approaches to calibrating a Heston model

The characteristic function of the Heston model, as modified according to Gatheral (2006), is given by:

φ_H(t; w) = exp[C(t,w)̅V + D(t,w)V₀ + iwln(S₀e^(rt))]

whereV ̅ is the long-term variance, V₀ is the initial variance, S₀ is the initial stock price, r is the risk-free rate, and w is the frequency variable. The coefficients C(t,w) and D(t,w) are given by:

C(t,w) = ((r i w - λ θ)/σ^2) * (1 - e^(-λ t)) + (θ/(2λ)) * ((λ - r i w) t - 2 ln((1 - g e^(-λ t))/(1 - g)))

and

D(t,w) = (1/σ^2) * (1 - e^(-λ t)) * ((r i w - λ θ)/λ - 1/2) + (1/λ^2) * {(λ - r i w)(1 - e^(-λ t)) - 2(ln(1 - g e^(-λ t)) - g e^(-λ t))}

where λ is the mean reversion rate, θ is the long-term variance, σ is the volatility of volatility, and g = (λ - r i w)/(λ + r i w) is the damping factor.

 

I always wondered about these insane statistical analyses equations I have seen for the BSM options...Do they predict where your option is going to go tomorrow, when Powell opens his mouth and testifies. or the NFP report on Friday?

It is a 1:1 bet on the market (or individual stock) going up or down. WTF does this nuclear particle physics math have to do with that?

 

Thank you ChatGPT , not too shabby.. unclear if worth time so far but It does know some stuf but like anything it depends on the 'user'

this is actually a rather profound result that was not known to be possible before'

https://math.stackexchange.com/ques...he-hawkes-process-with-multi-exponential-kern

 

well, it works, great, now to test the inversion and implement the heston characteristic... then expand that out into the lifted heston then i'll have a rough volatilty model up and going ready to be calibrated.. then the joint SPX/VIX calibrator not far behind

 

you have to finagle it, and treat it like its some autistic genius savant who took a bunch of acid and takes everything literally and lives by the lyrics of this song

 

previous reply was meant for you KS

 

You mean the post where you say that to get a good answer out of chat gpt you have to "treat it like its some autistic genius savant who took a bunch of acid and takes everything literally...?"

That sounds like a lot of work! How many hours of back and forth before you were able to get it to produce the FourierTransform in the FourierTransformTest class in the screengrab posted above?

 

more than I'd like but i was moving quite slow damn neck pinched. piece of cake now that i figured out the technique, i could see it becoming a more streamlined feature

 

I still apparently haven't got it down:

Q) ChatGPT, can you prove the Riemann Hypothesis for me?

A) I'm sorry, but I cannot prove the Riemann Hypothesis for you. The Riemann Hypothesis is one of the most famous unsolved problems in mathematics, and it has remained unproven for over 160 years despite the best efforts of many mathematicians...