Variance Swaps Explained | Mechanics & Use | FRM Part 1 | CFA Level 3
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- Опубликовано: 28 июн 2024
- In this video from the FRM Part 1 and CFA Level 3 curriculum, we take a look at Variance Swaps and explore their mechanics and through a simple example how they can be put to use in practice. We also go through the specifics of how realized variance is calculated, how are variance swaps priced and sized (i.e. setting of variance notional). For more videos related to FRM Part 1 preparation, please head over to the course page (www.finRGB.com/courses/frm-pa....
*FRM Learning Objective* : Describe and contrast volatility and variance swaps.
*CFA Learning Objective* : Demonstrate the use of volatility derivatives and variance swaps.
I thank you very much, Sir, for briefing the concept of the volatility derivative-variance swap. I do have one question if you can add about "why we trade variance swap over volatility swap"? I have seen many materials from google but am not satisfied, Can you address it in simple what do we mean when we say variance swap is convex with volatility? I can't wait for your feedback apart from the resources people put on google. Thanks in advance.
Hello Kudus, "convex with respect to volatility" means that if you were to plot the payoff of the variance swap against realized volatility, you will observe that as realized volatility increases, the payoff does not increase in a straight line fashion, but rather non-linearly (and, at an increasing rate). This aspect follows directly from the formula: Payoff = Nvar * (Realized Volatility ^ 2 - Strike Volatility ^ 2).
The convex payoff coming from a Variance Swap makes it attractive to an investor looking for a volatility based position as a hedge against risks of extreme events (a convex payoff provides you boosted gains when volatility does spike upwards). Also, from a theoretical perspective, (in comparison to volatility swaps) variance swaps are more efficiently replicated and hence valued) using portfolio of options.
@@finRGB Do vol swaps have negative convexity or do the var swaps just have a higher non linear slope?
Very clear explanation on this, although one question I was left with:
- When checking the Settlement Amount, can you please advise how do you got the 50k? As per my calculation, doing the 1250 * the different between realized and implied variance doesn't get me there. Can you please just come back on this point?
Really cool video and really appreciate the work done here!
Hello Pedro. The 50k is the "vega notional" i.e. the approximate gain / loss when the realized volatility deviates from the strike by 1 percentage point. If you were to start with 1250 variance units as a given, a realized volatility of 21 (i.e. 1 point away from strike of 20) gives a payoff of 1250 * (21*21 - 20*20) = 51250 (which is close to the vega notional of 50k).
@@finRGB thank you for the reply! One follow up: we now get a close value. The value that is actually paid is the even 50k or the approximate value from the calculation? Is this standard or is there any wording from confirmation to confirmation that settles this "dispute"?
Just ask because those discrepancies usually fall outside of the acceptance tolerance that a lot of big banks/companies have.
Another question as well, if I may. If we have a basket of 2 underlyings on 1 Variance Swap, let's say that we have some units of S&P 500 and some units of Nikki 225. Each index has their own Strike value. For us to be able to calculate the Settlement amount, we would just aggregate the realized strikes and implied strikes of both and do the calculation? By this logic using the total number of units, instead of the individual value.
@@pedrolanca6597 The payoff will be Number of Variance Units (i.e. 1250) * (Realized Variance - Strike Variance). The vega notional is just a construct that is used to arrive at the size of the variance swap i.e. number of variance units = vega notional / (2 * strike).
@@finRGB thank you again for the explanation!
Final question from my end here. If we were doing a Variance Swap over 2 different indexes (on the same trade though), for example S&P500 at 23% initial strike + Nikkei 225 at 25% strike, and let's say we had 750 units for each (1500 total). Let's also say that at maturity they both finished with a realized strike of +1%.
To calculate the payoff for this example, would I just need to do 1500*(24*24-23*23 + 26*26-25*25)? Or a separate calculation would be needed here?
Again, thanks a lot for the help, as this has been the best explanation on this I've seen so far.
@@pedrolanca6597 If two indices are involved and it is a single trade, you need to think of the weighted combination of the two indices as a "basket". There will be a single strike variance corresponding to the basket (and not a separate one for each component). This video here talks about such a swap: ruclips.net/video/GSzeRTgR0r4/видео.html
Shouldn't the variance be the sum from i=1 to N instead of N-1? The division by N-1 is fine, but the sum must include all terms, doesn't it?
We are assuming that we have N prices with us P_1, P_2, ..., P_N. These N prices observed over N days give rise to N-1 daily holding periods and hence N-1 returns. That is why our summation goes from 1 to N-1. Since it is a sample of returns we should have divided by N-2 to make the variance estimate unbiased. We are assuming here that N is big enough so that division by N-2 or N-1 doesn't make a big difference.