How to interpret N(d1) and N(d2) in Black Scholes Merton (FRM T4-12)

[@rejtinger]

if probability of option being exercised increases, the value of that option decreases.. that does not sound right, does it...(?)

[@tristanbosnyak8632]

this helped me on my journey to calculate my fathers monthly hair loss

[@hernanalzate1582]

what a shame, the excel spreadsheet no longer exists!

[@speisequark2]

Is it ok to use a negative riskfree rate r in that model?

[@benpierce2202]

Which version of John Hull's book do you use for this example?

[@mitchellrosenthal6305]

Can you explain what the terms inside of "d1" actually mean? I believe d1 is a Z-score of some type.

[@riverallen1571]

I recommend actually watching the video if you want to know what d1 means.

[@ohad157]

I love it that you have a gamer's channel name

[@Alexander-pk1tu]

thank you sir! I liked your video very much.

[@shahbazh2530]

What is the sound of the cricket?

[@ammadurrahman5321]

awesome xplaination;;;;;

[@penspinner]

For the calculation of d1 and d2, does the So number in ln (So/k) change when dividend yield is introduced? In the GARP textbook it seems like it does not change for continuous dividend, but for discrete dividend they would replace So with (So - discounted discrete dividend).

[@bgvianyc]

When returns are not normally distributed could one simply replace the normal distribution with the alternative distribution or are additional changes required to the formula?

[@speisequark2]

Thank you so much! Your video helped me a lot!

[@riverallen1571]

Do you have any opinions on using delta as an approximation to probability of in the money?

[@Hamromerochannel]

This was by far the best explanation of d1 and d2. Thank you

[@annabellam.4983]

That uploaded excel sheet was super great!! Thanks a lot!

[@bionicturtle]

Thank you for watching! We are happy to hear that it was so helpful.

[@katienorris8341]

Thanks, this is a great explanation! Very helpful

[@etenat8772]

amazing explanation

[@bionicturtle]

Thank you for watching!

[@ttijp153]

Thank you so much professor! so helpful.

[@johnpalma7265]

Nice

[@hbahou]

if N(d1) is the option's delta, why don't we just refer to it as 'delta' in the BSM formula instead of confusing everybody?

[@bionicturtle]

Sometimes words alone are confusing, when you really want to understand something or are quantitatively inclined. As a normal CDF, it has familiar properties, some discussed; e.g., it is a probability function. But "delta" by itself, could be ambiguous. The put option's delta, for example, is N(d1) - 1. If the stock pays a dividend, then "delta" is N(d1)*exp(-qt). I realize some people just want easy words because, you know, math is hard, but under your approach, people are likely to confuse all "deltas" with N(d1), or if the stock pays a dividend, to forget the delta is N(d1)*exp(-qt). So your approach would be more confusing IMO.

[@mff812]

Very good effort Sir

[@victorlh7417]

In the formula of d1 and d2 the part of (r + sd^2/2) T, what does that measures?

[@sujan6146]

mean of the data

[@TrangHuyen-vj3ne]

what is dividend yield in black scholes used for? can i find dividend yield in financial report of company?

[@etenat8772]

you can calculate dividend yield yourself. it's dividend per share/price of stock. When dividends are paid out it reduces the stock price by that amount (assuming no frictions). this topic is about price appreciation so we need to consider how dividend payments restrict capital appreciation

[@tradegood]

you can easily get it by: (cash dividend/current stock price) -> 10$/25$ = 40% DY. Dividend is usually a part of the profit that the company shares with its shareholders (approved during shareholder meeting)

[@johnpalma7265]

Trang Huyen : Many of the Black Scholes videos don't include the dividend in the formula.The dividend sometimes denoted by (q) is included to get a more accurate result for d1 in cases where there is a dividend.

[@indradipbanerjee4013]

Should the stock be assumed to grow at the risk free rate or should the baseline be growth at cost of equity rate?

[@sigmamu6745]

Stock grows at drift rate. Mu. Look it up.

[@jiaminzhu406]

Great explanation. I'm still a bit confused with N(d1), when you say the underwater price is counted as zero. If I denote p1 = N(d1) and p2=N(d2), and forget assume q and r are both zero, is it true that Sp1 = (S-K)p2 + K ?

[@richardreid8016]

I believe N(d2) is the probability that the option will end in the money and N(d1) is how far in the money will it end up.

[@易哲源]

N(d1) is the conditional probability by assuming S>K and thus SN(d1) is the conditional expectation of S. Note that N(d1) would always bigger than N(d2) due to the conditional probabilities. Mathmatically, SN(d1) = E(S|S>K)*N(d2).

[@lawjef]

I know you de-emphasized it in the sheet (denoted by the light grey font) but the "d2" formula is technically incorrect. The part on the far right "d1 - sigma * sqrt(T)" is correct, but the formula to the left of it should be "[formula that is already there] - sigma * sqrt(T)"

[@bionicturtle]

Actually the d1 and d2 are CORRECT. σ*sqrt(T) = σ^2*T/[σ*sqrt(T)], is how the (+σ^2/2) switches to a (-σ^2/2). But thanks for the feedback.