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Aug
18
comment How to calibrate a volatility surface using SVI
Thanks for your answer of question 1). Whast do you mean by scaleless?
Aug
16
comment How to calibrate a volatility surface using SVI
@Farahvartish Thanks for the link. I already checked that question and the code in the answer as well. As you can see, I already posted there a comment. However, in the mean time additional question came up and I thought its better to split it and post a complete new question.
Aug
16
asked How to calibrate a volatility surface using SVI
Aug
15
comment Local volatility SVI parametrization
May I ask you a small question about your code? When you fit the whole surface (SSVI), why are you recalibrate the slice afterwards? according to ( arxiv.org/pdf/1204.0646.pdf ) you chould choose $\phi (\theta) = \frac{\eta}{\theta^\gamma(1+\theta)^{1-\gamma}}$, eq 4.5 on page 17. Given the constraint should result in a complete free of static arbitrage surface, or am I missing someting?
Aug
5
comment Greeks of a swaption using Brigo
I will reward the bounty tm. On the app there isnt a button to reward it. Many thanks for your patience and explanations. This was very helpful.
Aug
5
comment Greeks of a swaption using Brigo
Very interesting. I thought it was by purpose to use the black 76 because of future payoffs like in a future case. About the different definition: thats maybe the most confusing part in FI. There are alot of slightly different definition of similar things, eg duration etc. That makes it at the beginning much more confusing than the equity casr
Aug
5
accepted Greeks of a swaption using Brigo
Aug
5
comment Greeks of a swaption using Brigo
maybe my last comment was not that clear. A swaption is like a call on a future, isn't it? That's the reason why uses the Black 76 formula for quoting. Therefore, in the equity world (call on a future) your delta is $\beta N(d_1)$ since your underlying is tradable. You have the discount factor in front. However, taking in FI the derivative wrt to the underlying $A_{\alpha,\beta}$ cancels the discount (annuity) part, which seems counter intuitive. That was my question in the last comment
Aug
5
comment Greeks of a swaption using Brigo
thanks gordon. I really like the paper! Maybe one last question. In the equity case, i.e. call on a future $F$: $C=\beta(t)E_Q[\frac{1}{\beta(T)}(F-K)^+|\mathcal{F}_t]$. Using Black 76 we see that the forward delta, $\frac{dC}{dF} = \frac{1}{\beta(t)}N(d_1)$. $F$ is the underlying and can be traded. Why do we have there a discounting factor? It seems to me, one can't really make a linke between equity and the FI case.
Aug
4
comment Greeks of a swaption using Brigo
Many thanks Gordon! Its much clearer now.
Aug
4
comment Greeks of a swaption using Brigo
thanks a lot for your explanation and the link. What would be interesting to know why exactly $A_{\alpha,\beta}$ is considered to measure the change. Sure it is a tradable asset, but the connection to the swaption / swap is not fully clear yet (to me). For example, a swap can also be decomposed into FRA's contracts which are tradable asset. I'm new to these things and still lacking of the intuition. Thanks for your help and the pdf.
Aug
3
revised Greeks of a swaption using Brigo
edited title
Aug
3
comment Greeks of a swaption using Brigo
@GabrielePompa exactly, In equities you have a bound of the delta. Why can it exceed 1?
Aug
2
comment Greeks of a swaption using Brigo
@AlexC Yes, I mean D.Brigo and his famous text book
Aug
2
comment Greeks of a swaption using Brigo
@GabrielePompa Hi, I added an example. I hope it is clear now.
Aug
2
revised Greeks of a swaption using Brigo
added 531 characters in body
Jul
29
asked Greeks of a swaption using Brigo
Jul
6
awarded  Notable Question
Feb
15
awarded  Tumbleweed
Feb
14
accepted swaption model for forward swap rate