What kind of mathematical relationship can we find between the forex pairs?

<p id="isPasted">Forex pairs are traded in the foreign exchange market, where one currency is exchanged for another. The exchange rate between two currencies is determined by a number of factors, including economic and political conditions, interest rates, and market sentiment. As such, the relationship between forex pairs can be complex and dynamic.</p><p>One mathematical relationship that is commonly used to describe the relationship between two forex pairs is a correlation. Correlation measures the degree to which two variables move in relation to each other. In the context of forex pairs, correlation measures how two currency pairs move in relation to each other over a given time period.</p><p>A positive correlation between two currency pairs means that they tend to move in the same direction. For example, if the EUR/USD pair rises in value, then the GBP/USD pair may also rise in value. On the other hand, a negative correlation between two currency pairs means that they tend to move in opposite directions. For example, if the USD/JPY pair rises in value, then the EUR/USD pair may fall in value.</p><p>Traders often use correlation as a tool to diversify their portfolios and manage risk. By selecting currency pairs that are negatively correlated, for example, traders can reduce their overall portfolio risk and protect themselves against large losses.</p>

<p>Forex pairs are typically inversely related, meaning that when one currency in a pair strengthens, the other currency weakens. This is because currencies are always traded in pairs, so when one currency is bought, the other currency in the pair is simultaneously sold. The relationship between forex pairs can be mathematically represented through their exchange rates, which indicate the price at which one currency can be exchanged for another. The exchange rate of a forex pair is affected by various factors such as economic indicators, geopolitical events, and central bank policies.</p>

<p id="isPasted">The relationship between forex pairs can be expressed mathematically using cross-rates and implied correlation coefficients.</p><p>Cross-rates</p><p>A cross-rate is the exchange rate between two currencies expressed in terms of a third currency. For example, the EUR/USD cross-rate is the exchange rate between the euro and the US dollar, expressed in terms of the Japanese yen (JPY). Cross-rates can be calculated using the following formula:</p><p>A/B = (A/C) * (C/B)</p><p>Where:</p><ul><li><p>A is the currency being quoted</p></li><li><p>B is the base currency</p></li><li><p>C is the common currency</p></li></ul><p>For example, the EUR/USD cross-rate can be calculated as follows:</p><p>EUR/USD = (EUR/JPY) * (JPY/USD)</p><p>Implied correlation coefficients</p><p>An implied correlation coefficient is a measure of the relationship between two forex pairs based on their implied volatilities. Implied volatilities are the expected future movements of a currency pair. The implied correlation coefficient between two forex pairs can be calculated as follows:</p><p>rho = (IV1 - IV2) / (IV1 + IV2)</p><p>Where:</p><ul><li><p>rho is the implied correlation coefficient</p></li><li><p>IV1 is the implied volatility of the first currency pair</p></li><li><p>IV2 is the implied volatility of the second currency pair</p></li></ul><p>The implied correlation coefficient ranges from -1 to 1. A positive correlation coefficient indicates that the two currency pairs tend to move in the same direction. A negative correlation coefficient indicates that the two currency pairs tend to move in opposite directions. A correlation coefficient of 0 indicates that the two currency pairs are not correlated.</p><p>Examples of mathematical relationships between forex pairs</p><p>The following are some examples of mathematical relationships between forex pairs:</p><ul><li><p>EUR/USD and GBP/USD</p></li></ul><p>The EUR/USD and GBP/USD cross-rates are positively correlated. This is because the euro and the British pound are both major currencies that are traded against the US dollar.</p><ul><li><p>EUR/USD and USD/JPY</p></li></ul><p>The EUR/USD and USD/JPY cross-rates are negatively correlated. This is because the euro and the US dollar tend to move in opposite directions against the Japanese yen.</p><ul><li><p>AUD/USD and NZD/USD</p></li></ul><p>The AUD/USD and NZD/USD cross-rates are positively correlated. This is because the Australian dollar and the New Zealand dollar are both currencies that are traded against the US dollar.</p><p>It is important to note that the mathematical relationships between forex pairs are not always constant. They can change over time due to changes in market conditions.</p>