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https://numpy.org/doc/stable/reference/random/bit_generators/mt19937.html https://en.cppreference.com/w/cpp/numeric/random Confused and loose post: what is the goal? There is no point trying to write your own RNG (and this holds for 95% of quants).

stochastic process is nothing more than just a a sum of random variable (as increments). That description is not even wrong.

A bit of a preview of some topics Several chapters are devoted to FDM for 2-factor European/American options We tested the relatrve performance on spread options for the same level of accuracy: 1 Saulyev ADE : 1 second 2 Barakat and Clark 2.2 3 Yanenko 4.2 4 "Classic" ADI 4.0 (4 times slower!)...

What about energy markets? a lot of pricing, hedging and optimisation of high-factor American spread options and much more. (real optons as they are called). I imagine a lot of opportunity here, based on anecdotal evidence.

APL is is very powerful and influential language. The last time I used it was when I was teaching numerical methods to senior undetgrads at Maynooth University in 1980. It's a pity that C++ does not support its n-d data structures. APL kind of reminds me of Python Pandas. The APL keyboard was...

APL, wow!

One-liners in OOP 1. Multiple inheritance was not a good idea. C++ does not support interface keyword. The AI community used MI a lot in the 90s. 2. Not evertyhing is an object. Behavioural commonality is not structural commonality.This messes up class hierarchies. 3. Deep class hierarchies...

Anyways, fiddle-faddle language skirmishes in the last 40 years are of no consequence in the bigger scheme of things. A major blunder in the 1990s leading to the current software legacy crisis was: 1. Structured Analysis bad, OOP good (actually, I use the two since 1995 in my From Chaos to...

Back to the Future Contect Diagram very important. https://en.wikipedia.org/wiki/Structured_analysis

Absolutely! I have been waiting on this feature since 1996 but it has taken some time for the industry to realise that pure OOP is not enough!! The related analysis is called Functional Decompositon in combination with my Domain Architectures. In order to use C++ modules (I discuss them in the...

Some book updates from my own pen // PDE/FDM 2022 eBooks will publish on March 11, 2022. In store date (the date books are available at retail) is March 17, 2022...

Last but not least, like Toyota and Carlsberg , the two Quantnet C++ courses are probably the best on the planet I have been told :cool:

Thanks. I started maths in 1971 LOL. I got my 1st FEM course in 1974. I would say major blocks in my Pure maths course (analysis) are vital. Regarding numerical analysis, it is not necessary to know the theoretical stuff but more a good hands-on feeliing on how to use the methods and after...

Hi alovya, I was planning to writing up a small response offline indeed. I am not in IB or a headhunter but my focus is on learning important stuff in maths, C++,. Python. My online courses are on www.datasim.nl and I do much of everything. Have a look at your convenience and let me know if you...

It's not every day one comes across someone with FEM and computational fluid dynamics. It was an area I worked in both in academia and industry It turns out that my PhD research in 1980 could be direct;ly applied to PDE in finance. I have written up here for FDM...

Tbe best course is QN C++ but maybe wait a few year before doing it.

I get quite a few invitations in LI and sometimes when I scrolled down I can see a copy of the certiicate. That was a while back so maybe things have changed in this regard.

I second Quasar. Forking out 15K is a lot. set up a plan and a timespan and execute it.

Regading ODE/PDE courses, this course does all the ODE and PDE stuff in other generic engineering-style courses as well as finance-related topics such as popular Black Scholes, CIR, HW PDE + FDM, as well as my own research on resolving a number of misconceptions on how PDE is used in finance...

A possibility is to upgrade or learn new skills. e.g. become a professional programmer or data science. Do you use Slang etc.?

Some general remarks 1. Strengthening of maths skills is a good idea, in partricular more focus on analysis type stuff beyond linear algebra and its applications in Econometrics Some universities have ODE/PDE as prerequisite probably because they are important in their own right as well as...

"I definitely agree that the Advanced C++ course would be a great way to hone your skills. The prerequisites for the advanced course are as follows: · Proficiency in OOP, inheritance, polymorphism. · Proficiency in generic programming (C++ templates). · Deep understanding of C/C++ memory...

Out of curiosity ... are names like Calculus (1 to n) and their contents standardised in the States?

Calculus III/Vector Calculus Has the title changed on the fly? :LOL: It's Vector Calculus/Vector Analysis. Anyways, what's in a name? BTW in which courses do people learn real and complex analysis?

In my days the above Calculus III would be desribed as Mathematical Methods 231. Useful course but it is not hard analysis and I don't see it used much. Just saying. Other maths for say ML is needed.

I doubt it very much.

'better' when comparing X and Y 'best' when comparing X,Y,Z, ...

C++ is a skill and this course has evolved to its current streamlined form down all those years, It is a big skill.

Succes! Ik heb deze cursus ontwikkeld! De eerste C++ cursus ooit in NL was in Amsterdam 1990, georganiseerd door miijn bedrijf Datasim. (Hotel Americain, Amsterdam)

remember, OP has a degree in LAW. And the top US/UK MFE coursee are very quantitative. I think your post is not very accurate.

Probably not.

Any updates, Aaron? what's the landscape in 2022? @Aaron Brown

Gil Strang is probably the best maths educator around. His focus is mostly linear algebra and his videos are excellent, especially his linear algebra videos. Actually, he was PhD supervisor of my PhD supervisor, so he is my academic grandfather :) I usually write all my own stuff. My...

Black Scholes pde 101

Here are some <<detailed>> testimonials fron real students on the QN C++ Course. https://quantnet.com/threads/c-online-programming-cert-testimonials.9227/page-12 It would not be rocket science/neuro-surgery to standardise course review processes.

And writing contracts

Then you are not looking hard enough.

Which book? Have you tried Wikipedia?

Is this homework? Do you read books?

Yeah, maybe waiit 10 years to see how that ML pans out. Then you can do a PhD for fun.

You do a PhD not for the money, but because you REALLY want to. You are on your own and don't expect supervisor to be alwaay accessible. And Pay <<< prop shop. topic of deep learning/machine learning in Finance. Bleeding edge, what will ML look like in 2025?

Very interesting article.

This book is good and maybe a precursor to Shreve. https://www.amazon.com/ELEMENTARY-STOCHASTIC-CALCULUS-Statistical-Probability/dp/9810235437

That's why I prefer Glasserman .. he integrates the two approaches. Horses for courses.

Depends how you define stochastic calculus. Because you will only half understand stochastic calculus by studying theoretical SDEs. It is too one-sided; besides most SDEs don't have analytic solutions. Ideally, you need to learn Measure Theory and Lebesgue Integration as foundation. How in...

It has no numerics. Even Euler method only gets a one-line mention.

Why has no one mentioned Glasserman (2004)?

Content aside, I hate the writing style, tone, random topics. It's all over the place. It is a Molly Bloom soliloquy internal monologue but with punctuation.

It's not rocket science.

Try this line

Undergraduates nor MSc don't do "research".

I studied analisi numerica in Pavia some years ago. And I did 5 years of private lessons the hard-core way. Knowing Latin is useful. I would say it is never too late as such altho' I would recommnend to hurry up. Festina lente.

No problem. It's just native English screechers might get confused. severe lack of programming and data science/ML knowledge. These days you won't get far without them. This should be clear at this stage. I definitely need to study after my PhD. Probably too late. IMHO Why not try to embed...

small question: in the title, by "Academy" you probably mean "academia"? Academy is a highly overloaded word. Some people mighy confuse it with Hollywood.

Count me in! I can give an advanced C++ course on the way there to keep people sharp. We need a good internet connection with the TAs.

Any plans, Devon :-)

ODE Gradient Systems for Optimisation in Finance and Machine Learning, new Perspectives https://www.linkedin.com/pulse/ode-gradient-systems-optimisation-finance-machine-learning-duffy/

Here's an interesting approach: using ODEs to solve optimisation problems. High potential. // TestExp5.cpp // // Using ODEs for optimisation. The very very simplest example to show how it works in the scalar // case. // DJD // Systems? this is an execise. // // //...

非常感谢你，达菲博士。看来我应该专注于更基础的数学和统计学知识。 Thank you very much, Dr. Duffy. It seems that I should focus on more basic mathematics and statistics. Wow! Did I say that? :)

Technology changes very quickly, so keep an eye on fundamental skills. semper discendum

"Data Science" means different things to different people..

Apart from anything else, C++ is a real skill to learn. If you master it you learn _any_ programming language, for sure. For UCB, you need ODE/PDE AFAIK.

Too difficult for the average newscaster :-)

C# is great. It has a lot of similarities with C++. Good luck.

Why?

A very general remark: most CS curricula don't have the kind of maths that is needed. They probably weren't built for that. And the maths in CS tend to be discrete data structures; little pure or applied analysis. Just saying.

we need a Greek letter \nu ??

I can imagine they are fast :-)

Some random remarks I suppose the world is changing. A while back traders would have quant developers helping them with Excel addins, coffee etc. I wrote a book on C# in 2013 with Andrea Germani (Lodi, Milano) who at the time was a trader and wrote his own code. I know several traders who have...

In my book this does not prove programming ability. It is however better than multiple choice questions. Do traders need to be able to write their own (production) C++ code?

The best way to get a good grounding in programming is C++. All the other languages might be OK in places, but thy don't cut the mustard. And that's the way it is.

, C++ is often not a key aspect that is assessed in the interviews and PDE pricing even less. General programming aptitude is. What is "general programming aptitude"? Sounds fuzzy. Is it just to write prototype proof-of-concept code or at the other extreme multithreaded event-driven frameworks...

I have been to NYC but never to Pittsburgh. It probably has changed a lot since my day. All I knew is that song by Pete Seeger, BTW wasn't CMU ranked #3 for 2022?

You were probably in a "real" pure maths department..

While on the 'bathwater' analogy ... In ML PDE/FDM with C++ is often used in the training for several reasons and researchers are working on new methods such as RKHS and nd PDE for ML algos. Here is a recent thesis with interesting conclusions...

The "elephant in the room" is the issue of how to write maintainable Python programs. No one talks about it... Sapir-Whorf strikes again. I'm talking about programming as a discipline and not ad-hoc "coding" as it is sometimes called. Maybe people just accept undocumented unmaintainable code...

Yes, I know. From a career viewpoint, knowing just Python may not be enough; it is a very useful tool, like Matlab. C++ is a skill and will be here forever. If you know C++ you can get the hang of Python in a few weeks, but not the other way around. Just saying.

While the production implementation is often in C++ and written by developers, prototyping is typically done in Python. Each organisation is different but some scenarios are (let's take a pricing library) A Quant 1 creates prototype in Python Quant 2 creates production version in C++ B Quant...

yeah; rent cost 3 punt (about 5 Euro) a week and a pint of Guinness cost 18 pence.

I do, but I did my Masters in 1975 (it cost 300 punt). And in those days there was no Quantnet C++ course.

Who is 'they'?

What does a 2-year degree in maths entail? It used to be 3 or 4 years?? Maybe I'm out of touch.

AFAIR Andy has written quite a bit https://quantnet.com/threads/how-to-display-c-code-and-math-beautifully.7552/ Even then, it is possible to do LATEX stuff, bung it into a pdf and then attach that pdf in your post.

My favourite subject was FA. It has _many_ applications . Numerical analysis A-Z . Finite Element Method (FEM) with Sobolev Spaces etc. . New advances in ML w.g. RKHS https://en.wikipedia.org/wiki/Reproducing_kernel_Hilbert_space

I suppose many people are more comfortable with linear algebra than with Cauchy sequences and real/functional analysis. This state of affairs is prevalent in current mainstream ML.

IMHO better to discuss NA and NM without code (code here just diverts attention). and maybe attachment >> insert code. tip #2 use LATEX.

Are the Olympiads mostly discrete maths/CS stuff? Many algos work in continuous space. e.g. PDE, SDE Just a random sample https://www.datasim.nl/onlinecourses/101/distance-learning-applied-numerical-methods Random example: 'pure' maths with applications...

I have MSc and Phd in Numercal Analysis. It is highly mathematical and you do things from first principles. Numerical Methods entails using the results of Numerical Analysis and apply them to real life (without necessarily knowing 100% how they work.) NM is a black box I/O function call thing...

what's 'pure mathematics'? e.g. Lie Algebras, Group Theoty or a wee bit more applied? Out of curiosity 1. How many pure mathemagicians can program in C++? 2. Can pure mathemagicians make the transition to algorithm? The "software" you learn in university is nothing like what you need later on...

Ok random question Do you know C++11, 14, 17, 20? I don't do interviews but if I did.... Compare your knowledge with the syllabus here https://quantnet.com/cpp/ or here https://quantnet.com/advancedcpp/ Without a degree, your background would be an unknown variable. Just saying. // If...

It comes from uni, and self studies, which all came before smart pointers where a thing. In general, I am not at all impressed with how in general many universities do C++ training. Self-study is not always optimal e.g. plucking silly examples from internet. The QN course has 10 well-defined...

BTW do you know that I provide C++ code for purchasers of the book? BTW I have an upcoming PDE/FDM book laying the foundations for the maths part of the C++ book...

financial firms going wild to hire C++ developers yes? edit: If I were in your role/position in general, I would have C++ and Python in my toolbox.

I am not able to say if C++ will get you a job in London, Maybe, it depends. Do you know finance? some C++ experience Can you quantify that? My 2nd edition may or may not be too advanced. A C++ programmer has no problems learning Java. The other way around is trickier (Java protects you from...

The Tory Brexiters are great ones for meaningless buzzwords World-class scientists Trading nation We was tricked by those EU negotiators etc.

How to? BitMatrix, ByteMatrix std::{bitset, byte} Advantages?

NYC $2200 p/m... cheaper than Dublin or Amsterdam..

Always good to think of problems up front. Otherwise it's a solution looking for a problem. http://tvmet.sourceforge.net/introduction.html

What are the applications in finance for fixed-size matrices?

C++ header files are .hpp

You're welcome. I have no idea of what GRE is :) We didn't have it in my day. Will you watch the rugby match IRL-NZ this weekend. (kiwi?)

C++ is important. Baruch for example has it as a prerequisite AFAIK. Apart from anything else, it is a useful skill to have and it kind of proves programming ability. You never know what the future brings. For UCB, one course needed is ODE/PDE, for example this...

the notation m << .. is kinda non-standard and a bit weird. See how Python does it. And Boost uBLAS. C++ initialisation https://en.cppreference.com/w/cpp/language/initialization

https://en.cppreference.com/w/cpp/algorithm

Is there not a standard STL algorithm? A while loop with nested if else might be 1) slow, 2) shaky/flaky, 3) difficult to maintain. e.g. arrays of length 1'000'000, exception handling etc. It looks like reinvention of wheel. It means less time for 'bigger' stuff. BTW what's a good rationale...

@APalley @Andy Nguyen

Exsan, how does your work compare to similar stuff in Boost Intrusive https://www.boost.org/doc/libs/1_77_0/doc/html/intrusive.html

Concepts are the heaviest addition, and are really a paradigm shift. Indeed, but once you get the hang of it it becomes easier. I have lots of practical examples. Really exciting. It's all got to do with deciding at which (meta) level to define and subsequently, use "things". // Interface...

C++20 as well!

Apart from anything else, I suppose programming skills in C++ and Python would do no harm.

Hard to say. The requirements are not precise enough. It's a huge area. Try looking 1. Glasserman 2004 Monte Carlo Methods 2. Duffy and Kienitz 2009 Monte Carlo Frameworks in C++. These kinds of questions have been on QN for years now, some would say ad nauseam.

I took a random sample "formulate, use and analyze the main numerical methods for stochastic differential equations, based on Monte Carlo stochastics and partial differential equations," Wow. It could mean anything. It is not specific enough. "The second one is computational methods for...

That's wasn't my question, really. Github is basically a disk. Not all organisations take this approach. Don't see pacemaker/medical software in this way any time soon.

physics / pure maths backgrounds: IMO more experience with numerical+applied maths is much better. And real programmng (I don't mean coding) skills.

"I found my Theoretical Physics (TP) program at Edinburgh fantastic: It was incredibly tough going, but as Daniel Duffy mentioned had little or nothing to do with finance." Maths is useful in finance, TP uses maths ==> TP is useful in finance? Just asking. BTW what stuff from TP was most...

Thanks for the feedback. Regarding courses, there are various options depending on what your requirements are. We can discuss by email if you like. There is also a student discount scheme. I am also the originator of QN C++ course that I recommend if you wish to learn C++ for your job.

Would the average Dutch national want to emigrate to Australia? It's so far away. Just saying.

What happens if someone has to modify or debug this code?

int xx = 2; int yy = xx++*++xx; int xx2 = 2; int yy2 = --xx2-++xx2; std::cout << "yy, yy2: " << yy << "," << yy2 << '\n';

Code is undocumented :-)

I am beyond retirement age and no plans to retire (BTW I can't be fired). Looking back on many gov schemes (at least one was officially PONZI) I can say without reservation that they are out to fleece me,

And when you get a pension, it is taxed with your other income.

This is a great exercise; put on your thinking cap! First, you have to understand the problem. After understanding, make a plan. Carry out the plan. Look back on your work. How could it be better?

KKOP is excellent, also for PDE. One of the best! For the rest, I cannot say; it is a combination of > 20 books, articles and my own work down the years ;) piques my interest the most My forthcoming PDE/FDM does it all :coffee:

What;'s the goal/rationale in studying this book? there are 100s of books on PDE, many are focused on wave/hyperbolic equations. It's looks OK (feels a bit 60s, nothing wrong with that) but is typically what 2nd year applied maths undergrads do. And ODE -> PDE -> comp finance is a better path...

Do you have the link to Strauss, please?

Good luck.

This book looks kind of interesting as an application area of probability. https://www.amazon.co.uk/Numerical-Probability-Introduction-Applications-Universitext/dp/3319902741

In an attempt to predict the future, a good knowledge of probability and measure could be a prerequisite for Functional Analysis and Machine Learning applications. Would Leonhard Euler be a C++ programmer were he alive today? Imagine implementing Euler's method?

Sure :-) dduffy@datasim.nl

Quasar is not the first to have issues with understanding measure theory and its applications to finance. My understanding of the mismatch between theory and practice is caused by: 1. Authors tend to be pure mathematicians who seem to have little interest in/knowledge of the applied and...

ODE Gradient Systems for Optimisation in Finance and Machine Learning, new Perspectives ODE Optimisation, initial remarks Daniel J. Duffy 2021-9-24 ** More to come.. a lot of research opportunities .. Few are acquainted with these techniques. We include some references on methods to solve...

Maybe book by Sean Dineen? https://www.amazon.com/Probability-Theory-Finance-Mathematical-Black-scholes/dp/0821894900/ref=sr_1_3?dchild=1&qid=1632486404&refinements=p_27%3ASean+Dineen&s=books&sr=1-3#customerReviews

Cheap at half the price, is it serious .. 25.95 Euro for a chapter???? BTW wasn't this topic already discussed here several times?

You don't say.

You mean, like these Illinois lads?

What kinds of specific roles did you have in those 17 years? Are you a decent programmer? How's the maths savvy? And .. what's the interest in finance?

I (external) supervised quite a few MSc theses there until recently. Some very good students. See 2019 2020 Blogs on www.datasim.nl for several theses. https://www.datasim.nl/blogs/26/msc-theses-on-machine-learning-and-computational-finance-2019...

Have you looked at University of Birmingham?

Maths is not about doing exams and jumping through hoops. Maths is about learning and doing stuff.

And good programming skills (C++, Python,..)

fairly good undergraduate in economics contains enough math depends

To be a "quant" a decent knowledge of maths and programming is needed. The "maths" in Economics is probably not enough.

Princeton has a good reputation.

Yes, I'm in the lap of luxury. Maybe Boost Process (heavyweights tasks)? https://www.boost.org/doc/libs/1_76_0/doc/html/process.html

Like judo = std::list<technique> technique == get it work -> get it right -> get it optimised

Newbie question.. https://onlinelibrary.wiley.com/doi/epdf/10.1002/wilm.10647 absolutely in C++11. threads, tasks and futures. Discussed in my C++ 2018 book and QN Advanced C++ course. Recommend doing some research. // Just got an 8-core machine today. What can I in heaven's name use it for...

I'm sure you will learn a lot here. Actually, I taught C++ to WBS finance students in 2019/early 2020. Good luck. // R (and Matlab!) is too simplistic for maths people. It is more of a tool for MBA. C++ and maths are a more natural mix.

Welcome. BTW did you have any exposure to C++ at Warwick?

Prego :cool:

6th word, 1st sentence?

You want to live life in the fast lane, what?

You could start by basing the course on my numerous books in this area. www.datasim.nl BTW my PDE book will soon be published. I have lots of project suggestions. To date, I have been external supervisor for roughly 40 MSc thesis for UK/US universities...

"Quant role" is a wide concept.

https://en.wikipedia.org/wiki/Hedge_(finance)

Given that I live in the UK (London) and the educational system is far behind the US one In what sense?

I have originated the following (BTW I also originated Quantnet C++ courses). They are online, hands on and exams/certificate. There are focused on finance and have more depth and breadth than university offerings I give student prices. https://www.datasim.nl/onlinecourses...

I used this for Basic in GE in a special room; it was deafening

I use UNICOMP model M classic. It's great. I got from a quant... his colleagues found it too noisy, the keyboard, not the quant.. https://www.theverge.com/22369731/unicomp-mechanical-keyboard-new-model-m-review-price

OLS can tolerate observation errors in y only but not in x. If x has observation errors, then we need ODR https://en.wikipedia.org/wiki/Deming_regression#Orthogonal_regression https://docs.scipy.org/doc/scipy/reference/odr.html

here is the slide show of my talk next Wednesday. https://www.datasim.nl/application/files/1416/2964/2727/PDE_and_FDM_in_Computational_Finance_25_August_2021OFFICIAL.pdf

If I were in such a position in my career. I would do both C++ and Python are a good combination. It is an investment in your future career. If you make the time and have a few quid to spare it is what I would do.

Small remark on new(?) C++ behaviour. Interesting to see how legacy code reacts. Seems that the C++ compiler reacts differently these days to template protected data t; if you want to directly access t in derived class you must use this->t (BTW for concrete types you can get away with just...

float x = 0.1; x -= 0.1; double y = 0.1; y -= 0.1; std::cout << "x, y: " << x << "," << y << '\n';

Nope https://en.wikipedia.org/wiki/Ordinary_least_squares https://en.wikipedia.org/wiki/Gradient_descent

And the right way to do OOP inheritance, no silly classes for cats and dog, woof(), miaow()

Unfortunately, self-taught or university style is sub-optimal in this case. In my case, I was the first C++ programmer in the Netherlands in 1989.

My rough guess is at least 8 hours per week is necessary. I am the originator so my estimate does not include the upper limit (in theory 24/7 :)). decent C+ background This could mean anything, big spread. Most institutes I've seen are far behind the QN C++ course (which is based on 30 years...

25 August 2021 https://www.linkedin.com/events/6833423790865715200/ Thalesians Partial Differential Equations (PDEs) and Finite Difference Method (FDM) for Computational Finance Daniel J. Duffy, Datasim In this talk we give an overview of the numerical solution of PDEs using finite...

C++ Nostalgia. In the old days there was no string class. Here's how we did it. You can run the "1992" code. // // dynstr.hxx // // This class creates and manipulates variable length character strings. // // (C) Copyright Datasim BV 1992-1995 // // The information contained in this file is...

You are welcome. These 2 books together discuss it all PDE and FDM. BTW for 2018 C++ book, email me for source code when purchased.

The Quantnet C++ course is good preparation indeed. You won't have too many problems. Good luck! BTW you might like to know that my new PDE book will be published in a few months.

I have not tried it myself because in general PDE/Finite different models are much better. Having said that, lattice methods for American equity options are good. Is it not a barrier option?? I was told that Vasicek on a tree is a terrible choice of model implementation and that one should...

Thank you. I wrote that article 10 years ago. The nice thing now is that threads (and tasks!) are supported in C++11 and porting code is more or less changing namespace boost to std.

When students say "calculus" a question could be to explain (construction of) Riemann, Lebesque and {Riemann, Lebesgue} Stieltjes integration and compute them by hand on let's say the function f(x) = 4x(1-x) using pencil and paper. These are very concrete questions. Seeing how there are used...

C++20 has it.

Unfortunately, it's the way you are saying it that gets me, It is incorrect and naive. But that's my experience and opinion. Try to tone it down a bit and be more factual. Anyhoo, no problem.

here's another great tip for Quasar and everyone 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...

Many politicians are like that..

It's funny, but I can't remember ever getting good ideas sitting behind a laptop. Usually, ideas come at random moments and places. Like Eureka?

Your interpretation of my words. I am asking a simple question. I am not taking about outsourcing, more about software products. I looked up Yandex .. it's registered in Schiphol (Amsterdam) as an NV (anonymous company) as we call it in NL. Turnover in 2014 was quite modest. I wouldn't call it...

@ptf You also wrote this, which is a bit strange According to some research billions of dollars are due to fact of memory leak in C/C++, which requires very high skill on the developers. When it comes to quantitative finance, same thing. No matter how many good students you teach, they make...

Which C++20 (trendy) syntax are you using? Most is C++11. Just saying. Please post the code as an attachment so that the QN members can experiment with the code. Many are up to speed with C++11 and beyond (including myself ):ninja:

“The first rule of discovery is to have brains and good luck. The second rule of discovery is to sit tight and wait till you get a bright idea.” George Pólya

relevant example Compute implied volatility using . Newton . Banach . Aitken Compare .. These in my 2018 C++ book.

Even for M = 1.0e+9 etc. it will be a challenge for methods that use derivatives. It is like a boundary/internal layer problem SHGO is a global optimiser that finds all roots. https://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.shgo.html It's very easy to use. from...

For example. and 1) several roots, 2) no roots are possible.

Another way to solve fixed point x = g(x) is to solve it as a least-squares minimisation problem min (x - g(x))^2. And use favourite optimiser.

QN C++

Do you already know C++11? or even C++03?(?) BTW C++17 is only a stepping stone to C++20. TBH I don't think you are ready. It's like judo white>yellow->orange->green->blue->brown->black and you in C++ terms? You can do all these algos in C. Or Python.

A nice feature of fixed point/contraction theorems is they converge for any initial guess in contrast to say Newton's method.

https://www.datasim.nl/onlinecourses/97/distance-learning-ordinary-and-partial-differential-equations https://www.datasim.nl/testimonials And my new PDE/FDM book for finance will be out on a few months (Wiley) My course is accredited by at least one major university. This course is the only...

and experimentally.

Now, the icing on the cake: solve x^2 = 2 by fixed point theorem and measure (monotonic!) convergence. Linear. https://en.wikipedia.org/wiki/Aitken%27s_delta-squared_process

https://en.wikipedia.org/wiki/Banach_fixed-point_theorem

I have created a video on C++20 here (BTW I am the originator of these courses) Blogs - Videos :: Datasim If you are serious, C++ Concepts are a big deal. Watch this space.

https://www.efinancialcareers.co.uk/news/2021/07/modern-c-finance-jobs?utm_source=GLOBAL__ALL_ENG&utm_medium=SM_LI&utm_campaign=ED_NEWS Python has become a necessary language to learn if you want a job in finance. However, while students everywhere are becoming minor Python coders, the fact...

so, a user error?