- Bijih besi
- Correlation swap
- Correlation trading
- Variance swap
- Kendall rank correlation coefficient
- Basis swap
- Credit default swap
- Power reverse dual-currency note
- Debt-for-nature swap
- Correlation attack
- Discrete Fourier transform
correlation swap
Correlation swap GudangMovies21 Rebahinxxi LK21
A correlation swap is an over-the-counter financial derivative that allows one to speculate on or hedge risks associated with the observed average correlation, of a collection of underlying products, where each product has periodically observable prices, as with a commodity, exchange rate, interest rate, or stock index.
Payoff Definition
The fixed leg of a correlation swap pays the notional
N
corr
{\displaystyle N_{\text{corr}}}
times the agreed strike
ρ
strike
{\displaystyle \rho _{\text{strike}}}
, while the floating leg pays the realized correlation
ρ
realized
{\displaystyle \rho _{\text{realized }}}
. The contract value at expiration from the pay-fixed perspective is therefore
N
corr
(
ρ
realized
−
ρ
strike
)
{\displaystyle N_{\text{corr}}(\rho _{\text{realized}}-\rho _{\text{strike}})}
Given a set of nonnegative weights
w
i
{\displaystyle w_{i}}
on
n
{\displaystyle n}
securities, the realized correlation is defined as the weighted average of all pairwise correlation coefficients
ρ
i
,
j
{\displaystyle \rho _{i,j}}
:
ρ
realized
:=
∑
i
≠
j
w
i
w
j
ρ
i
,
j
∑
i
≠
j
w
i
w
j
{\displaystyle \rho _{\text{realized }}:={\frac {\sum _{i\neq j}{w_{i}w_{j}\rho _{i,j}}}{\sum _{i\neq j}{w_{i}w_{j}}}}}
Typically
ρ
i
,
j
{\displaystyle \rho _{i,j}}
would be calculated as the Pearson correlation coefficient between the daily log-returns of assets i and j, possibly under zero-mean assumption.
Most correlation swaps trade using equal weights, in which case the realized correlation formula simplifies to:
ρ
realized
=
2
n
(
n
−
1
)
∑
i
>
j
ρ
i
,
j
{\displaystyle \rho _{\text{realized }}={\frac {2}{n(n-1)}}\sum _{i>j}{\rho _{i,j}}}
The specificity of correlation swaps is somewhat counterintuitive, as the protection buyer pays the fixed, unlike in usual swaps.
Pricing and valuation
No industry-standard models yet exist that have stochastic correlation and are arbitrage-free.
See also
Variance swap
Rainbow option
Sources
Meissner, Gunter (2014). Correlation risk modeling and management : an applied guide including the Basel III correlation framework-- with interactive models in Excel/VBA. Wiley. p. 11. ISBN 978-1118796900.