I searched a long time for someone who could properly explain d1 and d2 and where all the variables comes from. This was the perfect explanation, I understand everything now! Thank you!
hi, I actually work on CEO delta vega" option price sensitivity " using BS model, in BS model we have some input arguments,i-e stock price, exercise price, the maturity or expiration date, risk-free rate, and return volatility. my question is if an option grant in the year 2011 and exercise till 2014, which means that typical option has 3 years' time maturity . in estimation which year value of "risk-free rate, and return volatility, dividend yield " should be taken to get the result ?? looking forward to your response...
viewers beware there are two terrible errors within this video. First, the mean is NOT r-sigma^2/2 but rather (r-sigma^2/2)t. Second, the video does not explain how volatility is annualized and thus in order to de-annualize the equation you have to divide by root time. This is why the equation seen at 11:53 is not the same as the real one. Please like this comment so others can see it.
Well in some ways u r RIGHT, but I wouldn't say those are terrible errors. When I notice the differences between this video and my textbook, I found out that in this video, factors like "r" or "sigma" are "real factors" while in questions they tend to be like "annual RF+150days". Always remember to pre-process them into "real, usable" factors, like a discount factor(e^(-r*T))(T=150/365).
Thank you so much!! This is definitely the best video I've ever watched about explaining the black-scholes formula and the problem that has confused me for 2 years has finally became clear!!!
Where does the (T-t) multiplied on the (r - 0.5*sigma^2) and the denominator (square root(T-t)) come in for d2? It's in the formula at the beginning but not the derived d2?
This was the best explanation of N(d2) I have encountered to date. However, the absence of a similar video on N(d1) makes the experience as a whole feel somewhat unfulfilling. If you could fill this void, it would be greatly appreciated by many who are looking for a deeper understanding of this difficult and complex topic. Thank you.
I'm having the same problem. N(d1) is also the delta of C with respect to S; but I still don't understand it intuitively even after watching many other videos. Why does S * dC/dS give the payout, from which you can then subtract N(d2)?
This is not what the central limit theorem says. The central limit theorem says if you look at enough values of a MEAN, the MEAN will follow a normal distribution. There's no reason why the daily return should follow a normal distribution.
Furthermore the normal distribution portion simply comes from the solution of the black-scholes equation (which is really just a 1D diffusion equation from physics, the solution of which is a gaussian or normal CDF)
I suppose, could you not, take samples from amongst the previous year's daily returns...for example..fifty-two 7 day periods (I know, don't include weekends, holidays, etc), take the mean of each of those, plot them, and get a normal distribution?
@@yoyomcg It's misleading to say B-S eq comes from diffusion/brownian motion as if all diffusion involves a normally distributed random walk. But otherwise good comment
@@ecpgieicg No, I meant taking maybe say a rolling 5 days of daily returns (eg. 0.5%, -0.2%, 1.0%, -0.4%, 0.3%) and taking the mean, then moving forward to the next day, taking the next rolling 5 days, and so on. We wouldn't have just 7 data points in this case, we'd have somewhere over 45 or so I think if we're talking about a year's worth of "weekly" average returns.
The formula explained at the end of video from time 10:15 onwards is wrong... The presenter forgets to use the expiration time in the formula and also forgets to multiply sigma with under root of T-t.. Reliability of the video is not sure...
It is not correct, The reason he did not include time factor because he has taken time to be 1 year, so it doesn't matter if you include 1 in the formula or not!
11:09 you wrote an extra negative sign in the equation but it disappeared in the next slide so it didn't make your final answer wrong, but just want to point it out for everyone.
I’m sorry but that is not at all simply explained. Consider the audience (peeps) who don’t understand, and explain it to them in terms they’d understand. That is quite easily done - make it relatable.
When pricing a stock option, “today’s” stock price must discount the present value of all expected future dividends too, as any dividends payed directly reduces the value of the stock.
if you discount the free cash flow to the firm and then subtract the debt obligations plus interest, you do not have to do such a complicated thing because basically stock is price is a present value of free cash flow that is "dividend-able."
which is why using the prepaid forward price of the stock is the appropriate generalized way to do it, for discrete dividends this would mean subtracting the pv of the dividends, dividends can also be deal with using a continuous dividend model, where dividends are assumed to be paid out constantly and continuously, ancd thus FpS= S0e^-delta(T-t)
You do know that Charlie Munger and Warren Buffett have said that no serious trader would use Black-Scholes, don't you? You might want to listen to their explanation of why.
Hello sir.... good afternoon....had go through your entire video but....I couldn't getting your video related Norma distribution curve video to help understand for black n scholes model.... it could could very helpful to us .....if provide link....here.....thank you 🙏🙏
Can you please explain why K (the strike price) is being multiplied by N(d2)?That is, why is there a need to multiply the strike price by the probability that the stock price will be at or above the strike price at expiry ? The strike price is already known and will remain fixed until expiry, so why are we multiplying it by a probability?
can knowing this stuff make one wealthy as an independent investor? this stuff seems like it holds the secrets to investing...or at least knowing how to invest better.
+EvaSlash The people behind Black - Scholes formulas have thought of the same thing, and so they were profitable during the first 3 years until the black swan event, their Long Term Capital Management company went bankrupt owing billions of dollars, sadly academic people were usually terrible traders.
Thanks for the explanation, very clearly explained what n(d2) is. However, I am still figuring out the rest of the equation. For example, why do we multiple n(d2) by -ke^-rt? What is the relationship of n(d2) with the present value of k? And Also the first half of the equation of Sn(d1) was left unexplained. So the title was a bit misleading. But thank you very much for explaining what n(d2) is.
Thanks for the video. It was very instructive. A question about the price model: At 4:30 you talk about how volatility erodes the rate of price change, but why variance? since variance has units of sigma^2 and the random component units of sigma*sqrt(t) and the rate of change 1/t . In physical models usually those units are the same, if not non-dimensional. thanks in advance!
Great video, after watching this a conversation between Albert Einstein and Charles Chaplin came to my mind, it goes something like this: -C: Everyboy admires you despite no one being able to understand you. I really enjoyed your videos despite feeling a bit dumb during some parts, looking forward to explore the rest of your videos.
Is the volatility used in black scholes model formula historical volatility or implied volatility ? On google it’s very confusing to understand this formula as everyone shows different meaning. Can anyone explain ?
One of the best explanations for N(d2). Wow, thats amazing understanding and interesting link to Z score. Thanks for sharing the insights and keep up the work.
So if my exam question will come up with a question : Explain how Black schole model is used to value option price . How the fuck can i write this under under around 1000 words , 2 hours exam 2 questions and multiple part
You define “N(d2)” as “The probability that the stock price will be at or above the strike price when the option expires.” The options Delta is also defined as the probability that the option expires ITM (in the money); which, as far as I can tell, is the same thing. With that said, after doing some additional research N(d1) is equal to the delta for a European Call option meaning the definition for N(d1) must be the same as your definition for N(d2). However, they are not the same mathematically, so I think your definition for N(d2) is wrong, or I’m not understanding the difference between your definition for N(d2) and the options delta.
If anyone ends up reading this, after some additional searching, it appears that delta is not exactly the probability of the option expiring at or in the money. This is widely stated because it’s generally a good rule of thumb; however, the math doesn’t hold up. The definition given in the video for N(d2) is correct. And the formula for a European Call Options’ delta = N(d1).
¿N(d2) no es la probabilidad de que el rendimiento se encuentre d2 desviaciones típicas por debajo del rendimiento medio? ¿Por qué hablar de precios cuando en la fórmula hay rendimientos?
Volatility understand. But even more important why is putting the risk back in means putting volatility in? I mean, I am absolutly not into this (chemical engineer) but volatility means for me the price is going up and down but with the expected value of 0 whereas a risk (e.g. my office burns down, I am fucking my customers wife and he finds out) has an expected value below 0... This confuses me. Can sb help?
So if my exam question will come up with a question : Explain how Black schole model is used to value option price . How the fuck can i write this under under around 1000 words , 2 hours exam 2 questions and multiple part. give advice pls senpai
I dont understand this , is it normal @@ . So if my exam question will come up with a question : Explain how Black schole model is used to value option price . How the fuck can i write this under under around 1000 words , 2 hours exam 2 questions and multiple part
hi, I actually work on CEO delta vega" option price sensitivity " using BS model, in BS model we have some input arguments,i-e stock price, exercise price, the maturity or expiration date, risk-free rate, and return volatility. my question is if an option grant in the year 2011 and exercise till 2014, which means that typical option has 3 years' time maturity . in estimation which year value of "risk-free rate, and return volatility, dividend yield " should be taken to get the result ?? looking forward to your response...
I searched a long time for someone who could properly explain d1 and d2 and where all the variables comes from. This was the perfect explanation, I understand everything now! Thank you!
hi, I actually work on CEO delta vega" option price sensitivity " using BS model, in BS model we have some input arguments,i-e stock price, exercise price, the maturity or expiration date, risk-free rate, and return volatility. my question is if an option grant in the year 2011 and exercise till 2014, which means that typical option has 3 years' time maturity . in estimation which year value of "risk-free rate, and return volatility, dividend yield " should be taken to get the result ??
looking forward to your response...
@@omersahil339 shouldn't be the same as other variables? Higher interest rate -> lower premium
thank you for coming to my aid. I now understand the Black and Scholes pricing model better than before.
Excellent explanation. Sincerely i felt lucky to encounter with this video
viewers beware there are two terrible errors within this video. First, the mean is NOT r-sigma^2/2 but rather (r-sigma^2/2)t. Second, the video does not explain how volatility is annualized and thus in order to de-annualize the equation you have to divide by root time. This is why the equation seen at 11:53 is not the same as the real one. Please like this comment so others can see it.
Is it still worth watching? I don't want to corrupt my knowledge
Well in some ways u r RIGHT, but I wouldn't say those are terrible errors. When I notice the differences between this video and my textbook, I found out that in this video, factors like "r" or "sigma" are "real factors" while in questions they tend to be like "annual RF+150days". Always remember to pre-process them into "real, usable" factors, like a discount factor(e^(-r*T))(T=150/365).
Thank you so much!! This is definitely the best video I've ever watched about explaining the black-scholes formula and the problem that has confused me for 2 years has finally became clear!!!
Thank you for making this formula easier to be imagined
Where does the (T-t) multiplied on the (r - 0.5*sigma^2) and the denominator (square root(T-t)) come in for d2? It's in the formula at the beginning but not the derived d2?
My question is solved perfectly. Thank you!
This was the best explanation of N(d2) I have encountered to date. However, the absence of a similar video on N(d1) makes the experience as a whole feel somewhat unfulfilling. If you could fill this void, it would be greatly appreciated by many who are looking for a deeper understanding of this difficult and complex topic. Thank you.
I'm having the same problem. N(d1) is also the delta of C with respect to S; but I still don't understand it intuitively even after watching many other videos. Why does S * dC/dS give the payout, from which you can then subtract N(d2)?
Excellent explanation and will use a similar explanation in my mathematic's investigation.
there was nothing simple about this video
That's about as simple as it's going to get.
This is beautiful, thank you so much for the uploads!!
Best Explanation I have ever read... very simple.. intuitively appealing... Thank you very much...
Thanks a lot for making this video. Excellent explanation. Could you please do a similar video explaining the derivation of N(d1) mathematically
Wow such an amazing explaination. Helping me get through my Actuarial Mathematics degree ! Keep up the good work
As simple as you can make it. There is really nothing simple bout Black-Scholes.
This is not what the central limit theorem says. The central limit theorem says if you look at enough values of a MEAN, the MEAN will follow a normal distribution. There's no reason why the daily return should follow a normal distribution.
Furthermore the normal distribution portion simply comes from the solution of the black-scholes equation (which is really just a 1D diffusion equation from physics, the solution of which is a gaussian or normal CDF)
I suppose, could you not, take samples from amongst the previous year's daily returns...for example..fifty-two 7 day periods (I know, don't include weekends, holidays, etc), take the mean of each of those, plot them, and get a normal distribution?
@@yoyomcg It's misleading to say B-S eq comes from diffusion/brownian motion as if all diffusion involves a normally distributed random walk. But otherwise good comment
@@Geotubest No. If you mean to average just 7 data points, you are far from enough to a result near convergence for most realistic scenarios.
@@ecpgieicg No, I meant taking maybe say a rolling 5 days of daily returns (eg. 0.5%, -0.2%, 1.0%, -0.4%, 0.3%) and taking the mean, then moving forward to the next day, taking the next rolling 5 days, and so on. We wouldn't have just 7 data points in this case, we'd have somewhere over 45 or so I think if we're talking about a year's worth of "weekly" average returns.
Phenomenal Explanation
I didn't get this. I want to learn all of this, where can I start?
Dude, you smashed it with this explanation. I have looked far and wide for a source of understanding on this topic but today my search ends. Thank you
You saved my life
Great vidio, helps understand the formula for people with economics background.
Janna K *video
The formula explained at the end of video from time 10:15 onwards is wrong... The presenter forgets to use the expiration time in the formula and also forgets to multiply sigma with under root of T-t.. Reliability of the video is not sure...
It is not correct, The reason he did not include time factor because he has taken time to be 1 year, so it doesn't matter if you include 1 in the formula or not!
+Manik singh is it because most options expire in less than one year?
11:09 you wrote an extra negative sign in the equation but it disappeared in the next slide so it didn't make your final answer wrong, but just want to point it out for everyone.
Best introduction to Black Scholes ever
How do you compute daily returns? Doesn't that require having access to all transactions ever made on a stock?
Perhaps the best explanation of N(D1) and N(D2) ever watched by me
Great explanation of N(d2). Desperate to find an equally in depth explanation of N(d1) but still looking.
Me too. Please share the link if you found one
Fijate el paper de Cox y Rubinstain. Es la misma lógica, pero la media en ese caso es ln r + 1/2 varianza, en vez de ln r - 1/2 varianza.
that was amazing!
I’m sorry but that is not at all simply explained. Consider the audience (peeps) who don’t understand, and explain it to them in terms they’d understand. That is quite easily done - make it relatable.
Beautiful explanation
When pricing a stock option, “today’s” stock price must discount the present value of all expected future dividends too, as any dividends payed directly reduces the value of the stock.
if you discount the free cash flow to the firm and then subtract the debt obligations plus interest, you do not have to do such a complicated thing because basically stock is price is a present value of free cash flow that is "dividend-able."
which is why using the prepaid forward price of the stock is the appropriate generalized way to do it, for discrete dividends this would mean subtracting the pv of the dividends, dividends can also be deal with using a continuous dividend model, where dividends are assumed to be paid out constantly and continuously, ancd thus FpS= S0e^-delta(T-t)
You do know that Charlie Munger and Warren Buffett have said that no serious trader would use Black-Scholes, don't you? You might want to listen to their explanation of why.
Spectacular. Thank you for this.
math is wrong, d2 lacks the square root time in denominator and the time component in the mean. Make another video or delete this one
Thank you so much sire!
That was the best explanation I could get.
Can you please give a video on Deriving N(D1) as well?
Hello sir.... good afternoon....had go through your entire video but....I couldn't getting your video related Norma distribution curve video to help understand for black n scholes model.... it could could very helpful to us .....if provide link....here.....thank you 🙏🙏
Can you please explain why K (the strike price) is being multiplied by N(d2)?That is, why is there a need to multiply the strike price by the probability that the stock price will be at or above the strike price at expiry ? The strike price is already known and will remain fixed until expiry, so why are we multiplying it by a probability?
can knowing this stuff make one wealthy as an independent investor? this stuff seems like it holds the secrets to investing...or at least knowing how to invest better.
+EvaSlash The people behind Black - Scholes formulas have thought of the same thing, and so they were profitable during the first 3 years until the black swan event, their Long Term Capital Management company went bankrupt owing billions of dollars, sadly academic people were usually terrible traders.
no
concise! wish to see some N(d1) breakdown soon
Es la misma lógica pero en ese caso la media es igual a ln r + la varianza/2, en vez de ser ln - varianza/2.
i have a question, if normal function is symmetrical then nd1 and nd2 should be same right... but they comes out to be different
3:23 Geometric Brownian motion*
Thanks for the explanation, very clearly explained what n(d2) is. However, I am still figuring out the rest of the equation. For example, why do we multiple n(d2) by -ke^-rt? What is the relationship of n(d2) with the present value of k? And Also the first half of the equation of Sn(d1) was left unexplained. So the title was a bit misleading. But thank you very much for explaining what n(d2) is.
great explanation
This video needs to be renamed "Black Scholes: As Simple An Explanation As Your Going to Get"
Thanks for the video. It was very instructive. A question about the price model: At 4:30 you talk about how volatility erodes the rate of price change, but why variance? since variance has units of sigma^2 and the random component units of sigma*sqrt(t) and the rate of change 1/t . In physical models usually those units are the same, if not non-dimensional. thanks in advance!
excellent explanation
Best! Brilliant and excellent work! Thanks!!!
Great video, after watching this a conversation between Albert Einstein and Charles Chaplin came to my mind, it goes something like this:
-C: Everyboy admires you despite no one being able to understand you.
I really enjoyed your videos despite feeling a bit dumb during some parts, looking forward to explore the rest of your videos.
Best video on this that can be found on the internet (at least in 2020).
This actually helped
This is the best explanation on youtube. Thank you!
N(z)=1-N(-z) ?
that is why i believe in probabilitys nothing less than 80% chance of success.
Awesome
*yawn* ... I really want to learn all of this, but it's just soooo boring!
Is the volatility used in black scholes model formula historical volatility or implied volatility ?
On google it’s very confusing to understand this formula as everyone shows different meaning.
Can anyone explain ?
IV
The best explanation I ever found! Thank you
This is way better than the MIT video on the same subject
Most logical and clear explanation of BSM model. Thank you for such a great work!
Great explanation that makes complex things simple!
This is a fantastic explanation: clear and also insightful.
One of the best explanations for N(d2). Wow, thats amazing understanding and interesting link to Z score. Thanks for sharing the insights and keep up the work.
Very helpful! Just for fun, could a kernel density of the periodic daily rate of return be used in place of the standard normal?
Amazing, very easy to understand
Thanks
lol this is easy, thanks for explaining it so well!
So if my exam question will come up with a question : Explain how Black schole model is used to value option price . How the fuck can i write this under under around 1000 words , 2 hours exam 2 questions and multiple part
this video is pure gold
You define “N(d2)” as “The probability that the stock price will be at or above the strike price when the option expires.” The options Delta is also defined as the probability that the option expires ITM (in the money); which, as far as I can tell, is the same thing.
With that said, after doing some additional research N(d1) is equal to the delta for a European Call option meaning the definition for N(d1) must be the same as your definition for N(d2). However, they are not the same mathematically, so I think your definition for N(d2) is wrong, or I’m not understanding the difference between your definition for N(d2) and the options delta.
If anyone ends up reading this, after some additional searching, it appears that delta is not exactly the probability of the option expiring at or in the money. This is widely stated because it’s generally a good rule of thumb; however, the math doesn’t hold up. The definition given in the video for N(d2) is correct. And the formula for a European Call Options’ delta = N(d1).
¿N(d2) no es la probabilidad de que el rendimiento se encuentre d2 desviaciones típicas por debajo del rendimiento medio? ¿Por qué hablar de precios cuando en la fórmula hay rendimientos?
WOW. nice explanation. finally I got it. thanks
This is actually the BEST explanation ever.
Brilliantly explained. Thank you so much.
i think you accidentally made d1 equation to d2
What stands sigma at 3:28 for=
Volatility understand.
But even more important why is putting the risk back in means putting volatility in?
I mean, I am absolutly not into this (chemical engineer) but volatility means for me the price is going up and down but with the expected value of 0 whereas a risk (e.g. my office burns down, I am fucking my customers wife and he finds out) has an expected value below 0...
This confuses me. Can sb help?
Bravo!
it is good to understand for beginner
Thank you!
Thank you , clear explanation !
why do we use -z score actually we are interested for z?
puts
Very easy
wealth bless you
Thanks
Fantastic explanation!
ขอบคุณค่ะ thx u :)
This is great!
why we use r - (sigma^2)/2 as drift?
you use it to caculate the mean vairance distribution, inside the exponent function
Beautiful! Thanks alot. Finally explained!
So if my exam question will come up with a question : Explain how Black
schole model is used to value option price . How the fuck can i write
this under under around 1000 words , 2 hours exam 2 questions and
multiple part. give advice pls senpai
I dont understand this , is it normal @@ . So if my exam question will come up with a question : Explain how Black schole model is used to value option price . How the fuck can i write this under under around 1000 words , 2 hours exam 2 questions and
multiple part
Not to worry,you'll do just fine.
Thank you so much! That awful!
Great
hi, I actually work on CEO delta vega" option price sensitivity " using BS model, in BS model we have some input arguments,i-e stock price, exercise price, the maturity or expiration date, risk-free rate, and return volatility. my question is if an option grant in the year 2011 and exercise till 2014, which means that typical option has 3 years' time maturity . in estimation which year value of "risk-free rate, and return volatility, dividend yield " should be taken to get the result ??
looking forward to your response...
there is nothing simple about this video
Thanks for the explanation! You get a like AND a subscribe!