The realized correlation is calculated as:

$$\rho_{\text{realized}} = \left(\frac{2}{n^2 - n}\right) \sum_{i > j} \rho_{i,j}$$

Therefore,

$$\rho_{\text{realized}} = \left(\frac{2}{3^2 - 3}\right)(0.24 + 0.26 + 0.36) = 0.28667$$

Then:

$$N (\rho_{\text{realized}} - \rho_{\text{fixed}}) = 0.28667 - 0.18 = 0.10667$$

The payoff of the correlation fixed rate payer at maturity is

\`$12` \text{ million} \times 0.10667 = \`$1.28` \text{ million}.

Things to Remember

• Correlation swaps are derivatives that allow investors to speculate on or hedge against changes in the correlation between two or more underlying assets.
• The payoff of a correlation swap is based on the difference between the realized correlation and the fixed correlation rate agreed upon at the inception of the swap.
• Correlation swaps are commonly used in the financial industry to manage correlation risk in portfolios.