market that has 99% probabilities to drop for $0,50 for sure youre going to make aloooot of money!

[@angeldiazgarcia7145]

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

[@PerfilievFinancialTraining]

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

[@JoseThomas-bq3bn]

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.

[@alexanderlapanowski3866]

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]

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]

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?

[@giovanniberardi4134]

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]

Thank you for sharing this!

[@Potencyfunction]

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.

[@nikolaykogut7546]

Thanks Sergei... I really liked the video

[@PerfilievFinancialTraining]

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

[@vishnukallingal7611]

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

[@kevw5473]

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

[@super9_55]

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

[@PerfilievFinancialTraining]

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

[@dam-ib9fs]

xD loved the skit entertaining & informational vid, ty

[@hellodre]

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]

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

[@hellotrading3245]

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

[@marysmith3710]

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

[@whaliensabr]

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

[@alejandrogaliana]

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]

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]

@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.

[@lulu-nz4dz]

so interesting！👍 enlightening and entertaining👍

[@bigal5413]

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]

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

[@Juoa794]

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]

@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.

[@gibsonmweene8898]

The writings are not clear use a more darker tip

[@sameerbhattarai2328]

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?

[@vaibhavchauhan7915]

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

[@Potencyfunction]

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 ?

[@dinkysniff]

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]

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]

Thank You soo much !

[@dinkysniff]

@@hamzamohammed3992 glad it helped!

[@Terminator_420]

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

[@Potencyfunction]

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

[@beelineunitel]

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.

[@packtradegroupveterans]

Wow just wow man

[@Revelcember]

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😁

[@hectordsd]

Please make a video explaining the basics of options

[@PerfilievFinancialTraining]

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

[@hectordsd]

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

[@AhmadAli-uu3tr]

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

[@sakshisoni396]

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?

[@tiago_holanda]

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

[@mihirbpi]

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?

[@enfantrouge666]

Thanks for sharing, now I can understand the model

[@PerfilievFinancialTraining]

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

[@dianaluna2263]

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

[@PerfilievFinancialTraining]

Thank you! Appreciate it.

[@MontyCantsin]

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?

[@anrm6]

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?

[@ramkhurana9590]

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

[@Gurugaming440]

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

[@tanchienhao]

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

[@Natasha-ky3uj]

Awesome! Thank you

[@PerfilievFinancialTraining]

Thank you for watching!

[@Aripb88]

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?

[@raulzevallos3399]

What happened with this magnificus channel, best ever

[@luisvalle8293]

crack. thanks.

[@fernandadelaflor2594]

Te amo demasiado

[@faithonchoke4430]

amazing video.thankyou

[@AbdulRaheemAziz7087]

good😀😀

[@alaataktokani8884]

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

[@Inbirman]

thank you, you explained it very clearly!

[@evdoxiapikouni545]

YOU ARE AMAZING. THANKS 🎁🎁🎁

[@marcogelsomini7655]

12:48 nice point!

[@TheKgpatriot]

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

[@nicolumps8362]

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

[@wenwendong4163]

Thank you great work

[@21sNeeo]

thanks you so much sir. really clear.

[@joaoviniciusalvesprado7423]

Thanks from Brazil, bro!

[@mohdharis4471]

how do you determine the number of steps?

[@armandomadero2930]

Sooo goood ! Thank you.

[@anshjain3169]

too helpful. also, love the enthusiasm.

[@melisaesgici2254]

Great video!!!! Thank you

[@chickensoup4479]

great videos bro keep going bros

[@Joey-pn8qp]

Best explanation I've seen on this topic!

[@MorganBrown]

Time for some new markers 😂

[@PerfilievFinancialTraining]

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

[@MorganBrown]

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

[@rudrapratapmahida1957]

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

[@PerfilievFinancialTraining]

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

[@pinaki_ghosh]

that call was amazing

[@user-wt8dt8zv1c]

Gosh thank you!!

[@wilsonhenriquezmora9017]

Thank you mate

[@ctoxyz]

love it! #mustsee

[@jcbprod]

The best teacher ever seen.

[@gabrielparreno10]

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

[@cesartonelli6943]

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]

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]

@@cesartonelli6943 Thank you for your explanations!