Differential Equations With Forex! | Forex Factory

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Differential Equations With Forex!

  • #1
  • First Post: Nov 1, 2007 6:51pm Nov 1, 2007 6:51pm
How Can Stochastic Differential Equations Be Applied To Forex?

I Took This Class And Didn't Realize That Black-sholes Formulas Are All Differential Equations. I Did Some Reseach On Differential Equations And Prices, And Only Found That These Equations Are Used In Options.................is Anyone Using Differential Euqations Solutions To Anything Related To Forex?
  • #2
  • Edited 6:22pm Nov 2, 2007 6:04pm | Edited 6:22pm
The Black-Scholes PDE describes how the value of the option varies with respect to the price of the underlying instrument and to time. One of the assumptions of the Black-Scholes model is that the price follows a geometric Brownian motion. What this basically means is that the model assumes that the movement of the price is random and therefore unpredictable. As a trader, what you want is a DE that describes how price varies with respect to time. As far as I know, there is no such DE.
Domo Arigato, Mr. Roboto!
  • #3
  • Nov 3, 2007 2:02am Nov 3, 2007 2:02am
Even if some were using DE's actively, you would not understand how to apply them without some serious mathematical background (graduate level mathematics).

There is a fair amount of research into SDE's. However, depending on how you think the market is structured the approaches can be very different.

Even if one were to come up with a reasonable model, it would still be subject to the problems inherent with such systems of equations, namely chaos. These functions usually exhibit poor mathematical convergence, and a very sensitive to their initial conditions. So while thy may provide good simulation tools or insights, market forecasting is no walk in the park.

Another aspect of these equations is that they rarely have any closed form solution, so it's not like you can just pump in a bunch of numbers and get out an answer. Numerical methods must be applied, and they can be quite computationally expensive.

It is an active area of research however.

~X~
  • #4
  • Nov 3, 2007 3:24am Nov 3, 2007 3:24am
Quoting Xyrus
Even if some were using DE's actively, you would not understand how to apply them without some serious mathematical background (graduate level mathematics).

There is a fair amount of research into SDE's. However, depending on how you think the market is structured the approaches can be very different.

Even if one were to come up with a reasonable model, it would still be subject to the problems inherent with such systems of equations, namely chaos. These functions usually exhibit poor mathematical convergence, and a very sensitive to their initial conditions. So while thy may provide good simulation tools or insights, market forecasting is no walk in the park.

Another aspect of these equations is that they rarely have any closed form solution, so it's not like you can just pump in a bunch of numbers and get out an answer. Numerical methods must be applied, and they can be quite computationally expensive.

It is an active area of research however.

~X~

So,

The only thing that does cover chaos is co-integration strategy?

If you make matlab software estimate equation for a curve and apply that equation to and SDE, can a solution be found? I want to implement this in matlab only.
  • #5
  • Nov 3, 2007 3:27am Nov 3, 2007 3:27am
Quoting Xyrus
Even if some were using DE's actively, you would not understand how to apply them without some serious mathematical background (graduate level mathematics).

There is a fair amount of research into SDE's. However, depending on how you think the market is structured the approaches can be very different.

Even if one were to come up with a reasonable model, it would still be subject to the problems inherent with such systems of equations, namely chaos. These functions usually exhibit poor mathematical convergence, and a very sensitive to their initial conditions. So while thy may provide good simulation tools or insights, market forecasting is no walk in the park.

Another aspect of these equations is that they rarely have any closed form solution, so it's not like you can just pump in a bunch of numbers and get out an answer. Numerical methods must be applied, and they can be quite computationally expensive.

It is an active area of research however.

~X~

So,

The only thing that does cover chaos is co-integration strategy?

 

  1. If you make matlab software estimate equation for a curve and apply that equation to and SDE, can a solution be found? I want to implement this in matlab only.

  • #6
  • Nov 4, 2019 12:42pm Nov 4, 2019 12:42pm
Differential equation for continuous waves (difference equation for discrete systems) can be applied to any represented wave.
the final solutions or compact formulas are simplified by using some transforms like Fourier or Laplace or Z-transform.

if you open any related nooks, usually in engineering field , you may realize when to use these methods.
each day 10%,,,, https://www.forexfactory.com/thread/1371538
  • #7
  • Last Post: Nov 5, 2019 12:35pm Nov 5, 2019 12:35pm
I will put some examples related to forex markets, using any "available shape", including price itself.
each day 10%,,,, https://www.forexfactory.com/thread/1371538
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