Pricing options via Fourier-Laplace inversion of characteristic function of Lifted Rough Volatility

[stochastix]

Sounds doable.. and as far as I can tell the matrix Riccati equation is required to find the steady-state solution via a a Newton-Raphson iteration .. once that is calculated, then plug that into the characteristic function and invert to calculate option prices and implied vols from the parameters .. the only part I am not quite so sure on right now is how to make the foward variance curve theta(t) in the model match the VIX future sterm structure model precisely, I'm thinking Newton polynomial interpolation of all the future contracts between now and expiration of the option im wanting to price, then differentiate that polynomial and that should be my E[V_s] over the tenor. https://quant.stackexchange.com/que...-model-via-fourier-laplace-inversion-of-chara

 

[panzerman]

You should ask this on the Wilmott forums. This question is likely way more advanced than the users here can answer.

 

[Overnight]

Sounds doable.. and as far as I can tell the matrix Riccati equation is required to find the steady-state solution via a a Newton-Raphson iteration .. once that is calculated, then plug that into the characteristic function and invert to calculate option prices and implied vols from the parameters .. the only part I am not quite so sure on right now is how to make the foward variance curve theta(t) in the model match the VIX future sterm structure model precisely, I'm thinking Newton polynomial interpolation of all the future contracts between now and expiration of the option im wanting to price, then differentiate that polynomial and that should be my E[V_s] over the tenor. https://quant.stackexchange.com/que...-model-via-fourier-laplace-inversion-of-chara

You are assuming a steady-state that will stay that way. Steady.

If Putin were to die tomorrow, the VIX futures curve you are looking at today is going to get wrecked tomorrow. Mathematics is too rigid, in my view, to be able to adapt to a rapidly-changing volatility environment. Just a few days ago the VIX was 30. Now it is 23. That is a sharp drop in a short amount of time. An inverted spike.

What mathematical model can adjust to that?

 

[TheDawn]

Sounds doable.. and as far as I can tell the matrix Riccati equation is required to find the steady-state solution via a a Newton-Raphson iteration .. once that is calculated, then plug that into the characteristic function and invert to calculate option prices and implied vols from the parameters .. the only part I am not quite so sure on right now is how to make the foward variance curve theta(t) in the model match the VIX future sterm structure model precisely, I'm thinking Newton polynomial interpolation of all the future contracts between now and expiration of the option im wanting to price, then differentiate that polynomial and that should be my E[V_s] over the tenor. https://quant.stackexchange.com/que...-model-via-fourier-laplace-inversion-of-chara

You might find this book "Fourier and Laplace Transform Inversion with Application in Finance" helpful. There is a chapter that specifically focuses on how to calculate options using the Laplace transform with a recursion algorithm. https://repub.eur.nl/pub/76954/EPS2014322LIS9789058923752.pdf

 

[stochastix]

You are assuming a steady-state that will stay that way. Steady.

If Putin were to die tomorrow, the VIX futures curve you are looking at today is going to get wrecked tomorrow. Mathematics is too rigid, in my view, to be able to adapt to a rapidly-changing volatility environment. Just a few days ago the VIX was 30. Now it is 23. That is a sharp drop in a short amount of time. An inverted spike.

What mathematical model can adjust to that?

Ye knows not to whom one is corresponding. I didn't say so, but i will be "perfectly hedging" as a byproduct of model implementation such that I'll be good as long as a nuke doesn't hit Chicago. I put in quotes because as we know we get very close to hedge within some epsilon.

What you mention tho is parameter drift over time and regime change. Etc. It's possible but that's a much more forecastable thing , in some sense than the variance process itself.

For instance. The Hurst exponent is almost universally about 0.1 across all timescales and asset classes.

If nuke hits , I live on 350 acres and my dad has a shitton of guns , we will figure something out.

Also I forecasted the old man who claimed his dad buried jimmy hoffa in a transit center in. New Jersey a full week before it went public . Once i also dreamt some fucks broke down my apartment door before it really happened , so , I'm not losing any sleep over it but thanks for your concern

 

[Overnight]

Ye knows not to whom one is corresponding. I didn't say so, but i will be "perfectly hedging" as a byproduct of model implementation such that I'll be good as long as a nuke doesn't hit Chicago. I put in quotes because as we know we get very close to hedge within some epsilon.

What you mention tho is parameter drift over time and regime change. Etc. It's possible but that's a much more forecastable thing , in some sense than the variance process itself.

For instance. The Hurst exponent is almost universally about 0.1 across all timescales and asset classes.

If nuke hits , I live on 350 acres and my dad has a shitton of guns , we will figure something out.

Also I forecasted the old man who claimed his dad buried jimmy hoffa in a transit center in. New Jersey a full week before it went public . Once i also dreamt some fucks broke down my apartment door before it really happened , so , I'm not losing any sleep over it but thanks for your concern

Holy shit! Great retort! Good luck when the nukes do not come! Stop trying to be a mathematical dick! You looking to get a Fields medal? It won't come with bull shit physics models on stock markets. My Lord!

 

[stochastix]

Holy shit! Great retort! Good luck when the nukes do not come! Stop trying to be a mathematical dick! You looking to get a Fields medal? It won't come with bull shit physics models on stock markets. My Lord!

yes but not for my work on trading! and rough volatility models are not bullshit, this one is a recent innovation made by Gatheral in 2019 or 2020 or so, a result that was previously though to be impossible, joint calibration with continuous sample paths.

haha, i love it, let me grab my lighter and wave it in the air, bahaha
'

 

[stochastix]

this year I'll be publishing the Riemann hypothesis proof, after that, how that relates to and completes Yang-Mills theory, after that, how that relates to negative mass and a unification of quantum mechanical axioms with relativity and somehow someone builds one of these, Anatomy of a Flying Saucer and then all bets are off, how many humans will comprehend the unified theory? I think a full understanding of the unified forces of nature from first principles would lead to a way to construct arbitrary matter from scratch(energy coming from somewhere i know), like replicators on star trek, since YM governs the dynamics of quarks and gluons etc, and furthermore it would be known how to generate negative mass or how to find and harness it, in any case, since it would then be known the full dynamics of quarks and an understanding of how gravity is mediated it could be known then if two hydrogen atoms could simply be arranged in a certain way of vibrating that would make them fuse without requiring star-like conditions, thereby enabling desktop fusion to power the replicators without risk of contamination if proper safety precautions are built in to prevent Putin-like people from farkin things up. negative mass is like wormholes, it can theoretically exist but no one claims to have observed it, though this sort of situation is tricky because Stephen Hawking proved that an entropy-reducing transformation would leave no observable evidence of it having-happened. Ponder that.

actually... im not eligible for a fields medal.. they are ageists and only award bounties to people "40 years old or less".. no worries, that particular reward was never a motivating factor

 

[Heydrrich]

this year I'll be publishing the Riemann hypothesis proof, after that, how that relates to and completes Yang-Mills theory, after that, how that relates to negative mass and a unification of quantum mechanical axioms with relativity and somehow someone builds one of these, Anatomy of a Flying Saucer and then all bets are off, how many humans will comprehend the unified theory? I think a full understanding of the unified forces of nature from first principles would lead to a way to construct arbitrary matter from scratch(energy coming from somewhere i know), like replicators on star trek, since YM governs the dynamics of quarks and gluons etc, and furthermore it would be known how to generate negative mass or how to find and harness it, in any case, since it would then be known the full dynamics of quarks and an understanding of how gravity is mediated it could be known then if two hydrogen atoms could simply be arranged in a certain way of vibrating that would make them fuse without requiring star-like conditions, thereby enabling desktop fusion to power the replicators without risk of contamination if proper safety precautions are built in to prevent Putin-like people from farkin things up. negative mass is like wormholes, it can theoretically exist but no one claims to have observed it, though this sort of situation is tricky because Stephen Hawking proved that an entropy-reducing transformation would leave no observable evidence of it having-happened. Ponder that.

actually... im not eligible for a fields medal.. they are ageists and only award bounties to people "40 years old or less".. no worries, that particular reward was never a motivating factor

Do you also believe in flat earth ?

 

[stochastix]

Do you also believe in flat earth ?

no you dumb trouser stain, did you not just read that I'm going to unify relativity with qm?
That's curved spacetime for an uneducated reactionary cleche spewing idiot like yourself