Interest Rate Term Structure Models: Introductory Concepts
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- čas přidán 5. 09. 2024
- Explains visually and mathematically the basic Term Structure modelling concepts, such as instantaneous forward rate, short rate, rolling bank account, zero coupon bond, and how they are linked together. Here is the outline of the content by timeline:
0:37/16:00: Explains the concept of the Term Structure and its dynamics
02:12/16:00: Explains visually the concept of the Instantaneous forward, and the Short rate
06:16/16:00: Explains visually what the objects of interest are in the Forward rate (HJM) vs Short rate models
7:10/16:00: Mathematical description of the price of the Zero coupon bond
9:59/16:00: Mathematical description of the value of the Bank account
11:29/16:00: Using Risk Neutral valuation formula, explains how the Zero coupon can be expressed in terms of the short rate
12:42/16:00: Shows how the Instantaneous forward can be expressed in terms of the Zero Coupon, by differentiating the Zero coupon price formula
13:22/16:00: Alternative way of showing the relationship between the Instantaneous forward and the Zero coupon as the limit of the Simple forward rate
14:29/16:00: Explains the relationship between the differential of the short rate, and the differential of the Instantaneous forward
very well explained indeed, I just started to watch but so far this could be one of the best tutorial on the net
Very clear introduction, I finanlly start understanding , f() and P() and r(), and that term, is time.
Thanks @Henrik Swedish!
No this was not a clear explanation at all. I understood nothing up to 7:00 and couldn't even go further than that
Please could you add a mathematical proof of the relationship between the differential of the short rate and the instantaneous forward rate. Great video. Thanks
Thanks! Please see the link to a video containing the alternative proof in the community tab!
Thanks for making a video on it!
One thing I never understand: how it is possible to obtain the interest rate curve of the next period? Should I sum the generated interest rate with the forward rates of the previous time, or should I multiply all obligations prices of the previous period by the generated interest rate? Or something else? Many thank for the answer…
Awesome video !! Very helpful!!
Thanks!
Thanks for this video !! A little loss after 14.29 but will try to figure it out. Other's are pretty clear IMO.
you're welcome! Don't give up! Any questions just let us know!
Thanks very much for the great video!
thank you @J Lo!
Awesome video
Thanks!
And could you please explain the link between what you called spot interest rate(y) and short rate(r)? Thanks!
This is a great explanation, thanks a lot for posting this !! I am a big fan of this channel
thanks!
It's not a great explanation. I understood nothing up to 7:00 and therefore couldn't even take it further than that
Is it true that at 6:23, the elements in the table are instantaneous forward rate, note as f(t, T), and short rate r(t) is defined as f(t,t), which means borrowing for instantaneous borrowing at t ? So the difference between short rate and instantaneous forward rate is just whether to borrow "now" and T-t time later from "now" ?
it's true, comfirmed by 14:49
Also In 5:00, Are you assuming that one month rate is the short rate by moving all the rows to the diagnoal form?? But it is also not enough again. for example the rate 0.79 in the 5th rows, it means from Feb 19 to Mar 18. however it is moved and then it means from Feb 19 to Feb 19! totally hard to understand
4:42 I think it is not enough to just say "pretending". How to justify changing the column index 0.083 to 0.000? for example, obviously the rate 0.76 is from Oct 18 to Nov 18. But if we change the column 0.000, it means from Oct 18 to Oct 18. It is too awkward
you had to make the comment about the time travel, i noticed the edit :)
Hello,
Great video and many thanks for sharing your knowledge.
I didn't get the part dr(t) = df(t, T) ... , around 15:30. How did you get this? Could you suggest any reference?
Thanks, again.
thank you!!
At 7:02 it says the short rate models take "the diagonal entries as inputs into the term structure equations to give you the whole term structure." what are these "term structure equations" ? Can you be clearer?
thanks for the comments! Here is another explanation! Short rate, say overnight, gives you the rate for borrowing overnight, but in the interest rate world, lending/borrowing can happen for any term - one month, 6 months, etc. So say time is today, and you know today's short rate, but you want to borrow for 6 months at a known rate, how could you determine the 6 months rate? Then how would you model the dynamics of this 6 month rate over time? This is where the term structure comes into play- because in general in the interest rate market, rate varies by the term. So the overnight rate varies over time, but so do the other rates. Short rate models take a simplistic view, but then their usefulness, at least historically, is judged by how well they explained the whole term structure. hope this helps!
I have no idea why you shift the table at 5:00. Why have you done this? How can this table have multiple rows? If today is 30 Oct 18, then how can we have any future rows? Don't lower rows signify instantaneous forward rates as seen at future dates, such as 30 Nov 18,which is in the future? How can we see a forward rate as if today were the future? Doesn't each row represent the yield curve as of the time in the far left column?
Hello again! I assume this relates to the previous comment, but let me know if it is still not clear!
This is the worst explanation I have ever seen. Confirmed by my friend who is an MEng from Oxford in aeronautical engineering and a 15 year quant trading professional at top investment banks and hedge funds. Why can't you just say that the short rate models take the current zero rates as seen in the market today (ie the current observed zero curve) and then simulates each of those observed zero rates into the future, which gives future simulated yield curved, expressed as future simulated instantaneous forward rates (calculated from the zero rates that the model has simulated into the future). FFS, such a poor explanation. Why couldn't you have provided a clear explanation rather than making stupid jokes?
I assume this again relates to the previous question, but if not then you can please re-phrase the question? To summarise, we are taking a view of the whole term structure of interest rates as opposed to just the overnight/short rate. Just modelling the short rate is nice in academic settings, but it is useless in real life/practice, as one has to face up to the whole term structure, hence the focus throughout the playlist is on the term structure.
@@quantpie I have asked one question on the video HJM framework after going through the video. Please answer it. There seem to be a bug there.
if the guy could speak in clear english, that would be helpful.
thank you! we have passed on the feedback to the IT guys who work on the speech. many thanks for the feedback!
yeah totally agree, if the guy could speak with less accent, that would be much better. Anyway, it helps clear my confusions, thanks