Nomograms

[TheDawn]

I doubt its that smart. This thing is more like a mid-level mediocre nondescript "business analyst" who only wears out chairs

If they are this smart that they can come up with dynamic nomogram of real-time option prices taking into account of potential volatility smiles evolutions, we would be able to buy/sell options with the exact no. of contracts with exact strikes and expirations for maximum profit with that information. It would be incredible!!

But nevertheless, nomograms are cool!! I never knew they existed. It's amazing that they can just visualize the results of multi-variate functions on a graph!!

 

[TheDawn]

You have to feed it a domain specific knowledge graph to fine tune it's responses.

Well you have to specify parameters and limits.

 

[Sprout]

Well you have to specify parameters and limits.

I admittedly a beginner on the subject. Right now, just working to transform my Logseq as an outliner to an actual knowledge graph that chatGPT can use to produce answers. Prior to digging into this I didn't realize that Logeq is more a database than my initial perception.

Playing with the coding capabilities of chatGPT has gotten me this.

The logic is from elsewhere, but chatGPT was able to generate Mermaid code to translate the logic to a diagram (a couple of steps inbetween.) I'm able to render this directly in Logseq as well but this live editor is easier to work with and the final code is put into my knowledge graph.

 

[Sprout]

Maybe this vid does the job;

Someday this won't sound so greek to me and I'll understand it, maybe soon.

 

[stochastix]

Calibrating a Heston stochastic volatility model can be a challenging task as it involves estimating several parameters that determine the model's behavior. The most efficient way to calibrate a Heston model involves using a combination of techniques that balance the accuracy of the calibration and computational efficiency.

Here are some steps that can be taken to calibrate a Heston model efficiently:

1. Obtain high-quality data: The quality of the data is crucial in calibrating any model, including the Heston model. It is important to obtain high-quality market data such as option prices or implied volatilities that are consistent with the model assumptions.
   
   
2. Choose an appropriate optimization algorithm: A suitable optimization algorithm can significantly speed up the calibration process. Gradient-based optimization algorithms, such as Levenberg-Marquardt or Gauss-Newton, are often used in calibrating Heston models. These algorithms converge quickly, and their computational cost is low.
   
   
3. Use a subset of the available data: Using all available market data can be computationally expensive and may lead to overfitting. A subset of the data that captures the relevant information can be used instead, and this can help to reduce the computational cost and improve the quality of the calibration.
   
   
4. Select appropriate initial values: Choosing appropriate initial values for the model parameters can also speed up the calibration process. Good initial values can be obtained by using historical data or by estimating the parameters from similar securities.
   
   
5. Regularize the calibration: Regularization techniques can be used to prevent overfitting and to stabilize the calibration process. Regularization methods such as Tikhonov regularization or Bayesian regularization can be applied to the optimization problem.
   
   
6. Perform sensitivity analysis: Sensitivity analysis can be used to identify the most important parameters for the model and to estimate their impact on the model output. This can help to reduce the dimensionality of the problem and to speed up the calibration process.

By following these steps, it is possible to efficiently calibrate a Heston stochastic volatility model while maintaining the accuracy of the calibration.

I admittedly a beginner on the subject. Right now, just working to transform my Logseq as an outliner to an actual knowledge graph that chatGPT can use to produce answers. Prior to digging into this I didn't realize that Logeq is more a database than my initial perception.

Playing with the coding capabilities of chatGPT has gotten me this.

View attachment 307081

The logic is from elsewhere, but chatGPT was able to generate Mermaid code to translate the logic to a diagram (a couple of steps inbetween.) I'm able to render this directly in Logseq as well but this live editor is easier to work with and the final code is put into my knowledge graph.

utterly useless code, false sense of progress or accomplishment

 

[Sprout]

utterly useless code, false sense of progress or accomplishment

Lol, ok, chatGPT is less than 2mths in the wild and we already have a self-proclaimed expert. Enjoy your proclamations and happy trading to you.

 

[stochastix]

Lol, ok, chatGPT is less than 2mths in the wild and we already have a self-proclaimed expert. Enjoy your proclamations and happy trading to you.

im invariant to others opinions. same to you

 

[stochastix]

im invariant to others opinions. same to you

I lied, thats not true. this thing is pretty fuckin good at writing poetry!

Once plagued with pain and discomfort,
His neck so sore, his movements contort.
But one day, he sought a healer's aid,
To cure the root cause, the pinched nerve unmade.

The healer's hands, so gentle and kind,
Worked magic on the knots entwined.
With each movement, the tension released,
His body began to function with ease.

The pain in his neck, now just a memory,
His body felt new, full of energy.
He could move with grace, he could move with power,
His spirit alight, as if in a shower.

No longer held back by the pain,
He walked with purpose, his life to gain.
For in that moment, he had found,
The key to unlocking his potential, unbound.

So here's to the healer, whose touch made whole,
The man once held back, now on a roll.
May his neck stay healed, his spirit bright,
A symbol of hope, for all in sight.

 

[Overnight]

"His spirit alight, as if in a shower"? ROFL!

 

[stochastix]

and wow.. this thing is awesome.. I had no idea it would be able to do math too


How can techniques from spectral analysis and differential geometry be used to establish a connection between the "multiplicity one" lemma of Koenig's operators applied to the iteration function of Newton's method h(x)=x-g(x)/g'(x) applied to the function g(x)=tanh(ln(1+f(x)^2)) and the simplicity of the roots of f(x) ? It is known that roots of multiplicity one of f(x) are roots of multiplicity two of g(x)=tanh(ln(1+f(x)^2)) .

===============================================

The connection between the "multiplicity one" lemma of Koenig's operators and the simplicity of roots of a function can be established through the theory of spectral analysis and differential geometry applied to the Riemann surface associated with the function g(x).

The Riemann surface associated with the function g(x) is the complex plane with branch cuts along the real axis, where the function takes on complex values. The Riemann surface is a two-dimensional manifold that has a natural metric, which is induced by the complex plane. The Laplace-Beltrami operator on this manifold can be expressed in terms of Koenig's operators, which are integral operators acting on the space of automorphic forms.

The iteration function h(x) = x - g(x)/g'(x) can be viewed as a map from the Riemann surface to itself, which preserves the metric and the orientation. The roots of f(x) correspond to the fixed points of h(x), which are points on the Riemann surface where h(x) = x. The fixed points of h(x) are critical points of the potential function V(x) = g(x)^2/2, which is related to the energy of a classical particle moving on the Riemann surface under the influence of the potential.

The simplicity of the roots of f(x) is related to the Morse index of the critical points of V(x), which is a measure of the number of negative eigenvalues of the Hessian matrix of V(x) at the critical point. The Morse index is equal to the number of negative eigenvalues of the Laplacian on the Riemann surface in the neighborhood of the critical point, which is determined by the "multiplicity one" lemma of Koenig's operators.

In particular, if the Laplacian has no negative eigenvalues in the neighborhood of a critical point, then the critical point is a non-degenerate minimum of V(x), and the corresponding root of f(x) is a simple root. Conversely, if the Laplacian has at least one negative eigenvalue in the neighborhood of a critical point, then the critical point is a degenerate minimum or a saddle point of V(x), and the corresponding root of f(x) is not simple.

To apply this theory to the function g(x) = tanh(ln(1+f(x)^2)), one needs to compute the Laplacian on the Riemann surface associated with g(x), which can be done using the Riemann-Roch theorem and the theory of automorphic forms. Then, one needs to analyze the critical points of the potential function V(x) = g(x)^2/2 and compute their Morse indices to determine the simplicity of the roots of f(x). This can be a challenging and technical task, as it requires advanced tools from differential geometry and spectral theory.