FRM: How d2 in Black-Scholes becomes PD in Merton model
Вставка
- Опубліковано 7 сер 2024
- In Black-Scholes, N(d2) is the probability that the option will be struck in the risk-neutral world. The Merton model for credit risk uses the Black-Scholes by treating equity as a call option on firm assets. In Merton, d2 becomes the "distance to default" and N(-d2) becomes the probability of default (PD). For more financial risk videos, visit our website! www.bionicturtle.com
It's the first time I'm seeing the normal bell curve on a line. Intuitively, it makes a lot of sense. Life just got more clear for me. Thanks
You're a god - I was listening 3 hours to my professor talking about this subject, listening to you, the same effect was reached within 10 minutes. Thanks!
wow...what a clear explanation.. Mr.Harper, you are awesome.
I am learning finance on my own; have watched Paul Wilmott's lectures in you tube, Horward lectures.. but nothing is as clear, concise and understandable as your short 10 min videos.. thanks a lot
Really nice explanation, all clear after the 10 minutes! - Thanks so much!
Thank you for watching! We are very happy to hear that our video was so helpful.
Excellent explanation - thank you.
Omg! this makes so much sense, thank you so much for keeping it straightfoward and simple to understand:))))
to medici 101: for an explanation of d1 learn how to find delta.
I am so impressed by this video. You managed to make intuitively understandable in 10 minutes a concept I didn't grasp through my whole time at b-school. Thanks!
This was an incredible video, thank you so much
thanks! Very Usefull!
i wish i can find a video explaining d1 as well ... this video was really good ... cheers
7:00
Why did we need to add a negative sign to d2 despite that we are looking at the right side of the bell curve?
keep up the good work ! Thank you for sharing :)
You're welcome! Thank you for watching! :)
@KoalaBearWarrior Like Black Scholes, the rates are all expressed in continuous frequency. At T0, LN(130/100) ~ 26%. At T1, LN(134/100) ~= 29.2. To use 0.74*130, is to use discrete: 134/100 - 1 = 34%. FWIW, they reconcile with R(c) = k*LN(1+R(k)/k). In this case, case R(c) = 1*LN(1 + 34%) = 29.2%
Best explanation so far! thank you :D
Hello sir, thanks a lot for this video. Really helpful. Can you please briefly write here how the volatility is factored in the form of GEOMETRIC MEAN? I am really curious to understand.
omg i just read the written version of this lol!! can't believe ur the same guy! THNK YOU SO MUCH
+Kuan-In Liao You're welcome! We are glad that our video was helpful!
+Bionic Turtle Please sir! help me with this! i don't know how to solve for the σV...
"Consider a company whose equity is 3 million euros. The volatility of equity is 0.80. The company’s debt is equal to 10 million euros and it must be paid in one year. The risk-free rate on the market is 5%
per annum."
Question 1: What are the values of Vo and σV?
Question 2: What is the probability of default of the company in one year?
I failed to find anywhere else apart from this video that risk free rate in BS model corresponds to the expected return in Merton model. Each paper I have encountered used the risk-free rate, not the asset growth (mu)
Can someone please clear this out for me
Thanks in advance
It looks like an ancient bow and arrow, which is also cool.
Is it should be d1? I saw in some formula, the second term in the numerator is u+sigma^2/2)*T, why? Thanks
I was thinking about the relationship between time and distance to default. It looks like the bigger the maturity, the bigger the distance to default (ceteris paribus). Does it make sense to assume that? However, this works only if the second term in the numerator is positive, so the price grows more than half of the variance.
Am I correct?
awesome thank you
Hi there, how do you get the PD figure by using a calculator, not excel. What would N be . For example, on the calculator I would put in ?*(-1.462) = 7.19%. How do you know what the '?' figure would be
Thanks
How would the formula works while adding dividend yield into it?
I am seeing this in 2020. Still useful
how would you predict the 5%? is there a matrix or external research that can predict the 5% based on industry types?
Hi David! Thanks for a great video. Can you tell me where I can find the explanation on how to determine the Firm Value, Volatility and the Expected Return?
www.bionicturtle.com/forum/threads/merton-model-a-summary-of-the-issues.5646/
I've always thought Peter Crosbie did a good job summarizing the calculations to which refer, here is copy of Modeling Default Risk by Crosbie (the KMV method is the same as Merton until the DD is retrieved, it varies after that): trtl.bz/2O9aECG
aWESOME PRESENTAION..THANKSS
at 4:00 you say the firm would have to drop by 26% before default. 0.74*130 = < 100 though, so I don't see why it should not bee a lot less than 26%
and really irritated with a few comments over here..guys..we are getting such valuable education in youtube for free (thanks Mr.Harper).. we cannot be complaining
Mr.Harper's videos are supplements; we should not expect him to teach everything over here.
is d2 the distance to default?
Hi Dominic, yes that is exactly correct! d2 is the distance to default. FWIW, it is the DD in returns(%) format and standardized (per the denominator) into a standard normal units. So it's a "normal returns" DD. It can be translated back/forth to the lognormal DD which is dollar-based. Like the BSM, the log returns are normal such that the values are lognormal. Thanks!
Hi. How can I contact you?. I may have some questions. I work in credit risk management but I don't know shit about finance because I graduated in Mechanical engineering
Hi Dominic you can reach me via our support forum at www.bionicturtle.com/forum (and my contact information is there). My email is davidh@bionicturtle.com. Thanks,
GOOD
Thank you for watching!
The d2 formula in BS is the risk-free rate under the risk-neutral measure. I am wondering why you are using mu which is the expected rate of return? Is there some difference of risk neutral probability and real world probability that I am missing here?
you are missing the entire point of the video, which is to compare d2 in BSM with distance to default (DD) in Merton model. Mathematically, Rf is BSM is replaced with mu in DD; the former is risk-neutral but the latter is a actual (future) distribution so it uses mu. Shallow mathematical difference but nontrivial difference between risk-neutral and "physical" distribution.
@@bionicturtle Thank you for replying! The comparison was clear to me, but I was unsure why BSM uses risk free rate but DD uses expected return. The latter part of the reply answered it, thanks again!
What citizenship u r ? To what flag pledge allegiance?Get verified now for free before Trump make it mandatory and u having to pay fee.