Multiverse Pricing Models

[marco_airoldi]

I will try to complete DFD very soon in such a way you can use it for part 2

 

[Daniel Duffy]

DFD

A DFD is a no-brainer but how many people initially explain things to others in this way before grunge code, for example?

 

[marco_airoldi]

I try to send you this very first version of the DFD of the paper. I found myself comfortable with this approach. Very useful for the upcoming paper rewriting. I hope I interpreted your suggestion correctly. I wanted to create a diagram that fits on one page, but I wouldn't have been able to include the tabs on the mathematical points. First attempt .... Goodbye, Marco

 

[Daniel Duffy]

Thanks, Marco.
I'll study it. BTW I want to ask Alan a few questions as well on W forum.

Crepi il lupo

 

[Daniel Duffy]

I looked at the DFD. At this stage I do not have enough information to go on. Some issues IMHO are:

1. The scope of the article is rather diffuse .. I would scope the problem to a well-known concrete problem and start again (e.g. take a 1-factor barrier option and work the whole process out A-Z with LATEX formulae and data).
2. Flag your assumptions ... what kinds of problems: 1, 2 factor etc., n factor, early exercise etc.
3. The Simplex method: personally, I don't encounter it a lot. Is it a bit antiquated, why was it chosen? It is a linear program with linear constraints.
a . Which classes of equity problems can it handle? What about non-linearity?
b . Does it always have a unique maximum?
c . Can Simplex be solved in polynomial time?
d . p. 12 or article: are you solving non-linear problems as a (sub-optimal as stated on page 20) as sequence of linear problems?
e . Precise formulation of input to Simplex. Does it satisfy the assumptions of Simplex?
4. Accuracy issues not quantified.
5. Which specific numerical methods: PDE/FDM, Fokker-Planck, Monte Carlo, calibration.
6. Transition matrix story A-Z needs attention.

//
the source of all great mathematics is the special case, the concrete example. It is frequent in mathematics that every instance of a concept of seemingly great generality is in essence the same as a small and concrete special case.
- Paul Halmos

 

[Daniel Duffy]

Ciao Marco,
The approach taken in this article (Monte Carlo in C#) might help (separation of concerns) is not a million miles away from the approach/recommendations here (especially Figures 1 and 2).

A useful quiz: "align" your DFD with context diagram Figure 1 (or 2).

 

[Daniel Duffy]

Re "can always be integrated out".

It's not clear to me what is being asserted.

It's true that, in Hidden Markov Models, for example, there is indeed a lot of integrating out. I have a whole chapter on "Stochastic Volatility as a Hidden Markov Model" in my "Option Valuation under Stochastic Volatility II" book.

Separately, Dupire/Gyongy theory does a lot of integrating out of univariate or multivariate stochastic volatility in the construction of a local volatility surface for diffusions.

However, there remains the problem of "re-calibration".

In any event, if you can make/prove a careful statement about the application of your theory to data generating processes with additional state variables (hidden or not), my suggestion is to include that in your paper.

I would like to this problem a bit of a whack in C++. Ideally, C++20 and possibly Boost C++ libraries.
Is there a defined process (input-processing-output)?

Some hints:

1. First, you have to understand the problem.
2. After understanding, make a plan.(algorithm)
3. Carry out the plan.
4. Look back on your work. How could it be better?

I need someone to do 1 (and maybe some of 2).

 

[Daniel Duffy]

Alan's chapter 5 has

Step I: Standsardised SDE
Step II: Discretize the SDE (Euler (x) and NR lattice (y), others?)
Step III: HMM structures (construct Q_n(x) matrix)
?? Step IV: what's next? is that section 5.5's use cases?

Fundamental data input?
Final output?