When looking through papers and online calculators I only find reference prices for Black's model not Vasicek's. My fixed income code is here. My tree algorithm is here.

Statistics: Posted by pfds — Yesterday, 12:57 pm

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And gamers are 50 years younger than us.

Cuch, now I am ashamed to be a boss at world of warships :(

Statistics: Posted by JohnLeM — February 20th, 2017, 3:52 pm

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Coming back from vacations, I started reading the posts I missed. Some first ideas :

1) The test suggested by Alan is quite interesting. I think it is a good benchmark for stochastic volatility PDE solver, even if I am not a specialist.

2) We should maybe start writing down a small article, integrating all PDE technologies wishing to compete. I will start writing down the first ideas. @Alan or @Paul, could Wilmott site be a recipient for this article ? Could you advise me to organize ourselves for sharing repository facilities ?

3) Since my methods are more experimental than yours, I will probably have to work harder than you to produce results. Thus I will probably have to convince internally to invest some time on this problem first. Note that I don't expect my solver to win the competition : as explained to Cuch, FD techniques should be more advantageous to use for 2-D problems than mine.

A repository to share things is an excellent idea, but I am not knowledgeable about those. Some may want to share codes, and some may not, but at a minimum it could be a place to share data and results more efficiently than in a thread. I suspect outrun may have some ideas?

Statistics: Posted by Alan — February 20th, 2017, 3:37 pm

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Billy7 wrote:Laptop CPU by any chance? It can easily make a difference of a factor up to 3! I find it funny how gamers (you know, kids playing video games!) usually have much higher spec laptops/desktops than people like us here!

Youth is wasted on the young.

Ain't that true...

Statistics: Posted by Billy7 — February 20th, 2017, 2:42 pm

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Laptop CPU by any chance? It can easily make a difference of a factor up to 3! I find it funny how gamers (you know, kids playing video games!) usually have much higher spec laptops/desktops than people like us here!

Youth is wasted on the young.

Statistics: Posted by Cuchulainn — February 20th, 2017, 2:17 pm

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Statistics: Posted by Billy7 — February 20th, 2017, 2:13 pm

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Laptop CPU by any chance? It can easily make a difference of a factor up to 3! I find it funny how gamers (you know, kids playing video games!) usually have much higher spec laptops/desktops than people like us here!

Yes, but that's not the point. Double Sweep needs less operations than Thomas, by any computer.

And gamers are 50 years younger than us.

Statistics: Posted by Cuchulainn — February 20th, 2017, 2:06 pm

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IMO GARCH should be put into another new thread as it has nothing much to do with John's original theme.

A proposal to split this thread has already been posed. So, let's do it!

Statistics: Posted by Cuchulainn — February 20th, 2017, 1:41 pm

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A micro optimiser regarding Godonov Double Sweep vs Thomas (ADI)

Where is this from, do they mention the CPU used, coding language, any parallelism etc?

Anyway, this is slightly different from Alan's "project" I think, which is to efficiently calibrate to GARCH using whatever ingredients work. It could be interesting to benchmark different PDE solvers in a separate topic maybe, in 1(BS) and 2D(Heston/GARCH), run some random tests as I did for the GARCH solver and and then compare average precision/runtime ratios. Also check delta/gamma. But first let's see some more numbers!

Statistics: Posted by Billy7 — February 20th, 2017, 1:24 pm

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Billy7 wrote:Well it would be funny if we end up using my solver, but I think that if Cuchulainn does his ADE and makes it robust with his bag of tricks like exponential fitting, it should probably be faster than my solver. But even so it would please me if my solver is tested by Alan and is proven robust and fast enough for calibration purposes.

For other PDE, the Saul'yev ADE is the fastest IMO. For UVM problems it is 40% faster than the most optimised Crank Nicolson method. With ADE we do not have to solve tridiagonal systems.

ADE is also suitable for nonlinear PDE and is easily parallelised (the Barakhat ad Clark version at least).

.

I have not yet done it for Heston. But it is on the cards but I want to finish a general PDE framework and document it! At this stage I am more concerned with the maths and numerics.

.

I reckon your method is ADI with Craig Sneyd style?

https://www.wilmott.com/wp-content/uplo ... 18_ade.pdf

Update: to quantify the lowest common denominator, I benchmark the 1 factor heat PDE and compare Crank Nicolson, ADE Saul'yev originale, ADE B&C.

ADE Saul'yev is fastest (3-4 times faster than CN, twice as fast as ADE B&C).

ADE B&C is [1.3, 2] times as fast as CN with comparable accuracy

BTW I am using Double Sweep for CN as it is ~20% faster than the Thomas algorithm.

Statistics: Posted by Cuchulainn — February 20th, 2017, 10:58 am

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Cuch and Alan both have a lot of experience collaborating on this website...and leading to interesting published work!

Statistics: Posted by Paul — February 20th, 2017, 9:03 am

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1) The test suggested by Alan is quite interesting. I think it is a good benchmark for stochastic volatility PDE solver, even if I am not a specialist.

2) We should maybe start writing down a small article, integrating all PDE technologies wishing to compete. I will start writing down the first ideas. @Alan or @Paul, could Wilmott site be a recipient for this article ? Could you advise me to organize ourselves for sharing repository facilities ?

3) Since my methods are more experimental than yours, I will probably have to work harder than you to produce results. Thus I will probably have to convince internally to invest some time on this problem first. Note that I don't expect my solver to win the competition : as explained to Cuch, FD techniques should be more advantageous to use for 2-D problems than mine.

Statistics: Posted by JohnLeM — February 20th, 2017, 8:57 am

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It shows that momentum like proper velocity has no upper limit,....

Combining with my findings here I get a maximum limit also on the proper velocity. For example for an electron we get a maximum proper velocity of

\begin{equation}

W_{max}=c\frac{\bar{\lambda}_e}{l_p}\sqrt{1-\frac{l_p^2}{\bar{\lambda}_e^2}}\approx c\frac{\bar{\lambda}_e}{l_p}\approx c\frac{3.861593\times10^{-13}}{1.616199\times10^{-35}} \approx 7.162957\times 10^{30} \mbox{ m/s}.

\end{equation}

That is an incredible number, but far from infinite.

A Maximum Limit on Proper Velocity

Approximately size of error by standard physics for maximum proper velocity of electron:

\begin{equation}

\frac{\infty-7.162957\times 10^{30}}{ 7.162957\times 10^{30}} \approx \infty :-)

\end{equation}

Statistics: Posted by Collector — February 19th, 2017, 11:52 pm

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