19. Black-Scholes Formula, Risk-neutral Valuation
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- čas přidán 5. 01. 2015
- MIT 18.S096 Topics in Mathematics with Applications in Finance, Fall 2013
View the complete course: ocw.mit.edu/18-S096F13
Instructor: Vasily Strela
This is a lecture on risk-neutral pricing, featuring the Black-Scholes formula and risk-neutral valuation.
License: Creative Commons BY-NC-SA
More information at ocw.mit.edu/terms
More courses at ocw.mit.edu
Some notable Timestamps:
03:49 Risk Neutral Valuation: Introduction
11:02 Binomial Tree example & Replicating Portfolio
22:32 Black-Scholes equation
33:33 Black-Scholes: Risk Neutral Valuation
36:06 Concluding example
His presentation is actually very clear and I love the examples he has given. So I don't know why there are a lot of bad comments. Thank you MIT for sharing this.
I doubt that. I've just started and the 2-horse example is unclear. For example, the slide does not say how much guy gets if the second horse wins, only how much guy loses if the second horse loses.
If horse A wins in that example for the 4 to 1 payout the bookie must pay 10,000 + 4(1,000)=$50,000 => bookie profits $10k because he had $60k in bets total
horse B wins with the 4:1 payout he loses $2,500 because he has to pay the better with a $50k bet 50,000(1.25)=$62,500 so he loses $62,500-$60,000=$2,500
He kinda went through it fast but the logic is clear
@nelsonmorrow5657 Im confused wouldn't it be...If A wins 4*10k+10k -50k = 0 and If B wins 50K/4 -10k =2500?
Many years later, the historians will write: “ long time ago, humans were obsessed with the money system they created that so many brilliant minds wasted their life on.”
A very common problem in academic lecture videos, unfortunately, is that the camera is more often on the speaker and not on the material.
I would pause at the slides to digest them before moving on.
I'm late, but most of these videos have the lecture notes and slides at the website in the description. It has the syllabus and even the book they are teaching from as well.
22:28 Black-Scholes equation
Great lecture, thank you Vasily
i think he explained the concept very well with some .business insights. I am happy
This is also a very good presentation.
The phone he whipped out startled me
He switched the signals on the call put parity formula. Good class besides that
absolutely awesome at 1.75 replay speed, but not at examples
“If you put $1 into cambridge bank then in a year you get nothing be ause rates are basically zero” hahaha best comedy ever
5% implied on the forward...ah, the good old days!
Hah)
@38:20
Bonds… looking into bonds… AMC/BBBY.. just seems like the next logical addition
9:14, Is that graph right? Why would the blue line go below the pink?
Good point. The only way to get the blue line below the pink line is to have a EUROPEAN put (can't exercise) and insanely high interest rates such that your option is worth discounted parity.
4*10000 -5000 =-10000 50000*1/4 -1000 =2500
Why is this video short compare to other videos in this series? Also 43:06, the signs of the put-call parity equation needs to be adjusted.
c + Ke^-rt = p + S mate
29:49 Blacksholes eq
In Soviet Russia, underlying puts you!
And it does not CALL you, so no warning.
Hello
what a world we live in right now ... interest rate Nov 2022 ...
The short story is that not even the MIT can come up with good teachers for this stuff: those who know, don't tell, and those who tell, don't know.
Finally some kids brave enough to say that "the king is naked".
What are you talking about. He explained it perfectly. It's a simple formula to create a price based on market transactions to forever sell derivative products for no risk.
I thought he explained it fairly well bar a few details I need to rewatch and I'm not versed in this stuff. I think it helps to look at it from the p.o.v. of a broker needing to set prices for derivatives such that they (the broker) bears none of the risk of the underlying asset, rather than the p.o.v. of Joe Bloggs the punter looking to profit from a trade. In the base case, the broker makes their money from a fee so don't care how the the underlying asset performs; therefore this Black-Scholes analysis solves a big problem for them. The fees are just excluded from the calculations he shows for simplicity since they would add another small term in the equations to be manipulated.
Don't be so harsh on him. He is just a guest lecturer from Stanley, not an educator of any sort. Lower your bars please.
Not a basic course on BSF - с первого разy бы не поняла.
The beyonce-knowles equation has helped me earn dozens of dollars on the options playing feild!!
I couldn't find much about it on Google. Can you provide a link and/or brief summary?
Lol....
@Nick de windt😂😂😂😂😂😂😂
6:50 "call option can be viewed as insurance against price going down." A insurance against price going down is called PUT.
+Samson Tsui Call option can be seen as insurance against price drop compares to actually long the stock. With call option your loss would be limited.
rene f are you serious? How?
@@jivillain bear in mind that Put + long stock = Call. So if you are already long the stock and you are looking for an insurance against price drop... you have to buy a put indeed. But if you want to invest on a stock with the protection, you can directly buy the call since its equivalent to stock+put.
wish the camera would stay on the slides rather than following the lecturer for a good fraction of the time.
6.57: 'Call option can be viewed as an insurance against the asset going down'. BUT If the value goes down you would not exercise your option, since you would not be willing to buy it at a predetermined 'higher' price than what is now in the market. I believe the put option can be viewed as an insurance!
Call option is the insurance against the price going up, you want to buy the underlying at the cheaper price even if it moves way higher,
Put option is insurance against the asset going down, you want to sell it to highest bidder, so that you don't loose money
Insurance with respect to Call options is only relevant for American options, since they have an opportunity cost assigned to the time you chose to exercise the option. It is generally suggested in case of a non-dividend paying stock to exercise the American Call option at expiry due to the time value of money. With American Put options, insurance is relevant because the optimal time to exercise the option is before the expiry date. The insurance is offered against price rise by call options and against the price falls by put options, but only for the American ones. This feature is of not of major importance when talking about European options.
guys... show some respect
Math is more of a merit based honor system. Just in case your bias is from a culture that respects teachers automatically. His was a nice yet impractical exercise, delivered with a distracting accent.
If Black-Scholes based on European option design was of much use. Everyone would be wealthy. Actually, this was a complicated exercise but aimed in the wrong direction for the problem that the title alludes to. One point that he omitted, was explaining the different versions that are in use by companies, of the Beta Greek.
2-Horse race example is unclear. The outcomes are poorly explained.
Edit: After struggling for a few minutes to follow his calculation of payout in the first example, I decided to skip this video.
it's the other way around
this guy apparently is not a real teacher..
Yifan Liu True, but he has world experience that is better than an academic teacher. Dr. Vasily Strela, Dissertation: Multiwavelets -- Theory and Applications, is a Research Affiliate in the MIT Department of Mathematics. He is also a Managing Director and the Global Head of Fixed Income Modeling at Morgan Stanley.
I miss Choonbum Lee
Fixed income modeling...now I understand why he sounded depressed after explaining the dollar invested at Cambridge savings bank is a dollar a year later, and didn't have to explain inflation to that crowd. Selling something you don't believe in, can be depressing. @@scottab140
Why dB=rBdt？
if you agree with the continuous compounding equation B=Bo * e^(rt), then dB/dt = r* Bo*e^(rt) = rB. rearrange the equation gives you dB = rBdt
@@jianweng3463 thanks!
He looks a lot like marshal from How I met your mother
lol no, not at all
Lmao he looks like Jason Segals dad acting like professor Mosby
I don't subscribe to the idea that it was a clear explanation. He's clearly talented, but his explanation simply was not clear. Put-Call parity shouldn't require such rigour. It's can be easily explained with no need for such abstraction...
Algorithomers sones plus formulares xser pisilon formulare strutarasters for in prol dell concienters plus mans
Excellent theoretical explanation for MIT students. Now let's do it in the real world with Federal Reserve and Central Banks saving the stock market forever "whatever it takes" (implicit PUT free option in the market) + negative interest rates. Welcome to the real Finance in Wonderland world kids :)
*this didn't age well with coronavirus impacting the economy and rendering "powers-that-be" powerless.*
Thanks for admitting you don't understand change of measure I guess?
This did not age well? Idk lol
This is riddled with errors. I am disappoint. Expiry time is the pink line for starters...
39:31
i wish i learned finanace in my earlier years, fuck .......
What the hell was that in his pocket...
probably the microphone
Instructor is certainly a smart guys who speaks full of fancy terms. You may need to study this topic before to connect to those finance English. Generally not a good lecture by explanation replying too much on slideshow as pointing fingers at part of a slide is like your friend tries to tell you where "there" to go while you are driving a car. This makes it a poor presentation relatively compared to other MIT OpenCourseWare lecture. Btw horse bet example is terrible, just skip that part.
Awful presentation of the topic. He knows how to derive it but shows his students nothing but a slideshow. Link the step and show the proofs man.
i appreciate his effort but seriously the teaching is si bland....
I found him interesting
Lol. He could be very berry smart, but me no understando.
Don't worry about it, the talk was aimed in the wrong direction and instead just delivered what you could read anywhere. Except in this case he drew out some math for us to see.
Lol.
horrible presentation.