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Mathematical Relationship between Forex pairs

  • #41
  • Dec 21, 2020 3:37am Dec 21, 2020 3:37am
I still will need a mathematical formula that can extract the value of each currency from the currency pairs.
Take these previously mentioned pairs as an example
eud/usd=a
usd/cad=b
eur/cad=c

Can we calculate the value of the eur and the cad and the usd at these a,b,c price levels?

Here the equations are rearranged:
eur=a*usd
usd=b*cad
eur=c*cad

Three unknowns and 3 equations. when i solve for any of eur or cad or usd, the result is nonsensical. So, is there another way to find usd, eur and cad?
  • #42
  • Dec 21, 2020 3:55am Dec 21, 2020 3:55am
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  • #43
  • Dec 22, 2020 7:18am Dec 22, 2020 7:18am
Quoting scalprobot
{quote} Does anybody know how to calculate the values for the currencies? JPY = 0.013634646434 NZD = 1.116199342 EUR = 1.820593234 GBP = 2.528542042 CHF = 1.6764157 CAD = 1.25116823 AUD = 1.193440337 USD = 1.647033311
In my opinion, those values are useless even if you know how to calculate it. Price changes over time and when the price changes those coefficient are also changed.
  • #44
  • Mar 13, 2021 9:38am Mar 13, 2021 9:38am
Quoting DragonChaser
This way we are identifying the relationship among the 8 major pairs and their relationship will be independent of time.
Yes, that right. Are you still involved in this?

Quoting DragonChaser
I still will need a mathematical formula that can extract the value of each currency from the currency pairs. Take these previously mentioned pairs as an example eud/usd=a usd/cad=b eur/cad=c Can we calculate the value of the eur and the cad and the usd at these a,b,c price levels? Here the equations are rearranged: eur=a*usd usd=b*cad eur=c*cad Three unknowns and 3 equations. when i solve for any of eur or cad or usd, the result is nonsensical. So, is there another way to find usd, eur and cad?
The "price" for each currency can be done in a lot of ways. I´ve done it with all majors pairs and obtain USD "price" and after that I get other prices.
  • #45
  • Mar 14, 2021 12:37pm Mar 14, 2021 12:37pm
Ive tried to build algorithms to see the Range, Correlation and over all relationship for years. I finally built my own basket analyzer to see the visual relationship as an aid to build an automated system. Its a real challenge to see the nuances in pairs.
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  • #46
  • Mar 24, 2021 4:37pm Mar 24, 2021 4:37pm
Quoting Zigiman
{quote} Yes, that right. Are you still involved in this? {quote} The "price" for each currency can be done in a lot of ways. I´ve done it with all majors pairs and obtain USD "price" and after that I get other prices.
Zigiman, message me.
  • #47
  • Mar 26, 2021 4:05am Mar 26, 2021 4:05am
Mathematician, send me a PM.

Regards
  • #48
  • Mar 31, 2021 12:49pm Mar 31, 2021 12:49pm
Quoting DragonChaser
{quote} Zigiman, message me.
I would like to, but I can't I don't have a permission. Still a "new member" on FF. I've filled my e-mail into my website information. Please visit my profile a contact me via e-mail, then I will delete my e-mail from FF.
  • #49
  • Apr 1, 2021 9:35pm Apr 1, 2021 9:35pm
Quoting Zigiman
{quote} I would like to, but I can't I don't have a permission. Still a "new member" on FF. I've filled my e-mail into my website information. Please visit my profile a contact me via e-mail, then I will delete my e-mail from FF.
my skype ID is chasingdragons
  • #50
  • Apr 5, 2021 6:36am Apr 5, 2021 6:36am
Ok guys, suppose we can determine the currencies(NOT currency pairs) that are weak or strong relative to each other in percentage value, how can we use the percentage value to determine the oscillation of the currency about its fair value?
  • #51
  • Apr 7, 2021 11:27am Apr 7, 2021 11:27am
Quoting DragonChaser
Ok guys, suppose we can determine the currencies(NOT currency pairs) that are weak or strong relative to each other in percentage value, how can we use the percentage value to determine the oscillation of the currency about its fair value?
The only method to do this is by the transformation of Huang Lee Jon.
  • #52
  • Apr 7, 2021 1:51pm Apr 7, 2021 1:51pm
Quoting mirko2017
{quote} The only method to do this is by the transformation of Huang Lee Jon.
I don't understand what you are saying
  • #53
  • Jan 31, 2022 10:40pm Jan 31, 2022 10:40pm
Quoting alphaomega
Something cool on this topic! https://www.youtube.com/watch?v=p8MqhRAom_s
The normal price feed from the broker platform will not yield this graph. So, what are the scales used on each of the axes?
  • #54
  • Feb 20, 2023 11:26pm Feb 20, 2023 11:26pm
Quoting DragonChaser
I still will need a mathematical formula that can extract the value of each currency from the currency pairs. Take these previously mentioned pairs as an example eud/usd=a usd/cad=b eur/cad=c Can we calculate the value of the eur and the cad and the usd at these a,b,c price levels? Here the equations are rearranged: eur=a*usd usd=b*cad eur=c*cad Three unknowns and 3 equations. when i solve for any of eur or cad or usd, the result is nonsensical. So, is there another way to find usd, eur and cad?
Oh hello DragonChaser. It's been years since I've checked FF, but I just recently saw this. I'm pretty sure I can answer your question here about solving the equations.

It's an interesting idea, and while it might seem like we have something to work with — because, as you pointed out, we have three equations and three unknowns — unfortunately, we really only have two independent equations.

I just took these prices from the market:

USD/CAD = 1.3472
EUR/USD = 1.0672
EUR/CAD = 1.4378

Keep in mind the notation here. What does USD/CAD = 1.3472 really mean? It means it takes 1.3462 Canadian dollars to equal 1 US dollar, so it means:
1 USD = 1.3472 CAD
(You can think of it as multiplying both sides of USD/CAD = 1.3472 by "CAD" so the "CAD"s cancel on the left side.)

Converting all the price equations, we get this:

USD = 1.3472 CAD
EUR = 1.0672 USD
EUR = 1.4378 CAD

Let's simplify to use a single letter per currency so that the algebra is more mathematical:

U = 1.3472 C
E = 1.0672 U
E = 1.4378 C

Now the last two equations can be set equal to each other since they both equal 'E':

1.0672 U = 1.4378 C

Now use the first equation (U = 1.3472 C) to substitute into the 'U' on the previous line:

1.0672(1.3472 C) = 1.4378 C
1.0672*1.3472 C = 1.4378 C
1.4377 C = 1.4378 C

As you can see, the left side basically just confirms the right side. The slight error (1.4377 vs 1.4378) is probably just because of rounding to 4 decimal places.
This last equation could basically be boiled down to 1 = 1, which means we have a degenerate equation. Really, it means that one of the three equations can be written in terms of the other two (for example EUR/USD * USD/CAD = EUR/CAD), so we don't really have three independent equations.

But if you're trying to get a single value for each currency, you don't need to do all of this. You can just measure each one in terms of something else. All prices are relative to something: Prices are always one thing given in terms of another thing. So if you just want to put these three currencies in terms that can be compared, just price each of them relative to gold or relative to some other currency, or really anything else. Here are the prices for each of the three currencies relative to GBP at the same point in time:

GBP/USD = 1.2030
GBP/CAD = 1.6208
EUR/GBP = 0.8872

Solve each equation for USD, CAD, or EUR:

USD = 1/1.2030 = 0.8313 GBP
CAD = 1/1.6208 = 0.6170 GBP
EUR = 0.8872 GBP (This one is already in terms of GBP.)

Since they're now all in terms of GBP, you can see that the EUR is the most valuable of the three, USD is not far behind, and then CAD is substantially less. (You can also see that GBP is worth more than each of these because it doesn't even take 1 GBP to make any one of these currencies.)

However, finding these comparable values of each currency doesn't really tell you much (in my opinion). I mean, currencies are just like other units. You can measure weight in kilograms or pounds. 1 kilogram = 2.2 pounds, they're just two different ways of measuring weight; one is smaller so it takes more of them to equal the same weight, but it's irrelevant. One Japanese yen (priced the same way, relative to GBP) is tiny compared to these other three currencies. A yen is worth less than a penny. But just that information alone that doesn't mean that we should go long or short in USD/JPY. Unfortunately, we have the much more difficult task of figuring out how these relative values of prices will change with respect to each other.
  • #55
  • Feb 21, 2023 5:37am Feb 21, 2023 5:37am
Based on your calculation, because the usd, eur and cad now have values relative to a single currency, the gbp, we can comfortably say that the eur is strongest, then the usd and then the cad is weakest. So, here is the importance of the calculation. eur is stronger than the usd and cad, so we can safely sell eurusd and sell eurcad, and sell usdcad.
  • #56
  • Feb 21, 2023 8:17am Feb 21, 2023 8:17am
Quoting DragonChaser
Based on your calculation, because the usd, eur and cad now have values relative to a single currency, the gbp, we can comfortably say that the eur is strongest, then the usd and then the cad is weakest. So, here is the importance of the calculation. eur is stronger than the usd and cad, so we can safely sell eurusd and sell eurcad, and sell usdcad.
No, what I am saying is that this approach does not tell you where the prices will go. For example, the Japanese yen has always been less than the US dollar. But that doesn’t mean that you should always go long in USD/JPY.
  • #57
  • Apr 16, 2023 10:28pm Apr 16, 2023 10:28pm
Quoting mathematician
{quote} When an opportunity like this arises, it's called triangular arbitrage. But there are algorithmic traders out there who have very fast computers and very fast connections to the market, and they are specifically looking for these arbitrage opportunities. Whenever they find them, they jump on them in the blink of an eye, and by trading large amounts over very small distances (and by competing with other traders trying to do the same), the gap quickly closes. In fact, it is because of arbitrageurs that these mathematical relationships hold....
Triangular Arbitrage does not occur when there is a mispricing between prices on the same broker. Mispricing on the same broker is literally non-existent. A broker keeps prices corrected on their own system by maintaining the mathematical relationship instantaneously.

Triangular Arbitrage opportunities occur when there is a mispricing between a broker and the interbank market or between brokers. This is where prices may go out of sync, where brokers do not have direct control on each others quotes.

However, the mispricing is usually so minor; that after commissions, spreads, fees, it would not even be worth it, even in the rare moment, the opportunity presented itself. For participants that are able to somehow secure zero fees, the mispricing is still so minor versus the risk of sudden volatility, especially with a large position.

ARB opportunities perform better on other asset classes, where there isn't an intrinsic mathematical relationship that holds the price together (like FX).
  • #58
  • Apr 17, 2023 1:40am Apr 17, 2023 1:40am
Quoting CFA
{quote} Triangular Arbitrage does not occur when there is a mispricing between prices on the same broker. Mispricing on the same broker is literally non-existent. A broker keeps prices corrected on their own system by maintaining the mathematical relationship instantaneously. Triangular Arbitrage opportunities occur when there is a mispricing between a broker and the interbank market or between brokers. This is where prices may go out of sync, where brokers do not have direct control on each others quotes. However, the mispricing is usually so minor;...
What do you think about index arbitrage? Constructing some custom index and trying to see if there is any relationship with some particular asset, maybe their linear combination is persistent? Struggling to find good approach to build such index for crypto..
  • #59
  • Last Post: Apr 18, 2023 3:38am Apr 18, 2023 3:38am
Quoting pizd0s
{quote} What do you think about index arbitrage? Constructing some custom index and trying to see if there is any relationship with some particular asset, maybe their linear combination is persistent? Struggling to find good approach to build such index for crypto..
I don't see why not. You can perform a multiple regression on it and see how it pans out, maybe discover a linear relationship that gives you a high adjusted R2.

A lot of this stuff is experimentation, playing around with data and often discovering things by accident.

Sometimes you may find that the most unexpected thing has a very high influence on the predictive quality of the dependent variable.

Just be careful with the pitfalls of regression, there's many of them.
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