simulating the (non-Markovian) quadratic rough Heston process? joint SPX&VIX option calibration

[stochastix]

https://nuclearphynance.com/Show Post.aspx?PostIDKey=199613

Euler-Maruyama
Euler-Heun
Milstein-Ito
Milstein-Stratonovich
Stochastic Runge-Kutta

which simulation method is going to work best?

this is similiar to the Heston model but the kernel is the Mittag-Leffler function so it is non-Markovian if α != 0.5

 

[Tony Optionaro]

Thanks for the link

 

[TheBigShort]

https://nuclearphynance.com/Show Post.aspx?PostIDKey=199613

Euler-Maruyama
Euler-Heun
Milstein-Ito
Milstein-Stratonovich
Stochastic Runge-Kutta

which simulation method is going to work best?

this is similiar to the Heston model but the kernel is the Mittag-Leffler function so it is non-Markovian if α != 0.5

I am curious to know how you are managing your short d5 VIX calls right now. IIRC a few weeks ago you were looking for a hedge, were you able to find one?

 

[longandshort]

What are you trying to do? You need to fit your model to a scenario just FYI.

 

[stochastix]

I am curious to know how you are managing your short d5 VIX calls right now. IIRC a few weeks ago you were looking for a hedge, were you able to find one?

last week was a bit rough but its still lookin good for expiry. bought a few OTM vix and spx calls to reduce vega

 

[stochastix]

What are you trying to do? You need to fit your model to a scenario just FYI.

I want to calibrate the model to current option prices and recalibrate frequently so as to forecast the probability of payoff. I did this with heston model before but heston is not good for short maturities . I don't want to blindly trust the implied probability shown by IB TWS software

 

[stochastix]

Simulating the rough Heston (quadratic or not) is a challenge because it is not Markovian . The lifted Heston model looks like a good alternative, its a superposition of classical Heston processes that works in the same spirit as the approximation of powerlaw kernels by sums of exponentials, https://arxiv.org/abs/physics/0605149. The Heston (Cox-Ingersoll-Ross) process naturally arises as the macroscopic limit from a microscopic hawkes process model . I did some work on this 2 years ago and reproduced the results in
Critical reflexivity in financial markets: a Hawkes process analysis

 

[stochastix]

last week was a bit rough but its still lookin good for expiry. bought a few OTM vix and spx calls to reduce vega

at the time, vega was still high, i didnt wanna pay that much to reduce it, now today I check and its almost 0. would be nice to put together a combo of some sort that would neutralize the sensitivity to implied VIX volatility and leave only sensitivity to VIX delta... if only we could trade VVIX options