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Cuchulainn
Posts: 20250
Joined: July 16th, 2004, 7:38 am
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Re: Is the type of mathematics found in finance limited?

July 15th, 2018, 11:02 am

Any concrete suggestions for alternative maths or just grumbling?
By the way, nobody cares about derivatives pricing any more, another PDE for fixed income.... yawn!
At least if it were a different PDE...but it's the same one every time. (There is the nonlinear wave equation model...Epstein & Wilmott...that's more interesting!)
A number of articles on UVM appeared in Wilmott.
and ... the same old FDM ... aka CN and ADI
 
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Paul
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Joined: July 20th, 2001, 3:28 pm

Re: Is the type of mathematics found in finance limited?

July 15th, 2018, 11:05 am

This one has no diffusion.
 
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Gamal
Posts: 1284
Joined: February 26th, 2004, 8:41 am

Re: Is the type of mathematics found in finance limited?

July 15th, 2018, 11:06 am

By the way, nobody cares about derivatives pricing any more
That's it. All or practically all is done. Banks will still employ IT guys to maintain the software and the research will move where it belongs - to the university. There are many proffessors in control theory who know nothing of control, they will make a perfect company for professors in derivatives pricing who know nothing of derivatives.
What we've experienced for the last 20+ years was the second Manhattan Project, an exception, not the rule. We should be grateful for being there but it's over.
 
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TinMan
Posts: 21
Joined: September 21st, 2006, 9:42 am

Re: Is the type of mathematics found in finance limited?

July 15th, 2018, 11:14 am

By the way, nobody cares about derivatives pricing any more
That's it. All or practically all is done. Banks will still employ IT guys to maintain the software and the research will move where it belongs - to the university. There are many proffessors in control theory who know nothing of control, they will make a perfect company for professors in derivatives pricing who know nothing of derivatives.
What we've experienced for the last 20+ was the second Manhattan Project, an exception, not the rule. We should be grateful for being there but it's over.
True.  So I don't see the substance to bemoaning the maths as being boring.  UVM??  Nobody cares.  FDM??, this is just an implementation, nothing new to do here.  I can't believe people are still churning out papers on the same old things, obviously the finance schools can't do anything else. 
If someone has an interesting model to apply to a finance problem let's hear it.  But if it's another pricing equation or numerical scheme, nobody cares! 
 
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Cuchulainn
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Joined: July 16th, 2004, 7:38 am
Location: 20, 000

Re: Is the type of mathematics found in finance limited?

July 15th, 2018, 11:46 am

It's inertia, I suppose. Replacing pricing libraries by new stuff ...

I can appreciate you want new stuff but you don't say why.. Paper models are probably the easy part but you have to get them into a computer.

Seriously, if you are bored it might be time to find a new vocation and go with the flow. Tempus fugit. 

Maybe AI? There again, everyone is doing it?
 
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Gamal
Posts: 1284
Joined: February 26th, 2004, 8:41 am

Re: Is the type of mathematics found in finance limited?

July 15th, 2018, 12:18 pm

When your own teeth are rotten you replace them with artifficial ones. The same with intelligence.
 
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Cuchulainn
Posts: 20250
Joined: July 16th, 2004, 7:38 am
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Re: Is the type of mathematics found in finance limited?

July 15th, 2018, 12:39 pm

When your own teeth are rotten you replace them with artifficial ones. The same with intelligence.
Most people go to the dentist's every 6 months for periodic checks.
 
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Gamal
Posts: 1284
Joined: February 26th, 2004, 8:41 am

Re: Is the type of mathematics found in finance limited?

July 15th, 2018, 12:55 pm

I know, it's worse with intelligence.
 
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TinMan
Posts: 21
Joined: September 21st, 2006, 9:42 am

Re: Is the type of mathematics found in finance limited?

July 15th, 2018, 1:03 pm

It's inertia, I suppose. Replacing pricing libraries by new stuff ...

I can appreciate you want new stuff but you don't say why.. Paper models are probably the easy part but you have to get them into a computer.

Seriously, if you are bored it might be time to find a new vocation and go with the flow. Tempus fugit. 

Maybe AI? There again, everyone is doing it?
Banks are not interested in replacing pricing libraries.  I didn't say I want new stuff, just challenging those who think we should be using other mathematical tools to suggest something concrete, not hand wave and waffle.
Finance is not a vocation, if someone has a better way to solve a problem let's hear it. 
Tinkering with numerical schemes doesn't qualify.
 
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Paul
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Joined: July 20th, 2001, 3:28 pm

Re: Is the type of mathematics found in finance limited?

July 15th, 2018, 2:26 pm

Agree that tinkering with numerical solutions doesn’t count.

Doesn’t have to be valuation! There are many things to quantify, optimize,...

The crucial role of randomness does rather lead to diffusion...undortunately.
 
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Cuchulainn
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Joined: July 16th, 2004, 7:38 am
Location: 20, 000

Re: Is the type of mathematics found in finance limited?

July 15th, 2018, 3:00 pm

For simple linear PDEs up to 2 factors  then simple numericals such as ADI and Crank-Nicolson are OK.
 
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katastrofa
Posts: 7440
Joined: August 16th, 2007, 5:36 am
Location: Alpha Centauri

Re: Is the type of mathematics found in finance limited?

July 15th, 2018, 5:03 pm

Any concrete suggestions for alternative maths or just grumbling?
By the way, nobody cares about derivatives pricing any more, another PDE for fixed income.... yawn!
I do simulations of microdynamics of systems of higher complexity than markets. Handling such problems requires a lot more mathematical and statistical analysis than coding. People tried to use PDE for similar purposes, but they failed.
 
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Cuchulainn
Posts: 20250
Joined: July 16th, 2004, 7:38 am
Location: 20, 000

Re: Is the type of mathematics found in finance limited?

July 15th, 2018, 5:49 pm

PDEs were not designed for high-dimensional problems. If they were, Lagrange would have done it years ago. It is trivial to write an n-d PDE on paper. Unfortunately, PDEs are not played on paper but on a computer, with lots of 'tinkering' before it really works. And we know all of you know.
Here is an article that claims it can solve 100 dimensional pdes using ML, BP etc. I find it inconceivable ..
https://arxiv.org/pdf/1706.04702.pdf
 
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Cuchulainn
Posts: 20250
Joined: July 16th, 2004, 7:38 am
Location: 20, 000

Re: Is the type of mathematics found in finance limited?

July 15th, 2018, 6:55 pm

By the way, nobody cares about derivatives pricing any more
That's it. All or practically all is done. Banks will still employ IT guys to maintain the software and the research will move where it belongs - to the university. There are many proffessors in control theory who know nothing of control, they will make a perfect company for professors in derivatives pricing who know nothing of derivatives.
What we've experienced for the last 20+ was the second Manhattan Project, an exception, not the rule. We should be grateful for being there but it's over.
True.  So I don't see the substance to bemoaning the maths as being boring.  UVM??  Nobody cares.  FDM??, this is just an implementation, nothing new to do here.  I can't believe people are still churning out papers on the same old things, obviously the finance schools can't do anything else. 
If someone has an interesting model to apply to a finance problem let's hear it.  But if it's another pricing equation or numerical scheme, nobody cares! 
You've been on Wilmott since 2006. How come it is only now that you are starting to speak your mind?

Just curious..what's the 'trigger' as it were?
 
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TinMan
Posts: 21
Joined: September 21st, 2006, 9:42 am

Re: Is the type of mathematics found in finance limited?

July 15th, 2018, 7:33 pm

Eh?  I have spoken my mind plenty of times.  Why can you not stay on the subject?
Put up or shut up guys, forget the snarky comments about AI, forget waffling about FD schemes, what interesting maths should we be using? What problem can you solve differently?